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SOP 24

Standard Operating Procedure 

for 

Calibration of Stopwatches and Timing Devices

1 Introduction

Purpose 

This procedure is used to calibrate Type I or Type II stopwatches and timing 

devices used by Weights and Measures officials, industrial, technical and other 

interests concerned with traceable time measurements. 

Type I: These stopwatches utilize digital, electronic circuitry to measure 

time intervals.

Type II: These stopwatches utilize analog, mechanical mechanisms to 

measure time intervals.

Applicable References 

NIST Handbook 44, Specifications, Tolerances, And Other Technical 

Requirement for Weighing and Measuring Devices, Section 5.55, 

Timing Devices.

NIST Special Publication (SP) 960-12, Stopwatch and Timer 

Calibrations.

NIST Handbook 105-5: Specifications and Tolerances for Field 

Standard Stopwatches.

NIST SP 432: NIST Time and Frequency Service.

Range and Scope

Detailed measurement ranges, standards, equipment, and uncertainties for this 

SOP are generally compiled in a separate document in the laboratory.

Limitations

Limitations of this method and the applicable services that can be offered can 

be determined by calculating an uncertainty associated with the method that 

will be used to provide the comparison of time to customer devices being 

calibrated. The expanded uncertainty with this procedure must be less than or 

equal to one third (≤ 1/3) of the tolerance per NIST Handbook 105-5 when used 

for legal metrology applications which is 0.02 %. The primary factors limiting 

the calibration uncertainty are related to the human reaction time, standard 

deviation in operation and the resolution of the stopwatch or timing devices. 
 

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Prerequisites

Verify that the metrologist performing the calibration is trained and 

proficient in performing this procedure and that his/her start/stop 

response time is documented and available.

Standard reference time signals must be available that can provide 

suitable traceability to the International System of Units (SI). Several 

options may be considered as noted in section 2.3. Suitable reference 

standards are maintained, with traceability to the SI, by NIST.

Two stopwatches or timing devices with resolution of 0.01 s or better 

for determining human reaction time factors. 

No specific environmental conditions are required for this procedure. 

However, calibrations should be conducted under normal laboratory 

conditions due to the general design of timing devices and potential 

temperature influences both above and below standard laboratory 

conditions and environmental data for temperature, barometric pressure, 

and relative humidity should be recorded. For most stopwatches and 

timing devices used in weights and measures, the influence of the 

human reaction time in operating the device and the resolution of the 

device far outweigh environmental influence factors. 

A stopwatch support stand or lanyard that will hold a spring-driven 

Type II stopwatch or timing device in a vertical position for a repeat 

calibration.

2 Methodology

Summary

This procedure uses a NIST traceable audio time signal from a telephone (not 

cell phone) or shortwave receiver, or a time signal from the GPS satellites as 

the reference standard. The unknown stopwatch or timing device is started to 

coincide with the respective signal or indication for the standard, allowed to run 

a calculated interval, and then stopped to coincide with an additional signal 

from the reference standard. The correction, Cxn, for each run is calculated. 
 

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Caution: Calibration methods do not require opening the case of the stopwatch 

or timing device. A stopwatch or timing device should never be disassembled 

to measure the time base frequency by making a direct electrical connection.

Standards with suitable traceability and resolution must be available and may 

include one of the following. 

An operational shortwave receiver to receive the broadcast timing signal 

on one of the frequencies listed in Table 2, or;

A land line telephone to call one of the numbers listed in Table 2, to 

receive the broadcast timing signal; or 

A GPS master clock. Verify that the GPS Master Clock is locked to GPS 

signals. 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.

Symbols Used in this Procedure

Table 1. Symbols used in the procedure.

Symbol Description

ABS Absolute value, mathematical function

Cxn Correction of the unknown stopwatch or timing device

for each run

R Amount of rollover timea

X Unknown stopwatch or timing device being calibrated

Tol Tolerance

Tsn Elapsed time of the standard for each run

Tx Observed elapsed time of the unknown stopwatch or 

timing device

UTC1 Start of calibration in Coordinated Universal Time

UTC2 End of calibration in Coordinated Universal Time a The point where the elapsed time exceeds the maximum indication of time 

provided by the stopwatch. At the rollover point, the stopwatch automatically starts 

again at zero or shuts itself off. The user of the stopwatch must account for each 

rollover to correctly measure long elapsed times.
 

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Preliminary Procedure

Ensure proper preparation and operation of the stopwatch or timing 

device to be calibrated. Batteries should be fresh, if applicable. The 

mainspring on the device must be fully wound, if applicable. The 

metrologist should familiarize themselves with the operation of each 

button (e.g., start, stop, reset) on the stopwatch or timing device. The 

stopwatch or timing device should be operating smoothly and freely. 

Determine an appropriate calibration interval, e.g., 1 hour, 3 hour, 

24 hour

Ensure that a suitable calibration interval is used by using a one to five 

ratio of the estimated uncertainty to the applicable tolerance. The 

calibration interval may also require assessment of the type of stopwatch 

or timing device being calibrated to ensure it will continue operation for 

the required interval and to ensure it has sufficient resolution. 

2.5.2.1 Example tolerance calculation for calibration intervals.

60 min 60 s Tolerance: 3 h 0.02 % 2.16 s truncated to 2.1 s

h min

× ×× = Eqn. (1)

For this 3 hour example, the uncertainty must be less than 0.42 seconds

(and a 1 s resolution device is not suitable).

2.5.2.2 Uncertainty to tolerance ratio calculation.

2.1 s Uncertainty 5

< Eqn. (2)

A 1 hour calibration interval will require an uncertainty of less than 0.14 

seconds. The uncertainty must be less than 3.4 seconds for a 24-hour 

interval and a 1 s resolution device may be able to meet this requirement. 

Establish a Traceable Time Signal 

The same signal source must be used for both the start and stop times.
 

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Table 2. Reference calibration sources.

Service Location Telephone 

Number

Radio Call 

Letters

Broadcast 

Frequencies

NIST Ft. Collins, CO (303) 499-7111 WWV 2.5 MHz

5 MHz

10 MHz

15 MHz

20 MHz

NIST Kauai, HI (808) 335-4363 WWVH 2.5 MHz 

5 MHz 

10 MHz 

15 MHz

U.S. Naval 

Observatory (USNO)

District of Columbia (202) 662-1401 

(202) 762-1069

----- -----

USNO Colorado Springs, CO (719) 567-6742 ----- -----

National

Research Council

(NRC)

Ottawa, Ontario,

Canada

(613) 745-1576 

(English)

(613) 745-9426 

(French)

CHU 3.33 MHz

7.850 MHz

14.67 MHz

Note: Do not use local “time & temperature” telephone services, cell phones, or a time display from a radiocontrolled clock or a website as these sources are not considered traceable.

Obtain Human Response Time Bias Data

To determine the start/stop response of the metrologist, use a shortwave 

receiver for continuous broadcast of the timing signals (Note: a telephone can 

be used but there is a time limit of three minutes for each call). Hold a stopwatch 

in each hand and start both stopwatches simultaneously on a minute tone and 

then stop both simultaneously on the very next minute tone. Record the bias 

from the interval for each stopwatch each time a calibration is performed and 

add results to the laboratory response time control chart designated for that staff 

member. If the start time for each watch is reset, the start time, Tx1 will be zero 

in as shown in the Eqn. 7. See Section 4.1 to establish repeatability data and 

measurement assurance data. 

Measurement Procedure

Connect to the selected time signal (note that a telephone signal will be 

limited and will not continue to broadcast during the calibration 

interval).

Start the two laboratory stopwatches used for determining the 

metrologist start/stop time response on a minute tone and stop on the 

very next minute tone. Record the bias and plot on the Human Response 

Time control chart for that metrologist.
 

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Start the unknown timer at a minute tone and record the reference UTC 

time as UTC1.

At or after the previously determined calibration interval, connect to the 

time signal again if needed, then stop the unknown timer at a minute 

tone and record the UTC time as UTC2

Calculate elapsed time of the standard for the first run, Ts1, using 

Equation 3.

Calculate the unknown error for the first run, Cx1, by comparing the 

elapsed time of the standard, Ts1, to the observed elapsed time on the 

unknown timer, Tx, using Equation 4. Be sure to account for any 

rollover, R, in the unknown timer.

Calculate and determine the tolerance status using Equation 5.

If the unknown timer appears to be in tolerance switch hands used to 

calibrate each timer and repeat steps 2.7.3 through 2.7.7 to obtain the 

unknown error for run two, Cx2. Switching hands in this step is 

performed to eliminate potential errors with the human response time. 

Calculate and report the mean correction for the unknown, CCxx, using 

Equation 6.

NOTE: Spring driven Type II stopwatches shall be calibrated in two 

different orientations; horizontal (with dial face up), and vertical (with 

crown up). The main spring shall be fully wound before each run.

3 Calculations (Measurement Equations)

Calculate the Elapsed Time for each Run for the Standard, Ts1 and Ts2 using Eqn. 

3.

T UTC UTC sn = −1 2 Eqn. (3)

Calculate the Error for each Run for the Unknown, Cx1 and Cx2 using Eqn. 4 and 

add applicable Rollover, R.

( ) C TRT xn x = +− sn Eqn. (4)

Calculate and Determine the Tolerance Status for each Run where the values 

pass using Eqn. 5 when the absolute value of the error plus the expanded 

uncertainty is less than the tolerance for the elapsed time (see Section 6.1 also).

Pass if: Tolerance for C U xn x + ≤ Tsn Eqn. (5)
 

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Calculate and Report the Mean Correction for the Unknown using Eqn. 6.

1 2 ( )

2

x x

x

C C C + = Eqn. (6)

Calculate the observed human response time bias using Eqn. 7.

Bias ( ) ( 21 2 1 ) = −− − T T UTC UTC x x Eqn. (7)

4 Measurement Assurance

Determine the human response time and bias components of the measurement 

process by conducting the human response time assessment as described in 

Section 2.6 for at least 10 cycles, switching the stopwatches into opposite hands, 

recording data for every event. Start a control chart for the response time for 

each metrologist who will be conducting timing calibrations. One additional 

cycle will be conducted for each stopwatch measurement and plotted on the 

control chart for all future calibrations. It is recommended that all laboratory 

staff use the same two stopwatches to establish bias and ensure that any 

differences detected are NOT due to differences in the accuracy of the 

stopwatches used. The bias is calculated using Eqn. 7.

An example of the initial chart data for the stopwatch data might look like this:

• Left Bias (watch 1) Right Bias (watch 2)

• Left Bias (watch 2) Right Bias (watch 1)

• Left Bias (watch 1) Right Bias (watch 2)

• Left Bias (watch 2) Right Bias (watch 1)

• Left Bias (watch 1) Right Bias (watch 2)

• Left Bias (watch 2) Right Bias (watch 1)

• Left Bias (watch 1) Right Bias (watch 2)

• Left Bias (watch 2) Right Bias (watch 1)

• Left Bias (watch 1) Right Bias (watch 2)

• Left Bias (watch 2) Right Bias (watch 1)

Observed differences in reaction time between the metrologist reaction 

and a reference signal are used to determine a typical bias for each 

metrologist.

Two response times are used to calculate a standard deviation to be 

plotted on a standard deviation chart. Response standard deviations are 

pooled to determine an accepted standard deviation. The observed 

repeatability of each calibration may be compared to the accepted 

standard deviation using an F-test. 

The repeatability data for the calibration is evaluated to ensure it is 

within acceptable limits. If the repeatability from the two runs is outside 
 

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the control limits, conduct a root cause analysis or troubleshoot the 

source of the problems before repeating the calibration or reporting 

calibration results. 

The measurement process may be duplicated with a suitable check standard(s)

to replicate the measurement process. However, one person may not able to 

actuate a standard, stopwatch or timing device being calibrated, and a check 

standard all at the same time and will need to offset the times at the next 

designated signal. Duplicate calibrations may be needed to calibrate check 

standards. Evaluate the check standard immediately after the runs to ensure the 

values are in control. Suitable check standards may be used to determine values 

for section 4.1. Differences in variability of Type I and Type II devices and 

associated resolutions (or absence of differences) will need to be verified. The 

check standard data will incorporate repeatability, bias, and resolution influence 

data; therefore, the laboratory should consider what uncertainty components 

could be double counted resulting in overestimated uncertainties. 

5 Assignment of Uncertainty

Examples of uncertainty budgets and sample data are presented in NIST SP 960-12, Tables 8, 

9, 10, and 11. The uncertainty is calculated according to NISTIR 6969, SOP 29 to ensure 

compliance with the Guide to the Expression of Uncertainty in Measurement. 

Uncertainty for the Standard, us

Determine the uncertainty for the standard based on the type of standard that is 

used for the calibration. See pages 31 and 32 in NIST SP 960-12. (This 

uncertainty is usually nearly negligible for telephone, radio, and GPS standards

compared to the human reaction time factors.) 

Uncertainty for the human reaction time repeatability, standard deviation of the 

process, sp

The standard deviation of two replicate runs are tracked over time and used to 

determine a pooled standard deviation associated with the repeatability of the 

measurement process. 

Uncertainty for the human reaction time bias, ub

A comparison between the absolute time values from the standard source and 

the check standard(s) are used to calculate a bias for each metrologist. The bias 

is calculated for at least 10 runs and is treated as a rectangular distribution.

Uncertainty for the resolution of the timing device, ur

The resolution of the instrument is treated as a rectangular distribution whether 

digital or analog (as analog timing devices also use discrete 1 s intervals). 
 

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Table 3. Example Uncertainty Budget Table.

Uncertainty Component 

Description Symbol Source Typical Distribution

Uncertainty for the reference 

standard us

NIST traceable time standard 

(telephone, receiver, GPS clock)

NIST website (SP 960-12)

Rectangular

Standard deviation of the 

process, human reaction time 

repeatability

sp

Laboratory assessments, pooled 

standard deviation Normal

Uncertainty of the human 

reaction time bias ub

Comparison of metrologist to 

reference signal Rectangular

Uncertainty of the stopwatch or 

timing device resolution ur Resolution of the instrument Rectangular

Calculate the combined uncertainty, uc, and the expanded uncertainty for the 

unknown stopwatch or timing device, Ux, using the root sum square method 

described in NISTIR 6969, SOP 29 and use the appropriate effective degrees of 

freedom to determine a coverage factor to provide an approximate 95 % 

confidence interval. 

Evaluate the uncertainty. Review the conformity assessment requirements in 

Section 6. to evaluate the adequacy of the uncertainty. A longer time interval 

for the calibration may be required, especially with timing devices with larger 

resolutions.

Report the calculated uncertainty to two significant digits according to SOP 29 

and issue a suitable uncertainty statement. 

6 Certificate

Report results as described in SOP No. 1, Preparation of Calibration 

Certificates. Report the measured time results (and the deviation of time values 

from the nominal time calibrated if applicable), the duration of the calibration 

conducted, and calculated uncertainties.

Conformity Assessment

A stopwatch is considered to be within tolerance when the absolute value of its 

error plus its uncertainty is less than or equal to the tolerance established in 

NIST Handbook 105-5. The tolerance is 0.02 % of the calibration interval with 

values truncated to the device resolution as needed. Provide a 

compliance/conformity statement on the calibration certificate if the stopwatch 

or timing device will be used for a weights and measures application.
 

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Example tolerance evaluation for a 3-hour interval on a device with 

0.01 s resolution:

60 min 60 s Tolerance 3 h 0.02 % 2.16 s

h min

=× × × = Eqn. (8)

0.25 s 0.35 s 0.60 s C U x x += + = Eqn. (9)

The value of 0.60 s is less than 2.16 s, thus is considered in tolerance.

Example tolerance evaluation for a 24-hour interval on a device with 1 s 

resolution, truncated to the nearest second:

60 min 60 s Tolerance 24 h 0.02 % 17.28 s, or 17 s h min

=× ×× = Eqn. (10)

15.0 s 3.5 s 18.5 s C U x x += + = Eqn. (11)

The value of 18.5 s is greater than 17 s thus is out of tolerance and would be 

rejected.

7 Acknowledgments and Validation 

Inputs to this procedure were submitted with procedures from the following State laboratories: 

Washington, Pennsylvania, California, and New York. The original version of SOP 24 was 

developed by Dan Wright and reviewed by SP 960-12 authors Jeff Gust and Mike Lombardi 

for suitability and compliance to requirements in SP 960-12 and good measurement practices. 

Modifications were made in Pennsylvania, California, and New York to introduce specific 

standards, applications, and recording approaches used in their laboratories. Users applying 

methods for weights and measures must make sure to use requirements in NIST Handbook 44 

as the over/under-registration limits in SP 960-12 are reversed.

Suitability and reproducibility of this procedure was successfully demonstrated through 

proficiency tests (PT) conducted among the following laboratories in report NAT-16-FT-M01 (as coded by OWM) for a 3-hour calibration interval who used SOP 24 as developed or 

modified in their laboratories: Pennsylvania, Troemner, New Jersey, New York, Connecticut, 

Ohio, California, Washington, and Hawaii; the highest normalized error (En) among these 

laboratories was 0.22. All precision assessments, Pn, were acceptable. Uncertainties varied for 

these laboratories from 0.068 s to 0.48 s. All participant values for the 3-hour calibration were 

within one third of the Handbook 44 tolerance that was specified as 1.875 s (0.017 %). Note 

that a tolerance of 0.02 % is specified in NIST Handbook 105-5.