960-12i

Jeff C. Gust

Robert M. Graham

Michael A. Lombardi

Stopwatch and

Timer Calibrations

(2009 edition)

Special

Publication

960-12

p r a c t i c e g u i d e

N I S T r e c o m m e n d e d

NIST Special Publication 960-12

Stopwatch and 

Timer Calibrations 

(2009 edition)

Jeff C. Gust

Richard J. Bagan, Inc.

Robert M. Graham

Sandia National Laboratories

Michael A. Lombardi 

National Institute of Standards and Technology

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

National Institute of Standards and Technology

Patrick D. Gallagher, Deputy Director

January 2009

NIST Recommended Practice Guide
Certain equipment, instruments or materials are identified in this paper in order to 

adequately specify the experimental details. Such identification does not imply recommendation by the National Institute of Standards and Technology nor does it imply the 

materials are necessarily the best available for the purpose. 

 

Official contribution of the National Institute of Standards and Technology; not subject 

to copyright in the United States.

_______________________________________

National Institute of Standards and Technology

Special Publication 960-12 Natl. Inst. Stand. Technol.

Spec. Publ. 960-12

80 pages (January 2009)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2009

For sale by the Superintendent of Documents

U.S. Government Printing Office

Internet: bookstore.gpo.gov Phone: (202) 512-1800 Fax: (202) 512-2250

Mail: Stop SSOP, Washington, DC 20402-0001 
iii

FOREWORD

Stopwatch and timer calibrations are perhaps the most common calibrations 

performed in the field of time and frequency metrology. Hundreds of United 

States laboratories calibrate many thousands of timing devices annually to 

meet legal and organizational metrology requirements. However, prior to the 

publication of the first edition of this guide in May 2004, no definitive text had 

existed on the subject. This NIST Recommended Practice Guide was created 

to a fill a gap in the metrology literature. It assists the working metrologist 

or calibration technician by describing the types of stopwatches and timers 

that require calibration, the specifications and tolerances of these devices, the 

methods used to calibrate them, and the estimated measurement uncertainties 

for each calibration method. It also discusses the process of establishing 

measurement traceability back to national and international standards. 

 Foreword v

v

ACKNOWLEDGEMENTS

The authors thank the following individuals for their extremely useful 

suggestions regarding this new revision of the guide: Georgia Harris and 

Val Miller of the NIST Weights and Measures Division, Warren Lewis and 

Dick Pettit of Sandia National Laboratories, and Dilip Shah, the chair of the 

American Society for Quality (ASQ) Measurement Quality Division.

 Acknowledgements v

vii

Contents

Section 1: Introduction to Stopwatch and Timer Calibrations............................ 1

1.A. The Units of Time Interval and Frequency ................................... 1

1.B. A Brief Overview of Calibrations ................................................. 3

1.C. Traceability and Coordinated Universal Time (UTC)................... 5

Section 2: Description of Timing Devices that Require Calibration .................. 9

2.A. Stopwatches .................................................................................. 9

2.B. Timers.......................................................................................... 13

2.C. Commercial Timing Devices....................................................... 14

Section 3: Specifications and Tolerances.......................................................... 15

3.A. Interpreting Manufacturer’s Specifications.................................. 15

3.B. Tolerances Required for Legal Metrology ................................... 19

Section 4: Introduction to Calibration Methods................................................ 23

Section 5: The Direct Comparison Method ...................................................... 25

5.A. References for the Direct Comparison Method ........................... 25

5.B. Calibration Procedure for the Direct Comparison Method.......... 29

5.C. Uncertainties of the Direct Comparison Method ........................ 31

Section 6: The Totalize Method ........................................................................ 39

6.A. Calibration Procedure for the Totalize Method............................ 39

6.B. Uncertainties of the Totalize Method ........................................... 41

6.C. Photo Totalize Method ................................................................. 45

Section 7: The Time Base Method.................................................................... 49

7.A. References for the Time Base Method ......................................... 49

7.B. Calibration Procedure for the Time Base Method........................ 49

7.C. Uncertainties of the Time Base Method ....................................... 53

Table of Contents v
viii

v Stopwatch and Timer Calibrations

Section 8: How to Determine if the Calibration Method Meets the Required

Uncertainty ...................................................................................... 55

Section 9: Other Topics Related to Measurement Uncertainty......................... 57

9.A. Uncertainty Analysis of Using a Calibrated Stopwatch to

Calibrate another Device.............................................................57

9.B. The Effects of Stability and Aging on Calibrations of 32.768 Hz 

 Crystals........................................................................................58

9.C. Factors That Can Affect Stopwatch Performance .......................60

Appendix A: Calibration Certificates................................................................63

Appendix B: References...................................................................................65
ix

List of Figures v

List of Figures

Figure 1. The calibration and traceability hierarchy.......................................... 6

Figure 2. Type I digital stopwatch ...................................................................... 9

Figure 3. Type II mechanical stopwatch ............................................................. 9

Figure 4. Interior of digital (Type I) stopwatch ................................................ 11

Figure 5. Inner workings of a mechanical (Type II) stopwatch or timer.......... 12

Figure 6. A collection of timers........................................................................ 14

Figure 7. Sample manufacturer’s specifications for a digital stopwatch

 (Example 1).......................................................................................16

Figure 8. Sample specifications for a digital stopwatch (Example 2).............. 18

Figure 9. Typical performance of quartz wristwatches using 32 768 Hz

time base oscillators........................................................................ 19

Figure 10. Portable shortwave radio receiver for reception of audio

time signals..................................................................................... 28

Figure 11. Reaction time measurements (four operators, 10 runs each)

for the direct comparison method.................................................. .33

Figure 12. Averaging measurement results for four different operators........... 34

Figure 13. Block diagram of the totalize method ............................................ 39

Figure 14. Using the start-stop button of the stopwatch to start the counter ... 40

Figure 15. Measured reaction times (four operators, 10 runs each) for 

totalize method................................................................................ 42

Figure 16. Mean reaction times (four operators, 10 runs each) for the 

 totalize method............................................................................... 43

Figure 17. Photo totalize start reading ............................................................. 45
x

v Stopwatch and Timer Calibrations

List of Figures, cont’d

Figure 18. Photo totalize stop reading .............................................................. 46

Figure 19. Ambiguous photo totalize reading................................................... 47

Figure 20. Time base measurement system for stopwatches and timers ......... 50

Figure 21. A time base measurement system for stopwatches and timers

with an integrated graphics display................................................ 52

Figure 22. Graph of the frequency stability of two stopwatches..................... 59

Figure 23. Factors that can change the quartz time base frequency ................ 60

Figure 24. Stopwatch accuracy versus temperature......................................... 61

Figure A1. Sample calibration certificate. (page 1) ......................................... 63

Figure A1. Sample calibration certificate. (page 2) ......................................... 64
xi

List of Tables

Table 1 - Metric prefixes (may be applied to all SI units).................................. 2

Table 2 - Unit values, dimensionless values, and percentages........................... 4

Table 3 - Type I and Type II stopwatch characteristics.................................... 10

Table 4 - Legal metrology requirements for field standard stopwatches and

commercial time devices.................................................................. 20

Table 5 - Comparison of calibration methods.................................................. 23

Table 6 - Traceable audio time signals............................................................. 25

Table 7 - The contribution of a 300 ms variation in reaction time to the 

 measurement uncertainty .................................................................. 30

Table 8 - Uncertainty analysis for direct comparison method (digital DUT) 

 using a land line ................................................................................ 36

Table 9 - Uncertainty analysis for direct comparison method (digital DUT) 

 using a cell phone.............................................................................. 36

Table 10 - Uncertainty analysis for direct comparison method (analog DUT) 

 using a land line .............................................................................. 37

Table 11 - Uncertainty analysis for totalize method ........................................ 44

Table 12 - The effect of the length of the measurement time on stability 

 (based on 25 readings) ................................................................... .51

Table 13 - Uncertainty analysis of using a calibrated stopwatch to calibrate 

 another device ................................................................................. 58

List of Tables v

1

1. INTRODUCTION TO STOPWATCH AND 

TIMER CALIBRATIONS

This document is a recommended practice guide for stopwatch and timer calibrations. 

It discusses the types of stopwatches and timers that require calibration, their 

specifications and tolerances, and the methods used to calibrate them. It also discusses 

measurement uncertainties and the process of establishing measurement traceability 

back to national and international standards. 

This guide is intended to serve as a reference for the metrologist or calibration 

technician. It provides a complete technical discussion of stopwatch and timer 

calibrations by presenting practical, real world examples of how these calibrations are 

performed. 

There are nine sections in this guide. Section 1 provides an overview, and serves as 

a good introduction if you are new to the field of metrology or to time and frequency 

measurements. Section 2 describes the types of timing devices that require calibration. 

Section 3 discusses specifications and tolerances. Sections 4 through 7 discuss 

calibration methods and their associated uncertainties. Section 8 provides additional 

information to help determine if the selected calibration method can meet the required 

level of uncertainty, and Section 9 discusses other topics related to measurement 

uncertainty. A sample calibration report and references are provided in the appendices. 

1.A. The Units of Time Interval and Frequency

Stopwatches and timers are instruments used to measure time interval, which 

is defined as the elapsed time between two events. One common example 

of a time interval is a person’s age, which is simply the elapsed time since 

the person’s birth. Unlike a conventional clock that displays time-of-day as 

hours, minutes, and seconds from an absolute epoch or starting point (such as 

the beginning of the day or year), a stopwatch or timer simply measures and 

displays the time interval from an arbitrary starting point that begins at the 

instant when the stopwatch is started. 

The standard unit of time interval is the second (s) [1]. Seconds can be 

accumulated to form longer time intervals, such as minutes, hours, and days; 

or they can be sliced into fractions of a second such as milliseconds (10-3 s, 

abbreviated as ms) or microseconds (10-6 s, abbreviated as μs). Table 1 lists 

these and other prefixes that can be used with seconds, as well as the multiples/

submultiples and symbols used to represent them. The second is one of the 

seven base units in the International System of Units (SI). Other units (most 

notably the meter and the volt) have definitions that depend upon the definition 

of the second. 

 Introduction v
2

v Stopwatch and Timer Calibrations

 

The SI defines the second based on a property of the cesium atom, and for 

this reason cesium oscillators are regarded as primary standards for both time 

interval and frequency. A second is defined as the time interval required for 

9 192 631 770 transitions between two energy states of the cesium atom to take 

place. The atomic definition of the second, together with current technology, 

allows it to be measured with much smaller uncertainties than any other SI unit. 

In fact, the National Institute of Standards and Technology (NIST) can currently 

measure a second with an uncertainty of less than 1 part in 1015, or more than 

1 billion (109) times smaller than the uncertainties required for the calibrations 

described in this guide!

The resolution of a stopwatch or timer represents the smallest time interval 

that the device can display. Resolution is related to the number of digits on the 

device’s display for a digital stopwatch, or the smallest increment or graduation 

on the face of an analog stopwatch. For example, if a stopwatch display shows 

two digits to the right of the decimal point, it has a resolution of 0.01 s (10 ms, 

or 1/100 of a second). This means, for example, that it can display a value of 

42.12 s or 42.13 s, but that it lacks the resolution to display 42.123 s. Resolution 

of 10 ms is common for digital stopwatches, but some devices have 1 ms 

resolution (0.001 s), or even smaller. For analog stopwatches, a common 

resolution is 1/5 of a second, or 0.2 s.

Table 1 - Metric prefixes (may be applied to all SI units).

Multiples and Submultiples Prefix Symbol

 

 1 000 000 000 000 = 1012 tera T

 1 000 000 000 = 109 giga G

 1 000 000 = 106 mega M

 1 000 = 103 kilo k

 1 = 100

 0.001 = 10-3 milli m

 0.000 001 = 10-6 micro μ

 0.000 000 001 = 10-9 nano n

 0.000 000 000 001 = 10-12 pico p

0.000 000 000 000 001 = 10-15 femto f
3

Although stopwatches and timers measure time interval, they do so by using 

a frequency source. Frequency is the rate of a repetitive event, defined as the 

number of events or cycles per second. The standard unit of frequency (f) is 

the hertz (Hz), which is not a base unit of the SI, but one of the 21 derived SI 

units. One hertz equals one event per second, one kilohertz (kHz) equals 103

events per second, one megahertz (MHz) equals 106 events per second, and so 

on. The period (T) is the reciprocal of the frequency, T = 1/f. For example, 

a 1 MHz sine wave would produce 106 cycles per second, or one cycle every 

microsecond.

A time base oscillator (sometimes called a clock or reference oscillator) 

produces the frequency signals used by the stopwatch or timer to measure time 

intervals. In today’s devices, the time base oscillator is nearly always a quartz 

crystal oscillator. However, older devices used either a mechanical oscillator, 

the alternating current (AC) line frequency (60 Hz in the United States), or an 

oscillator based on a tuned electronic circuit as their frequency source. The time 

base oscillator serves as the reference for all of the time and frequency functions 

performed by the device. The most common frequency used by quartz time 

base oscillators is 32 768 (= 215) Hz. In this case, when the stopwatch or timer 

has counted 32 768 oscillations from its time base oscillator, it then records 

that 1 s has elapsed. If you want to think of this time base as a clock, it “ticks” 

32 768 times per second, or once every 30.518 μs.

Throughout this guide, time interval is always presented in units of seconds (or 

fractions of a second), and frequency is presented in units of hertz (or multiples 

of a hertz). However, measurement uncertainties are presented as dimensionless 

values that represent a fractional percentage error. Since these dimensionless 

values are usually very small percentages, they are often expressed in scientific 

notation. For example, if a stopwatch has a measurement uncertainty of 1 

s over a time interval of 10 000 s, the uncertainty is expressed as either a 

percentage (0.01 %) or as a dimensionless value (1 × 10-4). Table 2 provides 

more examples.

1.B. A Brief Overview of Calibrations

Like all calibrations, stopwatch and timer calibrations are simply comparisons 

between the device under test (DUT) and a measurement reference, or standard. 

When a stopwatch or timer is calibrated, either a time interval standard or a 

frequency standard is used as the measurement reference. If a time interval 

standard is used, it is compared to the DUT’s display. If a frequency standard 

is used, it is compared to the DUT’s time base oscillator. Both types of 

calibrations are described in detail later in this guide.

Introduction v
4

v Stopwatch and Timer Calibrations

Table 2 - Unit values, dimensionless values, and percentages.

 Time 

uncertainty

Length

 of test

Dimensionless 

uncertainty 

(literal)

Dimensionless 

uncertainty

(scientific

 notation)

Percentage 

uncertainty

(%)

1 s 1 minute 1 part per 60 1.67 × 10-2 1.67

1 s 1 hour 1 part per 3600 2.78 × 10-4 0.027 8 

1 s 1 day 1 part per 86 400 1.16 × 10-5 0.001 16 

1 s 100 s 1 part per hundred 1 × 10-2 1 

1 s 1000 s 1 part per thousand 1 × 10-3 0.1 

1 s 10 000 s 1 part per 10 thousand 1 × 10-4 0.01 

1 s 100 000 s 1 part per 100 thousand 1 × 10-5 0.001 

1 ms 100 s 1 part per 100 thousand 1 × 10-5 0.001 

1 ms 1000 s 1 part per million 1 × 10-6 0.000 1 

1 ms 10 000 s 1 part per 10 million 1 × 10-7 0.000 01 

1 ms 100 000 s 1 part per 100 million 1 × 10-8 0.000 001 

Most of the calibrations described in this guide are laboratory calibrations, 

as opposed to field calibrations. To understand what this means, consider an 

example where a stopwatch is calibrated in the laboratory against a standard, 

and a calibration certificate and/or sticker are issued to the customer. That 

same stopwatch or timer can then be thought of as a field standard, a working 

standard, or a transfer standard, and used as the measurement reference during 

a field calibration. In other words, it can be brought outside the laboratory and 

used to calibrate another timing device, such as a parking meter. The same 

basic principles that apply to laboratory calibrations apply to field calibrations, 

although laboratory calibrations generally take longer and are made much more 

carefully because the required measurement uncertainties are smaller. Devices 

that are field calibrated are generally not used as a measurement reference for 

performing other calibrations. Instead, they are working instruments used 

for scientific, business, or legal purposes. Therefore, their calibration can be 

thought of as a periodic test or inspection that ensures that these devices are 

working properly and meeting their specifications.
5

 Introduction v

Common sense dictates that the measurement reference for any calibration 

(either the laboratory reference or the field standard) must always outperform the 

devices it needs to test. A parking meter, for example, might have an acceptable 

uncertainty of 1 % when timing a 5 minute interval (±3 s). A field standard 

stopwatch used to test a parking meter should be certified to an uncertainty small 

enough so that it contributes no significant uncertainty to the parking meter 

calibration. In other words, we need to be able to trust our reference so that we 

can trust our measurement of the DUT.

When a laboratory calibration is completed, the metrologist has determined 

the offset1

 of the DUT with respect to the reference. This offset can be stated

as a percentage or in units of time interval or frequency (or both) on the 

calibration certificate, and should be quantified with a statement of measurement 

uncertainty. Field calibrations are generally “pass/fail” calibrations. This means 

that the device is tested to see whether it meets its intended or legal metrology 

requirements, and it either passes or fails. If it fails, it is removed from service 

until it can be adjusted, repaired, or replaced.

1.C. Traceability and Coordinated Universal Time (UTC)

As previously discussed, when a device is calibrated by comparing it to a 

measurement reference, the reference must be more accurate (have lower 

measurement uncertainties) than the DUT. Otherwise, the measurement results 

will be invalid. How do we know the accuracy of the measurement reference? 

The answer is: we only know its accuracy if it has been recently compared to a 

more accurate standard. That more accurate standard needs to be periodically

compared to an even more accurate standard, and so on, until eventually a

comparison is made against a national or international standard that represents 

the best physical realization of the SI unit that is being measured (in this case, 

the SI second). This measurement traceability hierarchy is sometimes illustrated 

with a pyramid as shown in Figure 1. The series of comparisons back to the 

SI unit is called the traceability chain. Metrological traceability is defined, by 

international agreement, as:

The property of a measurement result whereby 

the result can be related to a reference through a 

documented unbroken chain of calibrations, each 

contributing to the measurement uncertainty. [3]

1

 The term ‘offset’ is commonly used in the discipline of frequency and time measurement and 

will be used throughout this text. In terms of the ISO Guide to the Expression of Uncertainty in 

Measurement [2], the offset would be considered the measurement result.
6

v Stopwatch and Timer Calibrations

Figure 1. The calibration and traceability hierarchy.

The definition of metrological traceability implies that unless the measured 

value is accompanied by a stated measurement uncertainty, the traceability chain 

is broken. It is the responsibility of the calibration laboratory to determine and 

report the uncertainty of its measurements to its customers so that metrological 

traceability is maintained [4].

The International Bureau of Weights and Measures (BIPM) located near Paris, 

France, is responsible for ensuring the worldwide uniformity of measurements 

and their traceability to the SI. The BIPM collects and averages time interval 

and frequency data from more than 60 laboratories around the world and 

creates a time scale called Coordinated Universal Time (UTC) that realizes 

the SI second as closely as possible. Thus, UTC serves as the international 

standard for both time interval and frequency. However, the BIPM does not 

produce a physical representation of the second; it simply calculates a weighted 

average that is published weeks after the actual measurements were made. 

This document, known as the BIPM Circular T, shows the time offset of each 

contributing laboratory with associated uncertainties, and can be downloaded 

from the BIPM web site (www.bipm.org). 

The laboratories that provide data to the BIPM maintain the oscillators and 

clocks that produce the actual signals that are used as measurement references. 

Most of these laboratories are national metrology institutes (NMIs) that serve 

as the caretakers of the national measurement references for their respective 

countries. Thus, to establish traceability to the SI for time interval and 

frequency calibrations, the traceability chain for a measurement must link back 
7

to signals that originate from an NMI or a national timekeeping laboratory. The 

NMI that is chosen as a reference must contribute to the derivation of UTC by 

sending its measurement data (with associated uncertainties) to the BIPM.

NIST is the ultimate reference point for most measurements made in the United 

States, and as such, submits time and frequency data to the BIPM. NIST

provides it own real-time representation of UTC, designated UTC(NIST), that 

is distributed to the public using a variety of radio, telephone, and Internet 

signals. These signals are described in more detail in Section 5, and can serve as 

references for measurements that are traceable back to the SI.

The traceability chain is easy to visualize if you think of it as a series of 

calibrations. Every link in the chain is a calibration; comparing a device to a 

higher standard, until eventually a comparison is made to the SI unit. Every 

calibration has some measurement uncertainty. At the top of the chain, the 

measurement uncertainties are so tiny they are insignificant to those of us who 

calibrate stopwatches and timers. For example, the difference between the 

best possible estimate of the SI second and UTC(NIST) is measured in parts in 

1016. This represents a time offset of less than 0.1 ns (10-10 s) over the course 

of a day. As we move down the traceability chain to the actual calibration of a 

stopwatch or timer, the uncertainties become larger and larger. For example, if 

the calibration laboratory uses an audio signal from NIST radio station WWV 

(Section 5) to calibrate its standard, the uncertainty of the received tones might 

be 1 ms. This uncertainty is still small enough for the WWV tones to be used 

as a stopwatch calibration reference, because the uncertainty introduced by an 

operator starting and stopping the watch (human reaction time) is much larger, 

typically tens or even hundreds of milliseconds. In summary, as long as each 

link of the chain and its uncertainty are known, traceability to the SI can be 

established.

Stopwatch and timer calibrations are among the least demanding of all time 

and frequency measurements. Relatively speaking, the instruments requiring 

calibration are low cost, and the acceptable measurement uncertainties can 

be quite large. Even so, for legal, technical, and practical reasons it is very 

important to establish traceability to the SI for these calibrations. If a valid 

traceability chain to the SI is established, it ensures that the working device was 

properly calibrated, and, if correctly used, will produce valid results.

 Introduction v

9

Section 2 

Description of Timing Devices that Require Calibration 

This section describes the various types of stopwatches (Section 2.A. Stopwatches) 

and timers (Section 2.B. Timers) that are calibrated in the laboratory. These types 

of stopwatches and timers are often used as transfer standards to perform field 

calibrations of the commercial timing devices described in Section 2.C.

2.A. Stopwatches

Stopwatches can be classified into two categories, Type I and Type II [5]. 

Type I stopwatches have a digital design employing quartz oscillators and 

electronic circuitry to measure time intervals (Figure 2). Type II stopwatches 

have an analog design and use mechanical mechanisms to measure time 

intervals (Figure 3). The key elements of Type I and Type II stopwatches are 

summarized in Table 3.

 Description of Timing Devices v

 Figure 2. Type I digital stopwatch. Figure 3. Type II mechanical stopwatch. 
10

v Stopwatch and Timer Calibrations

Table 3 - Type I and Type II stopwatch characteristics.

Description Type I Stopwatch

(digital)

Type II Stopwatch

(analog)

Operating 

principle

Time measured by division of 

time base oscillator

Time measured by mechanical 

movement

Time base

•	 Quartz oscillator •	 Mechanical mainspring

•	 Synchronous motor, electrically 

driven

Case •	 Corrosion resistant metal

•	 Impact resistant plastic

Crystal

•	 Protects display

•	 Allows for proper viewing

•	 May be tinted

•	 May employ magnification

•	 Protects dial/hands

•	 Allows for proper viewing

•	 Must be clear and untinted

Miniumum time 

interval

•	 48 hours without 

replacement of battery

•	 3 hours without rewinding

Start and Stop •	 Corrosion resistant metal

•	 Impact resistant plastic

Reset •	 Must reset stopwatch to zero

Split Time

(if equipped)

•	 Corrosion resistant metal

•	 Impact resistant plastic

Force to 

Operate Controls •	 Must not exceed 1.8 N (0.4046 lbf)

Dial and Hands

•	 Face must be white

•	 Graduations must be black or red

•	 Hands must be black or red

Required 

Markings

•	 Unique, nondetachable serial number

•	 Manufacturer’s name or trademark

•	 Model number (type I only)

Digital Display

•	 Providing delimiting 

character for hours, 

minutes, seconds (usually 

colon)

Minimum 

Increment •	 0.2 s

Minimum 

Elapsed Time at 

Rollover

•	 1 h •	 30 min

Physical

Orientation •	 Stopwatch meets tolerance regardless of physical orientation
11

2.A.1. Basic Theory of Operation

Every stopwatch is composed of four elements: a power source, a time base, 

a counter, and an indicator or display. The design and construction of each 

component depends upon the type of stopwatch.

2.A.1.a. Digital (Type I) Stopwatches

The power source of a Type I stopwatch is usually a silver-oxide or alkaline 

battery that powers the oscillator and the counting and display circuitry. The 

time base is a quartz crystal oscillator that usually has a nominal frequency of 

32 768 Hz, the same frequency used by nearly all quartz wristwatches. The 

32 768 Hz frequency was originally chosen because it can be converted to a 

1 pulse per second signal using a simple 15 stage divide-by-two circuit. It also 

has the benefit of consuming less battery power than higher frequency crystals. 

Figure 4 shows the inside of a typical digital device, with the printed circuit 

board, quartz crystal oscillator, and battery visible. The counter circuit consists 

of digital dividers that count the time base oscillations for the period that is 

initiated by the start/stop buttons [6, 7]. The display typically has seven or eight 

digits. 

 Description of Timing Devices v

Figure 4. Interior of digital (Type I) stopwatch.
12

v Stopwatch and Timer Calibrations

 Figure 5. Inner workings of a mechanical (Type II) stopwatch or timer.
13

 Description of Timing Devices v

2.A.1.b. Mechanical (Type II) Stopwatches

In a traditional mechanical stopwatch, the power source is a helical coil spring, 

which stores energy from the winding of the spring. The time base is usually 

a balance wheel that functions as a torsion pendulum. The rate at which the 

spring unwinds is governed by the balance wheel, which is designed to provide a 

consistent period of oscillation relatively independent of factors such as friction, 

operating temperature, and orientation. In most mechanical stopwatches, the 

balance wheel is designed to oscillate at 2.5 periods per second, which produces 

5 “ticks” or beats per second. The balance wheel is connected to an escapement 

that meters the unwinding of the coil spring and provides impulses that keep 

the balance wheel moving. It is this metered unwinding of the coil spring that 

drives the counter indicator. In this type of device, the counter is composed 

of a gear train that divides the speed of rotation of the escapement wheel to 

the appropriate revolution speed for the second, minute, and hour hands. The 

time interval from the counter is displayed either on a face across which the 

second and minutes hands sweep, or on a series of numbered drums or discs that 

indicate the elapsed time (Figure 5) [6].

Another form of the Type II stopwatch uses a timer driven by a synchronous 

motor that also drives the hands or numbered wheels. For this device, the power 

source is the 60 Hz AC line voltage. The power source drives an electric motor 

within the timing device. The time base is derived from the controlled regulation 

of the 60 Hz frequency of AC electric power as supplied by the power utility 

company. The frequency limits for distributed AC power in the United States 

are 59.98 Hz to 60.02 Hz, or 60 Hz ± 0.033 % of the nominal value. However, 

the actual frequency is controlled much more accurately than this, in order to 

advance or retard the grid frequency and synchronize the power distribution 

system [8]. The counter and display circuitry are similar to those used in the 

mechanical stopwatches previously discussed. 

2.B. Timers

Timers, unlike stopwatches, count down from a preset time period instead of 

counting up from zero. They can be small, battery-operated devices that are used 

to signal when a certain time period has elapsed, or they can be larger devices 

that plug into a wall outlet and control other items (Figure 6). A parking meter 

is an example of a countdown timer. Inserting a coin starts the internal timer 

counting down from an initial preset point. When the preset time has elapsed, 

the EXPIRED flag is raised.

 

One type of timer used extensively in industry is the process control timer. As 

their name implies, process control timers measure or control the duration of a 

specific process. For example, when a product is made, it may need to be heat 

treated for a specific length of time. In an automated manufacturing system, the 

process control timer determines the length of time that the item is heated. In 
14

v Stopwatch and Timer Calibrations

some applications, such as integrated circuit manufacturing, the timing process 

can be critical for proper operation.

Process control timers are also used in many different types of laboratory 

environments. Calibration laboratories use timers to calibrate devices such 

as radiation detectors, by regulating the amount of time that the device is 

exposed to the radiation source. The uncertainty in the time of exposure 

directly influences the overall measurement uncertainty assigned to the detector 

calibration. 

Timers are also used in the medical field. For example, medical laboratories use 

process control timers when specimen cultures are grown. Hospitals use timers 

to regulate the amount of medication given to patients intravenously. 

2.C. Commercial Timing Devices

Many types of timing devices are used every day in commercial applications. 

Parking meters, automatic car wash facilities, taxicab meters, and commercial 

parking lots are examples of entities that either charge a certain amount for a 

specified period, or provide a certain period of service for a specified amount of 

money.

The calibration requirements and allowable tolerances for these devices are 

usually determined on a state-by-state basis by state law, or locally by city or 

municipality ordinances. The allowable uncertainties are often 1 % or larger. 

Generic guidance is provided in Section 3.

Figure 6. A collection of timers.
15

Specifications and Tolerances v

Section 3

Specifications and Tolerances

Whether we are developing a calibration procedure, or performing an uncertainty 

analysis for a given calibration process, we need to be able to understand and interpret 

the specifications and tolerances for both the DUT and the test equipment associated 

with the calibration. This section reviews both manufacturer’s specifications and legal 

metrology requirements for stopwatches and timing devices.

3.A. Interpreting Manufacturer’s Specifications

When reviewing manufacturer’s specification sheets, it quickly becomes obvious 

that not all instrument manufacturers specify their products in the same way. 

This section defines and describes the most common types of specifications 

quoted for stopwatches and timing devices.

3.A.1. Absolute Accuracy Specifications

The absolute accuracy2 of an instrument is the maximum allowable offset from 

nominal. Absolute accuracy is defined in either the same units, or a fractional 

unit quantity of the measurement function for an instrument. For example, the 

absolute accuracy of a ruler might be specified as ±1 mm for a scale from 0 to 

15 cm. 

In the case of timing devices, it isn’t useful to provide an absolute accuracy 

specification by itself. This is because a device’s time offset from nominal will 

increase as a function of the time interval. If the timing device were able to 

measure an infinite time interval, the offset (or difference in time from nominal) 

of the device would also become infinitely large. Because of this, when timing 

devices are specified with an absolute accuracy number, it is also accompanied 

by a time interval for which this specification is valid. As an example, the 

absolute accuracy specification for the stopwatch shown in Figure 7 is 5 s per 

day. 

If the stopwatch in Figure 7 were used to measure a time interval longer than one 

day, we could determine a new absolute accuracy figure by simply multiplying 

the original specification by the longer time interval. For example 5 s per day 

becomes 10 s per two days, 35 s per week, and so on.

While it is usually acceptable to multiply the absolute accuracy specification by 

longer time intervals than the period listed in the specifications, caution must be 

2

 In this section, the term “accuracy” is used in order to allow the reader to correlate the concepts 

of this chapter directly with published manufacturer specifications. In terms of the ISO Guide to 

the Expression of Uncertainty in Measurement [2], the quantities associated with accuracy are 

understood to be uncertainties. 
16

v Stopwatch and Timer Calibrations

used when dividing the absolute accuracy specification for shorter time 

intervals than the period listed in the specifications. This is because for shorter 

measurements periods, a new source of uncertainty, the resolution uncertainty of 

the instrument, becomes an important consideration. For example, the absolute 

accuracy of the example stopwatch (Figure 7) during a time interval of 30 s is 

determined as

Handsome stopwatch with large 

display provides timing to 

1/100th of a second over a range 

of 9 hours 59 minutes and 59.99 

seconds.

Accurate to ± 5 s/day

Built-in memory recalls up to ten 

laps.

Clock function (12 or 24 hrs) 

features a programmable alarm 

with an hourly chime plus builtin calendar displays day, month 

and date.

Countdown timer function 

features input ranges from one 

minute to 9 hours, 59 minutes.

Dimensions/Weight: 2.5 x 3.2 x 

0.8, (63 x 81 x 20 mm), 2.8 oz.

Water resistant housing is complete with lithium battery

•

•

•

•

•

•

Figure 7. Sample manufacturer’s specifications for a digital stopwatch (Example 1).

day 0.0017 s

2880

1

day

5 s 30 s

day

5 s    

Handsome stopwatch with large 

display provides timing to 

1/100th of a second over a range 

of 9 hours 59 minutes and 59.99 

seconds.

Accurate to ± 5 s/day

Built-in memory recalls up to ten 

laps.

Clock function (12 or 24 hrs) 

features a programmable alarm 

with an hourly chime plus builtin calendar displays day, month 

and date.

Countdown timer function 

features input ranges from one 

minute to 9 hours, 59 minutes.

Dimensions/Weight: 2.5 x 3.2 x.8: 

(63 x 81 x 20 mm): 2.8 oz.

Water resistant housing is complete with lithium battery

•

•

•

•

•

•
17

Specifications and Tolerances v

We can see from the specifications in Figure 7 that the stopwatch has a resolution of 

1/100 of a second, or 0.01 s. In this case, computing the absolute accuracy specification 

for a 30 s interval results in a number (0.0017 s) that is about six times smaller than 

the smallest value the stopwatch can display. Most manufacturers of timing devices 

do not consider the resolution of the product in their specifications, but we will include 

resolution uncertainty in our examples.

3.A.2 Relative Accuracy Specifications

While absolute accuracy specifications are helpful, sometimes it is more 

desirable to specify accuracy relative to the measured time interval. This makes 

its significance easier to understand. For this purpose, we define a quantity 

called relative accuracy:

Using the previous example from Figure 7, the stopwatch has an absolute 

accuracy specification of 5 s per day, so the relative accuracy is:

Note that because the absolute accuracy specification and the measured 

time interval are both expressed in seconds, the unit cancels out; leaving 

a dimensionless number that can be expressed either as a percentage or in 

scientific notation. Relative accuracy specifications can also be converted 

back to absolute time units if necessary. For example, Figure 8 shows the 

manufacturer’s specifications for a stopwatch that is accurate to 0.0003 % 

(although not stated, it is assumed that this percentage has been stated as a 

percent of reading or relative accuracy). To compute the time accuracy for a 

24 h measurement, we simply multiply the relative accuracy by the 

measurement period:.

This computation shows that this stopwatch is capable of measuring a 24-hour 

interval with an accuracy of about 0.26 s. However, it is again important to 

note that when measuring small time intervals, the resolution uncertainty of the 

stopwatch must be considered. For example, if the stopwatch in Figure 8 is used 

to measure a time interval of 5 s, the computed accuracy is much smaller than 

the resolution of the stopwatch:

Measured Time Interval

Absolute Accuracy Relative Accuracy =

-5 0.000 058 0.0058 % 5.8 10

86 400 s

5 s

1day

5 s Relative Accuracy      

0.0003 % 24 h  0.000 072 h  0.2592 s

0.0003 % 5 s  0.000 015 s
18

v Stopwatch and Timer Calibrations

Figure 8. Sample specifications for a digital stopwatch (Example 2).

3.A.3. Typical Performance

During the NIST centennial celebration of 2001, an exhibit at the NIST 

laboratories in Boulder, Colorado, allowed visitors to measure the time base 

accuracy of their quartz wristwatches. Over 300 wristwatches were tested. 

These wristwatches contained a 32 768 Hz time base oscillator, the same 

technology employed by a Type I digital stopwatch. The results of these 

measurements, showing the loss or gain in seconds per day for the watches, are 

summarized in Figure 9, and give some idea of the typical performance of a 

quartz stopwatch or timer. Roughly 70 % of the watches were able to keep time 

to within 1 s per day or better, a relative accuracy of approximately 0.001 % 

(1 × 10-5). About 12 % had a relative accuracy larger than 5 s per day, or larger 

than 0.005 %. It is interesting to note that nearly all of the watches in this study 

gained time, rather than lost time; and were presumably designed that way to 

help prevent people from being late. This characteristic will not necessarily 

apply to stopwatches and timers. 

Timer: 9 hours, 59 minutes, 59 seconds, 

99 hundredths.

Stopwatch: Single-action timing: timein/time-out; continuous timing; cumulative split, interval split and eight

memories. Triple display shows cumulative splits, interval splits and running 

time simultaneously.

Features: Captures and stores up to 

eight separate times. After timed event is 

complete, stopwatch displays information in its memory. Counter box shows 

number of split times taken. Solid-state 

design with an accuracy of 0.0003 %. 

Durable, water-resistant construction 

makes stopwatch suitable for eld use 

(operates in temperature from 1° to 

59 ° C [33 ° to 138 ° F]). With triple line 

LDC: top two lines are each 1/8 in. high 

(3.2 mm); third line is 1⁄4 in. high (6 mm).

Timer: 9 hours, 59 minutes, 59 seconds, 

99 hundredths.

Stopwatch: Single-action timing: timein/time-out; continuous timing; cumulative split, interval split and eight

memories. Triple display shows cumulative splits, interval splits and running 

time simultaneously.

Features: Captures and stores up to 

eight separate times. After timed event is 

complete, stopwatch displays information in its memory. Counter box show 

number of split times taken. Solid-state 

design with an accuracy of 0.0003 %. 

Durable, water-resistant construction 

makes stopwatch suitable for eld use 

(operates in temperature from 1° to 

59 ° C [33 ° to 138 ° F]). With triple line 

LDC: top two lines are each 1/8 in. high 

(3.2 mm); third line is 1⁄4 in. high (6 mm).
19

Specifications and Tolerances v

Quartz Wristwatch Performance

Figure 9. Typical performance of quartz wristwatches using 32 768 Hz time base 

oscillators.

3.B. Tolerances Required for Legal Metrology

General specifications for field standard stopwatches and commercial timing 

devices are provided in Section 5.55 of NIST Handbook 44 [9], and are 

summarized in Table 4. NIST Handbook 44 is recognized by nearly all 50 

states as the legal basis for regulating commercial weighing and measuring 

devices. However, some state governments and some regulatory agencies have 

other specifications that need to be satisfied for a given calibration. Therefore, 

be sure to check and understand the required tolerances and regulations for the 

types of calibration that a calibration laboratory is asked to perform [10].

The terms overregistration and underregistration are used when specifying 

the accuracy of commercial timing devices. The terms are used to describe 

conditions where the measurement device does not display the actual quantity. 

In timing devices, underregistration is the greatest concern, because an 

underregistration error occurs when the timing device indicates that the 

selected time interval has elapsed before it actually has. An example of 

underregistration would be paying for 10 minutes on a parking meter, and then

having the meter indicate that time had expired when only 9 minutes and 45 s 

had actually elapsed. 
20

v Stopwatch and Timer Calibrations

Table 4 - Legal metrology requirements for field standard stopwatches and 

commercial time devices.

Commercial 

timing 

device

Interval 

Measured

Overregistration Underregistration

Requirement Uncertainty Requirement Uncertainty

Parking 

meter

30 minutes 

or less None NA

10 s per 

minute, but 

not less than 2 

minutes

11.7 % to 

16.7 %

Over 30 

minutes 

up to and 

including 

1 hour

None NA

5 minutes 

plus 4 s per 

minute over 30 

minutes

Over 1 

hour None NA

7 minutes plus 

2 minutes per 

hour over 1 

hour

Time clocks 

and time 

recorders

3 s per hour, 

not to exceed 

1 minute per 

day

0.07 % 

to 0.08 %

3 s per hour, 

not to exceed 1 

minute per day

0.07 % to 

0.08 %

Taximeters 3 s per 

minute 5 %

9 s per minute 

on the initial 

interval, and 

6 s per minute 

on subsequent 

intervals 

10 % to 

15 %

Other timing 

devices

5 s for any 

interval of 

1 minute or 

more

NA 6 s per minute 10 %

NIST Handbook 44 [9] specifies that instruments that are required to calibrate 

timing devices must be accurate to within 15 s per 24 h period (approximately 

0.017 %). If stopwatches are used as the calibration standard, this becomes 

the minimum allowable tolerance for the stopwatch. Another reference, NIST 

Handbook 105-5 [5] states that the tolerance for instruments used to calibrate 

timing devices must be three times smaller than the smallest tolerance of the 

device being calibrated. Handbook 105-5 also provides a nearly identical 

specification for stopwatches, stating that the tolerance for stopwatches is 

±0.02 % of the time interval tested (approximately 2 s in 3 hours), rounded to 

the nearest 0.1 s.
21

Specifications and Tolerances v

The uncertainties listed above were meant to be achievable with Type II 

(mechanical) devices, but Type I devices are normally capable of much lower 

uncertainties. As a result, organizations and jurisdictions that rely exclusively 

on digital stopwatches (Type I) might require that devices be calibrated to a 

tolerance of 0.01 %, or even 0.005 %. For example, the State of Pennsylvania 

code [11] uses the same specifications as NIST Handbook 44 for mechanical 

stopwatches (15 s per 24 hours), but states that a quartz stopwatch shall comply 

with the following more rigorous standards:

(i) The common crystal frequency shall be 32 

768 Hz with a measured frequency within plus 

or minus 3 Hz, or approximately 0.01 % of the 

standard frequency.

(ii) The stopwatch shall be accurate to the 

equivalent of plus or minus 9 seconds per 24-hour 

period.

3.B.1. Time Clocks and Time Recorders

The specification for both overregistration and underregistration is 3 s per hour, 

not to exceed 1 minute per day.

3.B.2. Parking Meters

The specifications for parking meters have no tolerance for overregistration. 

Parking meters with a time capacity of 30 minutes or less are specified to 

have a maximum underregistration error of 10 s per minute, but not to exceed 

2 minutes over the 30 minute period. For parking meters with a capacity of 

greater than 30 minutes, but less than 1 hour, the tolerance for underregistration 

is 5 minutes, plus 4 s per minute for every minute between 30 minutes and 60 

minutes. Parking meters that indicate over 1 hour have an underregistration 

tolerance of 7 minutes plus 2 minutes per hour for time intervals greater than 

1 hour.

3.B.3. Other Timing Devices

All other timing devices have an overregistration tolerance of 5 s for any time 

interval of 1 minute or more and an underregistration tolerance of 6 s per indicated 

minute. If the instrument is a digital indicating device, the tolerance is expanded 

by one half of the least significant digit.

23

Calibration Methods v

Section 4

Introduction to Calibration Methods

There are three generally accepted methods for calibrating a stopwatch or timer: the 

direct comparison method, the totalize method, and the time base method. The first 

two methods consist of time interval measurements that compare the time interval 

display of the DUT to a traceable time interval reference. In the case of the direct 

comparison method, the time interval reference is normally a signal broadcast by an 

NMI, usually in the form of audio tones. In the case of the totalize method, the time 

interval reference is generated in the laboratory using a synthesized signal generator, 

a universal counter, and a traceable frequency standard. The third method, the time 

base method, is a frequency measurement. It compares the frequency of the DUT’s 

time base oscillator to a traceable frequency standard [12]. The properties of the 

three methods are briefly summarized in Table 5, and the following three sections are 

devoted to the three methods. Each section explains how to perform a calibration 

using each method, and how to estimate the measurement uncertainties.

Table 5 - Comparison of calibration methods.

 

 Method 

 Properties Direct comparison Totalize Time base measurement

Equipment Requirements Best Better Better

Speed Good Better Best

Uncertainty Good Good Best

Applicability Good Best Better

The methods used to estimate the uncertainty of measurement are described in the ISO 

Guide to the Expression of Uncertainty in Measurement (GUM) [2]. This guide does 

not attempt to summarize the GUM, but does strive to produce estimates of uncertainty 

that are consistent with the GUM. The resulting expanded uncertainty of measurement is 

presented with a coverage factor that represents an approximate 95 % level of confidence. 

25

Section 5

The Direct Comparison Method

The direct comparison method is the most common method used to calibrate stopwatches 

and timers. It requires a minimal amount of equipment, but has larger measurement 

uncertainties than the other methods. This section describes the references used for this 

type of calibration and the calibration procedure.

5.A. References for the Direct Comparison Method

The direct comparison method requires a traceable time-interval reference. 

This reference is usually an audio time signal, but in some cases a traceable 

time display can be used. The audio time signals are usually obtained with a 

shortwave radio or a telephone. Since time interval (and not absolute time) 

is being measured, the fixed signal delay from the source to the user is not 

important as long as it remains relatively constant during the calibration process. 

A list of traceable audio time sources is provided in Table 6.

Table 6 - Traceable audio time signals.

National 

Metrology 

Institute (NMI) Location Telephone numbers

Radio

call

letters

Broadcast 

frequencies

National Institute 

of Standards 

and Technology 

(NIST)

Fort Collins, 

Colorado, 

United States

(303) 499-7111 * WWV 2.5, 5, 10, 

15, 20 MHz

National Institute 

of Standards 

and Technology 

(NIST)

Kauai, 

Hawaii, 

United States

(808) 335-4363 * WWVH 2.5, 5, 10, 

15 MHz

United 

States Naval 

Observatory 

(USNO)

Washington, 

DC, 

United States

(202) 762-1401 *

(202) 762-1069 * ----- -----

The Direct Comparison Methods v
26

v Stopwatch and Timer Calibrations

United 

States Naval 

Observatory 

(USNO)

Colorado 

Springs, 

Colorado, 

United States

(719) 567-6742 * ----- -----

National 

Research Council 

(NRC)

Ottawa, 

Ontario, 

Canada

(613) 745-1576 @ 

(English language)

(613) 745-9426 @ 

(French language)

CHU 3.33, 7.850, 

14.67 MHz

Centro Nacional 

de Metrologia 

(CENAM)

Querétaro, 

México

(442) 215-39-02 * 

(442) 211-05-06 ! 

(442) 211-05-07 # 

(442) 211-05-08 ## 

Time 

announcements 

are in Spanish, a 

country code must 

be dialed to access 

these numbers 

from the United 

States, see www.

cenam.mx for more 

information.

XEQK 

(Mexico 

City)

1.35 MHz

Korea Research 

Institute of 

Standards and 

Science (KRISS)

Taedok, 

Science 

Town, 

Republic of 

Korea

----- HLA 5 MHz

National Time 

Service Center 

(NTSC)

Lintong, 

Shaanxi, 

China

----- BPM 2.5, 5, 10, 

15 MHz

_____________________________________________________________________________

* Coordinated Universal Time (UTC)

@ Eastern Time

! Central Time

# Mountain Time

## Pacific Time
27

Please note that local “time and temperature” telephone services are not 

traceable references and should not be used. For traceable calibrations, use 

only sources that originate from a national metrology institute, such as those 

listed in Table 6. The following sections briefly describe the various radio 

and telephone time signals, and provide information about the types of clock 

displays that can and cannot be used.

5.A.1. Audio Time Signals Obtained by Radio

The radio signals listed in Table 6 include a voice announcement of UTC 

and audio ticks that indicate individual seconds. WWV, the most widely used 

station, features a voice announcement of UTC occurring about 7.5 s before the 

start of each minute. The beginning of the minute is indicated by a 1500 Hz 

tone that lasts for 800 ms. Each second is indicated by a 1 kHz tone that lasts 

for 5 ms. The best way to use these broadcasts is to start and stop the stopwatch 

when the beginning of the minute tone is heard.

Most of the stations listed in Table 6 are in the high-frequency (HF) radio 

band (3 MHz to 30 MHz), and therefore require a shortwave radio receiver. A 

typical general-purpose shortwave receiver provides continuous coverage of the 

spectrum from about 150 kHz, which is below the commercial AM broadcast 

band, to 30 MHz. These receivers allow the reception of the HF time stations 

on all available frequencies. The best shortwave receivers are designed to 

work with large outdoor antennas, with quarter-wavelength or half-wavelength 

dipole antennas often providing the best results. However, in the United States, 

adequate reception of at least one station can usually be obtained with a portable 

receiver with a whip antenna, such as the one shown in Figure 10. This type of 

receiver typically costs a few hundred dollars or less.

HF radio time stations normally broadcast on multiple frequencies because 

some of the frequencies are not available at all times. In many cases, only one 

frequency can be received, so the receiver might have to be tuned to several 

different frequencies before finding a usable signal. In the case of WWV, 

10 MHz and 15 MHz are probably the best choices for daytime reception, unless 

the laboratory is within 1000 km of the Fort Collins, Colorado station, in which 

case 2.5 MHz might also suffice. Unless the receiver is near the station, the 

5 MHz signal will probably be the easiest to receive at night [13].

The Direct Comparison Method v
28

v Stopwatch and Timer Calibrations

Figure 10. Portable shortwave radio receiver for reception of audio time signals.

5.A.2. Audio Time Signals Obtained by Telephone

The telephone time signals for NIST radio stations WWV and WWVH are 

simulcasts of the radio broadcasts, and the time (UTC) is announced once 

per minute. The length of the phone call is typically limited to 3 minutes. The 

formats of the other broadcasts vary. The USNO phone numbers broadcast UTC 

at 5 s or 10 s intervals. The NRC phone number broadcasts Eastern Time at 10 

s intervals, and CENAM offers separate phone numbers for UTC and the local 

time zones of Mexico.

5.A.3. Time Displays

It might be tempting to use a time display from a radio controlled clock or 

from a web site synchronized to UTC as a reference for stopwatch or timer 

calibrations. As a general rule, however, these displays are not acceptable 

for establishing traceability. Nearly all clock displays are synchronized only 

periodically. In the period between synchronizations they rely on a free running 

local oscillator whose frequency uncertainty is usually unknown. And of course, 

an unknown uncertainty during any comparison breaks the traceability chain. 

For example, a low cost radio controlled clock that receives a 60 kHz signal 

from NIST radio station WWVB is usually synchronized only once per day. In 

between synchronizations, each “tick” of the clock originates from a local quartz 

oscillator whose uncertainty is unknown, and that probably is of similar or lesser 

quality than the oscillator inside the device under test. The NIST web clock 

(time.gov) presents similar problems. It synchronizes to UTC(NIST) every 10 

minutes if the web browser is left open. However, between synchronizations it 

keeps time using the computer’s clock, which is usually of poorer quality than 

a typical stopwatch, and whose uncertainty is generally not known. In contrast, 

each “tick” of an audio broadcast from WWV originates from NIST and is 

synchronized to UTC. Therefore, WWV audio always keeps the traceability 

chain intact.
29

There are a few instances where a time display can be used to establish 

traceability. One example would be a display updated each second by 

pulses from a Global Positioning System (GPS) satellite receiver. In this 

case, if the traceable input signal were not available, the display would stop 

updating. Therefore, if the display is updating, then it is clear that each “tick” 

is originating from a traceable source. However, nearly all GPS receivers 

have the capability to “coast” and keep updating their display even when no 

satellite signals are being received. In order for a GPS display to be used as a 

reference, there must be an indicator on the unit that shows whether the display 

is currently locked to the GPS signal, or is in “coast” mode. If the receiver is in 

“coast” mode, it should not be used as a calibration reference.

Another example of a traceable time display would be a digital time signal 

obtained from a telephone line, such as signals from the NIST Automated 

Computer Time Service (ACTS), which is available by dialing (303) 494-4774 

[13]. With an analog modem and simple terminal software (configured for 

9600 baud, 8 data bits, 1 stop bit, and no parity), you can view time codes on a 

computer screen, and use these codes as a reference in the same way that you 

would use the audio time announcements from WWV. However, the length of 

a single telephone call is limited to 48 s. In theory, Internet time codes could be 

used in the same way, but the transmission delays through the network can vary 

by many milliseconds from second to second. For this reason, the currently 

available Internet signals should not be used as measurement references.

5.B. Calibration Procedure for the Direct Comparison Method 

Near the top of the hour, dial the phone number (or listen to the radio 

broadcast) of a traceable source of precise time. Start the stopwatch at the 

signal denoting the hour, and write down the exact time. After a suitable time 

period (depending on the accuracy of the stopwatch), listen to the time signal 

again, and stop the stopwatch at the sound of the tone, and write down the exact 

stopping time. Subtract the start time from the stop time to get the time interval, 

and compare this time interval to the time interval displayed by the stopwatch. 

The two time intervals must agree to within the uncertainty specifications of the 

stopwatch for a successful calibration. Otherwise, the stopwatch needs to be 

adjusted or rejected.

5.B.1. Advantages of the Direct Comparison Method

This method is relatively easy to perform and, if a telephone is used, does not 

require any test equipment or standards. It can be used to calibrate all types of 

stopwatches and many types of timers, both electronic and mechanical.

The Direct Comparison Method v
30

v Stopwatch and Timer Calibrations

5.B.2. Disadvantages of the Direct Comparison Method

The operator’s start/stop reaction time is a significant part of the total 

uncertainty, especially for short time intervals. Table 7 shows the contribution 

of a 300 ms variation in human reaction time to the overall measurement 

uncertainty, for measurement periods ranging from 10 s to 1 day. 

Table 7 - The contribution of a 300 ms variation in reaction time to 

the measurement uncertainty.

Hours

 

 Minutes

 

Seconds

 

Uncertainty (%)

10 3

1 60 0.5

10 600 0.05

30 1800 0.01666

1 60 3600 0.00833

2 120 7200 0.00416

6 360 21 600 0.00138

12 720 43 200 0.00069

24 1440 86 400 0.00035

As Table 7 illustrates, the longer the time interval measured, the less impact the 

operator’s start/stop uncertainty has on the total uncertainty of the measurement. 

Therefore, it is better to measure for as long as practical to reduce the 

uncertainty introduced by the operator, and to meet the overall measurement 

requirement. 

To get a better understanding of the numbers in Table 7, consider a typical 

stopwatch calibration where the acceptable measurement uncertainty is 0.02 % 

(2 × 10-4). If the variation in human reaction time is known to be 300 ms for 

the direct comparison method, a time interval of at least 1500 s is needed to 

reduce the uncertainty contributed by human reaction time to 0.02 %. However, 

if we use a 1500 s interval, we could possibly be measuring the variation in 

human reaction time, and nothing else. Therefore, we need to extend the 

time interval so that human reaction time becomes an insignificant part of the 

measurement. For example, NIST Handbook 105-5 [4] states that a stopwatch 

is considered to be within tolerance if its time offset is 2 s or less during a three 

hour calibration. Three hours is a long enough time interval to exceed the 0.02 
31

The Direct Comparison Method v

% requirement and to ensure that the uncertainty contribution of human reaction 

time is insignificant. There is no hard and fast rule; the length of the calibration 

can vary according to each laboratory’s procedures, but it must be long enough 

to meet the uncertainty requirements for the device being tested. If your 

uncertainty requirement is 0.01 % or lower, the direct comparison method might 

not be practical.

5.C. Uncertainties of the Direct Comparison Method

The Direct Comparison Method has three potentially significant sources of 

uncertainty that must be considered: the uncertainty of the reference, the 

reaction time of the calibration technician, and the resolution of the DUT.

5.C.1. Uncertainty of the Traceable Time Interval Reference

If the reference signal is one of the telephone services listed in Table 6, two 

phone calls are usually made. The first call is made to obtain the signal to 

start the stopwatch, and the second call is made to obtain the signal to stop the 

stopwatch. If both calls are made to the same service and routed through the 

same phone circuit, the delay through the circuit should be nearly the same for 

both calls. Of course, the delays will not be exactly the same, and the difference 

between the two delays represents the uncertainty of the time interval reference. 

In most cases, this uncertainty will be insignificant for our purposes, a few 

milliseconds or less. For example, callers in the continental United States using 

ordinary land lines can expect signal delays of less than 30 ms when dialing 

NIST at (303) 499‐7111, and these delays should be very repeatable from phone 

call to phone call. Even in a theoretical case where the initial call had no delay, 

and the final call had a 30 ms delay, the magnitude of the uncertainty would be 

limited to 30 ms.

However, if an ordinary land line is not used, the uncertainties associated with 

telephone time signals must be assumed to be larger. For example, wireless 

phone networks or voice over Internet protocol (VOIP) networks sometimes 

introduce larger delays that are subject to more variation from phone call to 

phone call than ordinary land lines. If wireless or VOIP networks are used, 

however, it is reasonable to assume that the transmission delay does not exceed 

150 ms, since the International Telecommunication Union (ITU) recommends 

that delays be kept below this level to avoid the distortion of voice transmissions 

[14]. Calls made from outside the continental United States might occasionally 

be routed through a communications satellite, introducing delays of about 

250 ms. Although the use of satellites is now rare, if the first call went through 

a satellite, and the second call didn’t (or vice versa), a significant uncertainty 

would be introduced. Therefore, common sense tells us that a laboratory in 

Illinois (for example) shouldn’t start a calibration by calling the NIST service in 

Colorado, and then stop the calibration by calling the NIST service in Hawaii. 

Based on this discussion, it is recommended that an uncertainty of 150 ms be 
32

v Stopwatch and Timer Calibrations

assigned if wireless or VOIP networks are used, or 250 ms if calls are routed 

through a satellite.

During a single phone call, the uncertainty of the time interval reference is 

essentially equal to the stability of a telephone line (the variations in the delay) 

during the call. Phone lines are surprisingly stable. The ITU recommendations 

for timing stability within the telephone system call for stabilities of much less 

than 0.1 ms for the North American T1 system [15]. A NIST study involving the 

Automated Computer Time Service (ACTS), a service that sends a digital time 

code over telephone lines, showed phone line stability at an averaging time of 

1 s to be better than 0.1 ms over both a local phone network and a long distance 

network between Boulder, Colorado and WWVH in Kauai, Hawaii [16]. While 

it is not possible to guarantee this stability during all phone calls, it is reasonable 

to assume that the stability should be much less than 1 ms during typical 

calls, which are limited to about 3 minutes in length. Thus, the uncertainties 

contributed by phone line instabilities are so small that they can be ignored for 

our purposes.

If the radio signals listed in Table 6 are used as a reference instead of a 

telephone signal, the arrival time of the signal will vary slightly from second 

to second as the length of the radio signal path changes, but not enough to 

influence the results of a stopwatch or timer calibration. Shortwave signals 

that travel over a long distance rely on skywave propagation, which means 

that they bounce off the ionosphere and back to Earth. A trip from Earth to 

the ionosphere is often called a hop, and a hop might add a few tenths of a 

millisecond, or in an extreme case, even a full millisecond to the path delay. 

Normally, propagation conditions will remain the same during the course of a 

calibration, and the variation in the radio signal will be negligible, often less 

than 0.01 ms. Even if an extra hop is added into the radio path during the 

calibration; for example if a one hop path becomes a two hop path, the received 

uncertainty of the radio signal will still not exceed 1 ms [13]. 

If a traceable time display is used instead of a radio signal or telephone signal, it 

can generally be assumed that the uncertainty of the display is less than 

1 ms. This is because instruments that continuously synchronize their displays 

to traceable signals will normally have repeatable and stable delays. However, 

in order for this uncertainty estimate to be valid, be sure to use only time 

displays that meet the traceability requirements discussed in Section 5.A.3.

5.C.2. Uncertainty Due to Human Reaction Time

To understand the effect of human reaction time on stopwatch and timer 

calibration uncertainties, a small study was conducted at Sandia National 

Laboratories. Four individuals were selected and asked to calibrate a standard 

stopwatch using the direct comparison method. Two separate experiments were 

conducted. In the first experiment, the operators were asked to use a traceable 
33

The Direct Comparison Method v

audio time signal, and in the second experiment, the operators were asked to use 

a traceable time display. The time base of the stopwatch was measured before 

and after each test (using the Time Base Method), and its offset from nominal 

was found to be small enough that it would not influence the test. Therefore, 

differences in readings between the stopwatch being tested and the standard 

would be due only to the operator’s reaction time. Each operator was asked 

to repeat the measurement process 10 times, and the resulting 10 differences 

between the standard and the stopwatch were recorded and plotted (Figure 11).

As shown in Figure 11, the average reaction time was usually less than 

±100 ms, with a worst-case reaction time exceeding 700 ms. The mean and 

standard deviation for each operator was computed and graphed in Figure 12. 

This graph indicates that the average (mean) reaction time of the operator can 

be either negative (anticipating the audible tone) or positive (reacting after the 

audible tone). Figure 12 also shows that in addition to the average reaction time 

having a bias, the data is somewhat dispersed, so both elements of uncertainty 

will need to be considered in a complete uncertainty budget. For this 

experiment, the worst case mean reaction time was 120 ms and the worst case 

standard deviation was 230 ms. It should be noted that in the measurements 

recorded in Figure 12, Operators 1 and 2 had no previous experience calibrating 

stopwatches. Based on these results, it is recommended that each calibration 

laboratory perform tests to determine the uncertainty of their operator’s reaction 

time.

 Figure 11. Reaction time measurements (four operators, 10 runs each) for the 

direct comparison method.
34

v Stopwatch and Timer Calibrations

 

Figure 12. Averaging measurement results for four different operators.

When a traceable time display was used, the uncertainty due to human reaction 

time was found to be approximately the same as the human reaction time for 

an audible tone. Keep in mind that these results are presented to illustrate the 

nature of uncertainty due to human reaction time, and to provide a very rough 

estimate of its magnitude. We strongly encourage each person calibrating 

stopwatches and timers to perform repeatability and reproducibility experiments 

to help better determine the uncertainty of human reaction time. 

5.C.3. Device Under Test (DUT) Resolution Uncertainty

Since the direct comparison method requires observing data from the DUT

display, the resolution of the DUT must also be considered. For digital 

indicating devices, resolution uncertainty is understood to be half of the least 

significant digit, with an assumed rectangular probability distribution. For an 

analog watch, the same method of determining resolution uncertainty may be 

used because the watch moves in discrete steps from one fraction of a second to 

the next.

5.C.4. Uncertainty Analysis

This section provides an example of how data collected using the direct 

comparison method can be used to perform an uncertainty analysis. For 

this estimate of uncertainty we will include the mean bias as an estimate of 
35

The Direct Comparison Method v

uncertainty, rather than correcting for it, because the mean bias can be either 

negative or positive, and may vary from time to time for the same user [17]. 

In this calibration process, the mean bias can be considered a measurement of 

reproducibility, and the standard deviation a measure of repeatability.

5.C.4.a. Uncertainty Distributions

Because of the lack of knowledge regarding distributions of the mean bias 

and delay deviation between telephone calls, both components of uncertainty 

are treated as rectangular distributions. Since the resolutions of digital and 

analog stopwatches have known, discrete quantities, their distribution is also 

rectangular [12]. All other data are considered to be normally distributed.

5.C.4.b. Method of Evaluation

Even though the data provided in previous sections were treated statistically, 

they were collected from previous measurements, and not during the actual 

stopwatch calibration. Because the metrologist does not have statistical data 

based on a series of observations to support these uncertainties, they are 

identified as Type B.

5.C.4.c. Combination of Uncertainties

In the following examples, the uncertainty budgets were developed for a 

calibration using traceable land lines (Table 8 and Table 9), and for a calibration 

using a cellular phone or satellite signal (Table 10) based upon the data 

previously provided. The human reaction time was based on the worst case 

data presented in Section 5.C.2. The uncertainties are rounded to the nearest 

millisecond. The uncertainty components are considered to be uncorrelated, so 

they are combined using the root sum of squares method.
36

v Stopwatch and Timer Calibrations

Table 8 - Uncertainty analysis for direct comparison method (digital DUT) 

using a land line.

 

 Source of 

 uncertainty

Magnitude, 

ms

Method of 

evaluation

Distribution Standard 

uncertainty, ms

 Human reaction 

 time bias 120 Type B Rectangular 69 

 Human reaction 

 time standard 

 deviation

230 Type B Normal

(k = 1) 230 

 Telephone delay 

 deviation 30 Type B Rectangular 17 

 1⁄2 DUT 

resolution 5 Type B Rectangular 3

 Combined uncertainty 241 

 Expanded uncertainty (k = 2, representing approximately a 95 % 

 level of confidence) 482 

Table 9 - Uncertainty analysis for direct comparison method (digital DUT) 

using a cell phone.

Source of 

uncertainty

Magnitude, 

ms

Method of 

evaluation

Distribution Standard 

uncertainty, ms

Human reaction 

time bias 120 Type B Rectangular 69 

Human reaction 

time standard 

deviation

230 Type B Normal

(k = 1) 230 

Telephone delay 

deviation 150 Type B Rectangular 87 

1⁄2 DUT resolution 5 Type B Rectangular 3

Combined uncertainty 255 

Expanded uncertainty (k = 2, representing approximately a 95 % 

level of confidence) 511
37

The Direct Comparison Method v

Table 10 - Uncertainty analysis for direct comparison method (analog 

DUT) using a land line.

Source of 

uncertainty

Magnitude, 

ms

Method of 

evaluation Distribution Standard uncertainty, ms

Human reaction 

time bias 120 Type B Rectangular 69 

Human reaction 

time standard 

deviation

230 Type B Normal

(k = 1) 230

Telephone delay 

deviation 30 Type B Rectangular 17 

1⁄2 DUT resolution 100 Type B Rectangular 58 

Combined uncertainty 248 

Expanded uncertainty (k = 2, representing approximately a 95 % 

level of confidence) 495 

39

The Totalize Method v

Section 6

The Totalize Method

The totalize method partially eliminates the measurement uncertainty from human 

reaction time, but requires two test instruments: a calibrated signal generator, and a 

universal counter.

6.A. Calibration Procedure for the Totalize Method

The counter is set to TOTALIZE, with a manual gate. A signal from a calibrated 

synthesized signal generator is connected to the counter’s input, and the 

laboratory’s primary frequency standard is used as the external time base for the 

synthesizer and the counter (Figure 13). The frequency should have a period 

at least one order of magnitude smaller than the resolution of the stopwatch. 

For example, if the stopwatch has a resolution of 0.01 s (10 ms); use a 1 kHz 

frequency (1 ms period). This provides the counter with one more digit of 

resolution than the stopwatch. 

 

 Figure 13. Block diagram of the totalize method.
40

v Stopwatch and Timer Calibrations

To begin the measurement, start the stopwatch and manually open the gate of 

the counter at the same time. One way to do this is by rapidly pressing the startstop button of the stopwatch against the start button on the counter (Figure 14). 

Another method is to press the start/stop button of the stopwatch with one hand 

and simultaneously pressing the start/stop button of the counter. After a suitable 

period of time (determined by the calibration requirements of the stopwatch 

or timer being calibrated), use the same method to simultaneously stop the 

stopwatch and close the gate of the counter.

 

Figure 14. Using the start-stop button of the stopwatch to start the counter.

Once the counter and stopwatch are stopped, compare the two readings. Use 

the equation ∆t/T to get the results, where ∆t is the difference between the 

counter and stopwatch displays, and T is the length of the measurement run. For 

example, if ∆t = 100 ms and T = 1 hour, the time uncertainty is 0.1 s / 3600 s or 

roughly 2.8 × 10-5 (0.0028 %).

6.A.1. Advantages of the Totalize Method

When using the stopwatch’s start/stop button to open and close the counter’s 

gate, this method partially eliminates human reaction time, and therefore has a 

lower measurement uncertainty than the direct comparison method.
41

6.A.2. Disadvantages of the Totalize Method

This method requires more equipment than the direct comparison method.

6.B. Uncertainties of the Totalize Method

The factors that contribute to the measurement uncertainty of this method are 

discussed below.

6.B.1. Uncertainty of the Frequency Reference

A synthesized signal generator that was recently calibrated typically has a 

frequency uncertainty ranging from 1 × 10-6 to 1 × 10-9. If the signal generator 

time base is externally locked to a laboratory frequency standard such as a 

cesium oscillator or a GPS disciplined oscillator, the frequency uncertainty can 

be much smaller, typically parts in 1012 or less. 

6.B.2. Uncertainty Due to Human Reaction Time

This source of uncertainty is due to any difference between the starting of both 

the stopwatch and counter, and the stopping of both the stopwatch and counter. 

In order to estimate this source of uncertainty, a study was conducted at Sandia 

National Laboratories. Four individuals were selected and asked to calibrate a 

standard stopwatch using the totalize method, using one hand to start and stop 

the stopwatch, and one hand to start and stop the frequency counter. The time 

base of the stopwatch was measured before and after each test (using the time 

base method), and its offset from nominal was found to be small enough so that 

it would not influence the test. Therefore differences in readings between the 

stopwatch being tested and the standard would be due only to the operator’s 

reaction time.

Each operator was asked to repeat the measurement process 10 times, and the 

resulting difference between the standard and the stopwatch were recorded.

The Totalize Method v
42

v Stopwatch and Timer Calibrations

 Figure 15. Measured reaction times (four operators, 10 runs each) for totalize method.

As shown in Figure 15, the average reaction time was usually less than 40 ms. 

The largest deviation was about 90 ms. The mean and standard deviations for 

each operator were computed and graphed in Figure 16. The data demonstrates 

that the worst case mean reaction time was 27 ms, and the worst case standard 

deviation was 10 ms, which is a significant improvement over the direct 

comparison method. Subsequent measurements of human reaction time were 

made by placing the start/stop button of the stopwatch directly against the 

start/stop button of the frequency counter (as shown in Figure 12) so that both 

buttons were pushed at the same time. The experimental data showed that 

this method provided no significant advantage over using one hand to start the 

stopwatch and the other hand to start the frequency counter.
43

Figure 16. Mean reaction times (four operators, 10 runs each) for the totalize method.

6.B.3. Uncertainty Due to the Counter

For this method, the uncertainty of the counter is related to the counter 

resolution. The internal time base of the counter is not used, because the gate 

time is controlled by the manual start/stop function. This method does not use 

the counter gate or trigger, so the uncertainties associated with these functions 

are also eliminated. The counter is simply used as an event counting device, and 

the uncertainty is equivalent to ±1 least significant digit on the display. 

6.B.4 Device Under Test (DUT) Resolution Uncertainty

Since the totalize method involves observing data from the DUT, the resolution 

of the DUT must also be considered. For digital indicating devices, resolution 

uncertainty is understood to be half of the least significant digit, with a 

rectangular distribution. A rectangular distribution is also used for analog 

timers, since these devices move in discrete steps from one fraction of a second 

to the next.

The Totalize Method v
44

v Stopwatch and Timer Calibrations

6.B.5 Method of Evaluation

Since the sources of uncertainty in this calibration are different types, such 

as the absolute accuracy specification for reaction time, the relative accuracy 

specification for the frequency source, and an absolute specification of ±1 

count for the counter, it is necessary to define the calibration conditions and 

convert all specifications to a common format.

The uncertainty example in Table 11 assumes that the synthesized signal 

generator can produce a 1 kHz signal with an uncertainty of 1 × 10-8 or 

less. The stopwatch is compared to the counter for 3 hours (10 800 s). The 

stopwatch is started and stopped with one hand, and the counter is started 

and stopped with the other. The stopwatch is digital and the resolution is 

0.01 s. As in the previous uncertainty example, all sources of uncertainty 

are combined by root sum of squares, and uncertainties are rounded to the 

nearest millisecond.

Table 11 - Uncertainty analysis for totalize method.

Source of 

uncertainty

Magnitude, 

ms

Method of 

evaluation Distribution

Standard 

uncertainty, 

ms

Human reaction 

time bias 27 Type B Rectangular 16

Human reaction 

time standard 

deviation

10 Type B Normal

(k = 1) 10 

Synthesizer 

accuracy

 0 Type B Rectangular 0

Totalize counter 

resolution 1 Type B Rectangular 1

1⁄2 DUT 

resolution 5 Type B Rectangular 3 

Combined uncertainty 19

Expanded uncertainty (k = 2, representing approximately a 95 % 

level of confidence) 38 
45

The Totalize Method v

6.C. Photo Totalize Method

An alternative measurement technique to the totalize method previously 

discussed involves using a high speed camera (digital or film type). The 

equipment is set up in the same manner as in Section 6.A. In this method, 

both the stopwatch being calibrated and the universal counter are started in no 

particular order. When both instruments are counting, a photo is taken of the 

two instruments. Under appropriate shutter and lighting conditions, the resulting 

photo will clearly show the time displayed on both the stopwatch and counter.

Both readings are recorded as the initial measurements in the calibration. After 

an appropriate amount of time has elapsed, a second photo is taken and the 

displays are recorded as the closing measurements. The difference in elapsed 

time for the stopwatch is compared to the difference in elapsed time for the 

counter to determine the measured offset of the stopwatch.

Figure 17 shows that the initial counter reading is 53.980 s and the stopwatch 

is at 57.52 s. Figure 18 shows that the counter reading is 82.049 s and the 

stopwatch is at 1 minute 26.18 s (86.18 s). The elapsed time on the counter is 

82.049 – 53.980 = 28.069 s, and likewise the elapsed time on the stopwatch is 

86.18 – 57.52 = 28.66 s. This would indicate that over the 28 s interval, the 

stopwatch was in error by 0.59 s or approximately 1820 s per day.

 

Figure 17. Photo totalize start reading.
46

v Stopwatch and Timer Calibrations

Figure 18. Photo totalize stop reading.

WARNING NOTE - In order for this method to provide accurate results, the photo 

system must be set up in a manner that captures the stopwatch and counter display 

correctly. If the shutter speed is too slow, the images will not produce discernable 

information, as Figure 19 shows for the stopwatch. We could interpret this stopwatch 

reading with the 1/10 s digit as 9, 7, 3, or 4, and the 1/100 s digit as 3, 5, or 6.

Additionally, often when the photo yields a very clear display as in Figures 17 and 

18, the resulting measurement is not valid. This stopwatch was previously calibrated 

using other methods described in this book and was found to have an offset of less than 

1 second per day, which is significantly different from the photo totalize method results

indicated above. For this example and photo equipment setup, the method produced 

false results. Anyone using the photo totalize method must validate the measurement 

results of their measurement process by comparing results obtained for a particular 

instrument to other measurement methods discussed in this book.
47

The Totalize Method v

Figure 19. Ambiguous photo totalize reading.

Section 6.C.1. Advantages of the Photo Totalize Method

Using this measurement method, all uncertainty due to human reaction time is 

reduced to zero. This makes the estimate of measurement uncertainty smaller, 

and the amount of time needed to complete a calibration shorter than the direct 

comparison or totalize method. This method also makes it possible to calibrate 

multiple stopwatches at the same time, and then maintain the photos as archival 

data.

Section 6.C.2. Disadvantages of the Photo Totalize Method

This method can VERY EASILY produce erroneous results. As previously 

stated, the measurement results for the particular cameras used by the laboratory 

should always be compared to measurement results of the same unit under test 

using other methods described in this book.

49

The Time Base Method v

Section 7

The Time Base Method

The time base measurement method is the preferred method for stopwatch and timer 

calibrations, since it introduces the least amount of measurement uncertainty. Because 

the DUT’s time base is measured directly, the calibration technician’s response time is 

not a factor.

The exact method of measuring the stopwatch’s time base depends upon the type 

of stopwatch or timer being calibrated. If the unit has a quartz crystal time base, an 

inductive or acoustic pickup is used to monitor the stopwatch’s 32 768 Hz time base 

frequency on a calibrated frequency counter (the pickup is fed into an amplifier to 

boost the signal strength). If the unit is an older LED-type stopwatch, the frequency is 

usually 4.19 MHz. An inductive pickup can even be used to sense the stepping motor 

frequency of analog mechanical stopwatches, or the “blink rate” of a digital stopwatch 

display. Or, an acoustic pickup can be used to measure the “tick” of a mechanical 

stopwatch.

7.A. References for the Time Base Method

The reference for a time base calibration is the time base oscillator of the 

measuring instrument. For example, if a frequency counter is used, the 

measurement reference is the time base oscillator of the frequency counter. In 

order to establish traceability, the frequency counter time base must have been 

recently calibrated and certified. However, a better solution is to have the 

laboratory maintain a traceable 5 MHz or 10 MHz signal that can be used as 

an external time base for the frequency counter and all other test equipment. If 

an external time base is used and its measurement uncertainty is known, it is 

unnecessary to calibrate the internal time base oscillator.

7.B. Calibration Procedure for the Time Base Method

Two methods of calibrating a stopwatch time base are described below. One 

uses a commercially available measurement system; the other uses a frequency 

counter with an acoustic pickup. Note that neither calibration method requires 

opening the case of the stopwatch or timer. Keep in mind that you should 

never disassemble a stopwatch or timer and attempt to measure the time base 

frequency by making a direct electrical connection. The crystal oscillators in 

these units are very small, low-power devices. Their frequency can dramatically 

change if they are disturbed or loaded down by the impedance of a frequency 

counter, and in some cases they can even be destroyed by incorrect electrical 

connections.
50

v Stopwatch and Timer Calibrations

7.B.1. Using a Commercial Time Base Measurement System

Time base measurement systems are available from several vendors. One 

example of a commercially available time base measurement system (Figure 

20) is described here for the purposes of illustration. This unit measures 

the frequency of the time base oscillator, and converts this information to a 

display of seconds per day, or seconds per month. This same function could be 

performed with a sensor (acoustic or inductive pickup), a frequency counter, and 

the conversion formula described in the next section.

 

 Figure 20. Time base measurement system for stopwatches and timers.

The example unit uses a 4.32 MHz quartz time base oscillator as a measurement 

reference. In a 2 s measurement period (the shortest period used by the 

instrument), the oscillator produces 8 640 000 cycles, which equals the number 

of 0.01 s intervals in one day. Therefore, the instrument resolution is 0.01 s per 

day. Cycles from the DUT time base are counted by a sensor that is connected 

to the measurement system. The sensor uses the cycle count from the DUT to 

start and stop the cycle count from the reference time base. For a 2 s measurement 

interval, a 32 768 Hz DUT would stop the cycle count from the reference time 

base after counting to 65 536 (32 768 × 2). If the reference time base counted 

to 8 639 900 during this same interval, then the system would estimate that the 

DUT would gain about 1 s per day (100 × 0.01 s). 

The time base measurement system shown in Figure 20 allows the measurement 

interval to be set from 2 s to 960 s. Selecting an interval longer than 2 s is 

effectively the same thing as increasing the gate time on a frequency counter. It 

is important to measure for a long enough period to get an accurate and stable 

reading. When testing a 32 768 Hz quartz stopwatch, a 10 s to 12 s measurement 

is normally sufficient to obtain a reading stable to ±1 count. When testing an 

older mechanical (Type II) stopwatch, a longer measurement of 120 s or more 

may be required. Table 12 shows the effect that the length of the measurement 

time has on the stability of the stopwatch calibrator’s readings.
51

Table 12 - The effect of the length of the measurement time on stability 

(based on 25 readings).

Measurement time 2 s 10 s 12 s 20 s

Mean -0.03 -0.06 -0.06 -0.06

Standard deviation of the mean 0.0050 0.0012 0.0011 0.0006

Maximum 0.00 -0.05 -0.05 -0.06

Minimum -0.09 -0.07 -0.07 -0.07

Range 0.09 0.02 0.02 0.01

To support 0.01 s resolution, the instrument’s 4.32 MHz time base oscillator 

must be calibrated to within 1.16 × 10-7. If the instrument is calibrated to within 

specifications, the display uncertainty is ±0.05 s per day (maximum time base 

frequency offset of about 6 × 10-7). In all cases, the uncertainty of the time 

base oscillator relative to UTC must be known in order to establish traceability. 

The system can be calibrated by applying either a traceable 1 pulse per second 

(pps) signal to a pin connector on the back of the unit or a traceable 32 768 Hz 

reference signal to the sensor, or by extracting and measuring the 4.32 MHz 

signal directly with a traceable frequency measurement system.

The DUT can be a Type 1 stopwatch (both 32 768 Hz and 4.19 MHz devices can 

be measured), or a Type 2 mechanical stopwatch. The 32 768 Hz signal is picked 

up with an acoustic sensor, and then compared to the time base oscillator. A 1 Hz 

offset in the 32 768 Hz signal translates to a time offset of about 2.6 s per day. A 

capacitive sensor is used to detect the 4.19 MHz frequency of quartz time base 

oscillators, an acoustic or inductive pickup is used to sense the stepping motor 

frequency of analog mechanical stopwatches, and an inductive pickup is used to 

sense the “blink rate” of digital stopwatches. 

Front panel switches allow the operator to select the type of device being tested, 

the measurement interval, and whether the time offset should be displayed as 

seconds per day or seconds per month. Once these parameters have been chosen, 

the device is measured by simply positioning it on top of the sensor until a usable 

signal is obtained, waiting for the measurement interval to be completed, and 

then recording the number from the display. It is always a good idea to allow 

the stopwatch calibrator to complete at least two complete measurement cycles 

before recording a reading.

Figure 21 shows a more elaborate time base measurement system with some 

additional features. This device has a small LCD display with graphics 

capability, built-in temperature measurement capability, an RS-232 interface 

that allows measurement results to be transferred to a computer, and an optional 

Global Positioning System (GPS) satellite receiver that corrects and calibrates 

the quartz time base oscillator. Like the system shown in Figure 20, this system 

can measure the 32 768 Hz quartz crystal frequency of Type 1 stopwatches, the 

The Time Base Method v
52

v Stopwatch and Timer Calibrations

stepping motor frequency of analog stopwatches, and the “blink rate” of digital 

stopwatches. As an additional benefit, this system can measure the quartz crystal 

frequency and the stepping motor frequency at the same time. This can be useful 

if the device under test compensates for the frequency offset of the quartz 

crystal by applying corrections to the stepping motor, thus making the analog 

display more accurate than the time base (a common practice in analog quartz 

wristwatches). 

Figure 21. A time base measurement system for stopwatches and timers with an 

integrated graphics display.

7.B.2. Using a Frequency Counter and an Acoustic Pickup

If an acoustic pickup and amplifier are available, you can measure the frequency 

of a stopwatch time base directly with a frequency counter. The reading on the 

counter display can be used to calculate the frequency offset using this equation:

 measured nominal (offset)

nominal

f f

f f

− = ,

 

where f

measured is the reading displayed by the frequency counter, and fnominal is 

the frequency labeled on the oscillator (the nominal frequency it is supposed to 

produce).

If f

nominal is 32 768 Hz and fmeasured is 32 767.5 Hz, then the frequency offset is 

–0.5 / 32 768 or –1.5 × 10-5 or –0.0015 %. To get time offset in seconds per day, 

multiply the number of seconds per day (86400) and the frequency offset:

86 400 × (–1.5 × 10-5) = -1.3 s per day,
53

which means the stopwatch can be expected to lose 1.3 s per day. You might 

find it easier to note that a 1 Hz error in a 32 768 Hz device equates to a time 

offset of about 2.64 s, since 86 400 / 32 768 = 2.64. Therefore, a 2 Hz offset is 

about 5.3 s / day, a 3 Hz offset is about 7.9 s / day, and so on. If the acceptable 

tolerance is 10 s / day, then you’ll know that 3 Hz is well within tolerance.

These results show that even a low cost eight-digit frequency counter will 

provide more measurement resolution than necessary when measuring 32 768 Hz 

devices. The last digit on an eight‐digit counter represents 0.001 Hz (1 mHz), 

and a 1 mHz frequency offset represents a time offset of just 2.6 ms per day. 

Very few stopwatches or timers can perform at this level.

7.B.3. Advantages of the Time Base Method

The time base method completely eliminates the uncertainty introduced by human 

reaction time. The measurement uncertainty can be reduced by at least two 

orders of magnitude when compared to the direct comparison method, often to 

1 × 10-6 or less. This method is also much faster. The measurement can often be 

performed in a few seconds, as opposed to the several hours typically required for 

the direct comparison method.

7.B.4. Disadvantages of the Time Base Method

This method requires more equipment than the direct comparison method, and 

does not easily work on some electrical, mechanical, or electro-mechanical units. 

It also does not test the functionality of the stopwatch or timer, only the time base. 

Function tests need to be performed separately by starting the unit, letting it run 

for a while (a few minutes to a few hours, depending on how the unit is used), 

and stopping the unit. If the unit appears to be counting correctly, the displayed 

time interval will be accurate. 

7.C. Uncertainties of the Time Base Method

This method utilizes either a time base measurement system or a frequency 

counter with an acoustic or inductive pickup to measure the frequency of the 

device’s internal time base oscillator. If we use the time base measurement system 

shown in Figure 20 as an example, and take into account its specified accuracy of 

±0.05 s/day and its resolution of 0.01 s, then the measurement uncertainty equals 

0.05 s/day (50 ms/day). There is no uncertainty contributed by human reaction 

time, and the resolution uncertainty of the stopwatch calibrator is insignificant 

compared to its accuracy specification. Resolution uncertainty does not need to 

be considered, since data are not observed from the DUT’s display. Since there is 

only one uncertainty component, we did not include an uncertainty analysis table.

The Time Base Method v

55

Required Uncertainty v

Section 8 

How to Determine if the Calibration Method Meets the 

Required Uncertainty

The preceding sections have provided estimates of expanded measurement uncertainty 

associated with various types of stopwatch calibrations. It is important to ensure that 

the achievable measurement uncertainty is relatively small when compared to the 

stopwatch tolerance we are attempting to verify. For example, if we use the direct 

comparison method to calibrate a stopwatch with an accuracy of 5 s per day (0.01 s 

resolution), and we decide to use a calibration period of 5 minutes, the accuracy of the 

stopwatch over the 5 minute interval would be about 17 ms. The first problem arises 

in that the resolution of the stopwatch is 0.01 s, and cannot display 0.017 s, making the 

specification impossible to verify for this time period. Furthermore, the measurement 

uncertainty for the calibration process is 480 ms, approximately 28 times larger than 

the accuracy that we are trying to verify! Clearly a 5 minute calibration period for 

this stopwatch and calibration method is not adequate. Even a 1 hour calibration is 

inadequate, because the quantity required to be measured, now about 208 ms, is still 

less than half of the measurement uncertainty.

As stated in ISO/IEC 17025 [4], when a statement of compliance to a metrological 

specification is made (for example, is the DUT “in tolerance” or “out of tolerance” 

based on the manufacturer’s specifications), the laboratory must take the measurement 

uncertainty into account. It is the responsibility of the calibration laboratory to decide 

whether the measurement uncertainty associated with the calibration method is 

small enough to comply with the metrological requirement. Calibration laboratories 

generally use some sort of decision rule for determining whether the uncertainty 

associated with the calibration method is adequate. Examples of such rules are the N:1 

decision rule (where the tolerance of the instrument to be tested is N times larger than 

the calibration uncertainty and is mostly commonly stated as 4:1 or 3:1), or some form 

of guardbanding (where the calibration uncertainty or some fraction of it is subtracted 

from the DUT accuracy specification and the calibration results are acceptable only if 

the measured offset was within the guardband limit). Whatever the case, it is important 

to compare the calibration measurement uncertainty to the tolerance of the DUT, in 

order to ensure that the calibration process is valid.

To illustrate this, assume that a laboratory employs a 4:1 rule for acceptable 

uncertainty. This means that the expanded measurement uncertainty of the calibration 

must be four times smaller than the acceptable tolerance of the DUT in order to declare 

the unit in or out of tolerance. The laboratory is calibrating a digital stopwatch to a 

tolerance of 0.02 %, using the direct comparison calibration method via a telephone 

landline (Table 8). The estimated expanded measurement uncertainty for this method 

was 482 ms. In order for 482 ms to be one quarter of the tolerance of the DUT, the 

tolerance must be 1928 ms. The amount of time required to elapse on the stopwatch 

during the calibration would be at least:
56

v Stopwatch and Timer Calibrations

 .

For the same scenario, if we were trying to verify the stopwatch shown in Figure 8 to 

the manufacturer’s specification of 0.0003 %, the stopwatch would have to run for more 

than 1 week (178 hours, 31 minutes, and 7 s). This is impractical, and the laboratory 

that is testing to 0.0003 % would clearly want to consider the time base method as a 

much faster, more appropriate method.

1.928 s X s 9640 s 2 h 41 minutes

0.02 % = = =
57

Other Topics Related to Measurement Uncertainty v

Section 9

Other Topics Related to Measurement Uncertainty

This section discusses other important topics related to measurement uncertainty. 

The first involves estimating the uncertainty of a field calibration, where a reference 

standard stopwatch is brought into the field and used to calibrate another device. Next, 

the stability and aging of 32 768 Hz quartz crystal oscillators used in stopwatches and 

timers is discussed, followed by discussions of how the performance of a stopwatch 

can change when a new battery is installed, and how extreme temperature conditions 

can affect stopwatch performance. 

9.A. Uncertainty Analysis of Using a Calibrated Stopwatch to 

Calibrate another Device

A calibrated stopwatch is often used to perform field calibrations of other timing 

devices, such as an industrial timer or parking meter. In this example (Table 

13), we are calibrating an industrial timer with 1 s resolution. The reference for 

the calibration is a stopwatch that has a specified accuracy of 5 s per day (about 

208 ms per hour), 0.01 s resolution, and a calibration uncertainty of 

0.2 s per day (roughly 8 ms per hour). As previously discussed in Section 5.C.2, 

the human reaction time bias is 120 ms, and the human reaction time standard 

deviation is 230 ms. The measurement time for the calibration is 1 hour 

(3600 s). Using these values and the analysis provided in Table 13, the 

uncertainty of the industrial timer when measuring a 1 hour interval is 789 ms, 

or 0.02 %. All values in Table 13 are rounded to the nearest millisecond. 

When performing this analysis, it is important to include the specified accuracy 

of the reference stopwatch, which takes into account long-term sources of error 

during the calibration interval that may not have been noticeable during the time 

of calibration. It is also important to consider the uncertainty of the stopwatch 

calibration as part of the budget when using a stopwatch as a reference, because 

it may be relatively large when compared to the other sources of uncertainty in 

the measurement process. 
58

v Stopwatch and Timer Calibrations

Table 13 - Uncertainty analysis of using a calibrated stopwatch to calibrate 

another device.

Source of 

uncertainty

Magnitude, 

ms

Method of 

evaluation Distribution

Standard 

uncertainty, 

ms

Unit under test 

resolution

1⁄2 digit

500 Type B Rectangular 289 

Human 

reaction time 

bias

120 Type B Rectangular 69 

Human 

reaction time 

standard 

deviation

230 Type B Normal 

(k = 1) 230

Stopwatch 

accuracy

208 Type B Rectangular 120

Stopwatch 

resolution 

1⁄2 digit

 5 Type B Rectangular 3

Stopwatch 

calibration 

uncertainty

 8 Type B Normal 

(k = 2) 4 

Combined uncertainty 394 

Expanded uncertainty (k = 2, representing approximately a 

95 % level of confidence) 789 

9.B. The Effects of Stability and Aging on Calibrations of 32 768 

Hz Crystals

Aging is the systematic change in frequency over time due to internal changes 

in an oscillator. All quartz oscillators are subject to aging, and the rate at which 

they age is often a key factor in determining their calibration interval. The aging 

rate of a quartz crystal oscillator often depends upon its surface area to volume 

ratio, and small, low frequency crystals generally have low aging rates [18]. 

Thus, the 32 768 Hz crystals found in stopwatches and timers usually tend to 

age slowly and have very good long term stability, and their frequency changes 

by a surprisingly small amount over time.
59

Figure 22. Graph of the frequency stability of two stopwatches.

To illustrate this, Figure 22 is a graph of the frequency stability of two 

stopwatches that were continuously measured over a period of more than one 

month using a previously described (Section 7.B.1) time base measurement 

system. Both stopwatches were low cost devices; stopwatch A had a suggested 

list price of about $25 USD, and stopwatch B sells for about $55 USD. The 

laboratory temperature during the measurement was about 23 °C ± 1 °C. The 

graph shows the Allan deviation (ADEV) of each stopwatch for averaging 

times ranging from 0.5 days to 7 days. ADEV is a commonly used statistic for 

estimating frequency stability [19]. It differs from the conventional standard 

deviation because it does not use the average frequency as a point of reference. 

Instead, it compares the frequency offset of the DUT during each measurement 

period with its frequency offset during the previous measurement period. By 

doing so, it reveals how the frequency of an oscillator changes over time due to 

effects such as aging.

Stopwatch A had an average frequency offset (accuracy) during the test of about 

8 × 10-6. As indicated in Figure 22, the stability (ADEV) was slightly better than 

1 × 10-7 after one week, or about 80 times better than the accuracy. Stopwatch 

B had an average frequency offset (accuracy) during the test of about 5 × 10-7. 

Its stability as estimated with ADEV was near 7 × 10-8 after one week, or about 

seven times better than its accuracy. 

Other Topics Related to Measurement Uncertainty v
60

v Stopwatch and Timer Calibrations

Because of their slow aging rate, stopwatches tend to produce very repeatable 

results over long periods of time. When compared to the requirements for 

stopwatch calibrations discussed in Section 3, the small changes in frequency 

due to aging are usually insignificant. This makes it possible for a laboratory to 

allow long intervals (perhaps exceeding one year) between calibrations.

9.C. Factors That Can Affect Stopwatch Performance

Many factors can cause a quartz crystal oscillator to change frequency. Some of 

these are shown in Figure 23. Sharp temperature changes, vibration, and shock 

are some of the more common phenomena that can affect the time base on a 

day-to-day basis. Also, if power is removed from an oscillator and later restored, 

there can be a shift in the frequency. This is true of quartz crystal stopwatches 

when the battery is changed. This frequency change is usually small when 

compared to the stopwatch’s time base specifications, usually less than 10 to 

20 parts in 106 (~10 to 20 ms/day) and usually short-term, with the time base 

returning to its original frequency after a period ranging from a few hours to a 

few days.

 

Figure 23. Factors that can change the quartz time base frequency.

Temperature is perhaps the most important factor that affects quartz crystal time 

base performance. The quartz crystals used in wrist watch time bases are cut in 

such a way as to make them most stable near body temperature. The time base 

acts as a thermally stable oscillator while it is on a person’s wrist. Stopwatches, 

on the other hand, use quartz crystals that have been cut to be stable at or near 

room temperature. If they are used in very hot or very cold environments, the 

time base can vary by over 20 parts in 106

. Figure 24 shows the accuracy of a 

typical stopwatch over a temperature range of 0 °C to 50 °C (32 °F to 122 °F). 
61

As can be seen in the figure, the flat portion of the performance curve is near 

room temperature (23 °C or 73 °F), and drops off as the temperature increases or 

decreases. 

 

Figure 24. Stopwatch accuracy versus temperature.

Other Topics Related to Measurement Uncertainty v

63

Appendix A

Calibration Certificates

If a calibration certificate is issued for a stopwatch or timer, it should contain the 

information listed in Section 5.10 of ISO/IEC 17025 [4]. Some of the necessary 

elements are the name and address of the laboratory, the name and address of the client, 

the identification of the method used, and a description of the item being calibrated. A 

sample calibration certificate that is compliant with ISO/IEC 17025 is shown in Figure 

A1.

 

Figure A1. Sample calibration certificate. (page 1)

Appendix A v
64

v Stopwatch and Timer Calibrations

 

Figure A1. Sample calibration certificate. (page 2)
65

Appendix B

References

[1] B. N. Taylor and A. Thompson, (Eds.), “The International System of Units (SI),” 

Natl. Inst. Stand. Technol. Special Publication 330, 2008 Edition, March 2008. 

[2] BIPM/IEC/IFCC/ISO/IUPAC/IUPAP/OIML, Guide to the Expression of 

Uncertainty in Measurement (GUM), 1995.

[3] International Organization for Standardization (ISO), International Vocabulary of 

Metrology – Basic and General Concepts and Associated Terms (VIM), 2008.

[4] International Organization for Standardization (ISO), General Requirements for 

the Competence of Testing and Calibration Laboratories, ISO/IEC Guide 17025, 2005.

[5] R. J. Anderson and G. L. Harris, “Specifications and Tolerances for Field Standard 

Stopwatches,” Natl. Inst. Stand. Technol. Handbook 105-5, October 1997.

[6] Robbins, Michael, “Electronic Clocks and Watches,” Howard W. Sams Co., 

Indianapolis, IN, 1975.

[7] J. R. Vig, “Introduction to Quartz Frequency Standards,” Army Research and 

Development Technical Report, SLCET-TR-92-1, October 1992

[8] North American Electric Reliability Council (NERC), “Time Error Correction,” 

Standard BAL-004-0, April 2005. 

[9] T. Butcher, L. Crown, L. Sebring, R. Suiter, J. Williams, editors, “Specifications, 

Tolerances, and other Technical Requirements for Weighing and Measuring Devices,” 

Natl. Inst. Stand. Technol. Handbook 44, 2007 edition (updated annually).

[10] M. A. Lombardi, “Legal and Technical Measurement Requirements for Time and 

Frequency,” Measure: The Journal of Measurement Science, 1(3): 60-69, September 

2006.

[11] State of Pennsylvania code, 67 § 105.71(2), 2005.

[12] R. M. Graham, “Calibration Techniques for Stopwatches and Timers,” Proc. 2003 

National Conference of Standards Laboratories (NCSLI), 6 p., August 2003.

[13] M. A. Lombardi, “NIST Time and Frequency Services,” Natl. Inst. Stand. 

Technol. Special Publication 432, 71 p., January 2002.

[14] International Telecommunications Union (ITU), “One-way Transmission Time,” 

ITU Recommendation G.114, May 2003.

Appendix B v
66

v Stopwatch and Timer Calibrations

[15] International Telecommunications Union (ITU), “The Control of Jitter and 

Wander within Digital Networks Which are Based on the 1544 kbit/s Hierarchy,” ITU 

Recommendation G.824, March 2000.

[16] D. W. Allan, D. D. Davis, J. Levine, M. A. Weiss, N. Hironaka, and D. Okayama, 

“New Inexpensive Frequency Calibration Service from NIST,” Proc. 1990 IEEE Freq. 

Cont. Symp., pp. 107-116, May 1990.

[17] S. D. Phillips, K. R. Eberhardt, “Guidelines for Expressing the Uncertainty of 

Measurement Results Containing Uncorrected Bias,” Natl. Inst. Stand. Technol. J. 

Res., 102(5): 577-585, September-October 1997.

[18] J. R. Vig and T. R. Meeker, “The Aging of Bulk Acoustic Wave Resonators, 

Filters, and Oscillators,” Proc. 1991 IEEE Freq. Cont. Symp., pp. 77-101, May 1991.

[19] IEEE, “IEEE Standard Definitions of Physical Quantities for Fundamental 

Frequency and Time Metrology - Random Instabilities,” IEEE Standard 1139-1999, 

March 1999.

January 2009