Selected Laboratory and Measurement Practices 

and Procedures for Length Calibrations

(2014 Ed)

Jose A. Torres Ferrer

Office of Weights and Measures (contractor) 

Physical Measurement Laboratory 

Georgia L. Harris, editor

Office of Weights and Measures 

Physical Measurement Laboratory 

http://dx.doi.org/10.6028/NIST.IR.8028 

NISTIR 8028
 

This page is CODEN page on back of title page or Blank. 
 

 

NISTIR 8028

Selected Laboratory and Measurement 

Practices and Procedures for Length 

Calibrations

(2014 Ed)

Jose A. Torres Ferrer

Office of Weights and Measures (contractor) 

Physical Measurement Laboratory 

Georgia L. Harris, editor

Office of Weights and Measures 

Physical Measurement Laboratory 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.IR.8028 

October 2014

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Willie May, Acting Under Secretary of Commerce for Standards and Technology and Acting 

Director
 

This page is CODEN page on back of title page or Blank.
October 2014 

NISTIR XXXX i 

Foreword 

This NIST IR of Selected Publications was compiled as an update for a number of Good Laboratory 

Practices (GLP), Good Measurement Practices (GMP), Standard Operating Procedures (SOP), 

Statistical Techniques and Reference Tables. This is the fourth in a series of updates that also 

include: NISTIR 5672 (2014), NISTIR 6969 (2014), NISTIR 7383 (2013). 

This publication covers those GMPs and SOPs required for length calibrations as used in weights and 

measures applications. 

Most of these procedures are updates to procedures that were originally published in NBS Handbook 

145, Handbook for the Quality Assurance of Metrological Measurements, in 1986, by Henry V. 

Oppermann and John K. Taylor. The major changes incorporated 1) uncertainty analyses that comply 

with current international methods, 2) measurement assurance techniques using check standards or 

replicate measurements, and 3) No substantive changes were made to core measurement processes or 

equations. 

The following Procedure is new in the 2014 publication, but was prepared by Ken Fraley (retired, 

OK) and first made available as a draft for laboratories to follow in 2001: 

Standard Operating Procedures for: Calibration of Pi Tapes (23) 

Appendix B of SOP 10 was prepared by Karen Bryan (previously with NC) and first made available 

as a draft for laboratories to follow in 1996. 

 
October 2014 

NISTIR XXXX ii 

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NISTIR XXXX page iii 

Table of Contents 

Foreword i

Good Measurement Practices 

2 Reading the Center of Graduations When Using a Microscope GMP 2-1 

8 Reporting Tape Calibrations GMP 8-1 

9 Equations for Metallic Tapes GMP 9-1 

Standard Operating Procedures 

10 Calibration of Rigid Rules SOP 10-1 

11 Calibration of Metal Tapes – Bench Method SOP 11-1 

12 Calibration of Metal Tapes – Tape-to-Tape Method SOP 12-1 

23 Calibrations of PI Tapes – Bench Method SOP 23-1 

 
NISTIR XXXX page iv 

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Good Measurement Practices 

 
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October 2014 

GMP 2 Page 1 of 2 

GMP 2 

Good Measurement Practice 

for 

Reading the Center of Graduations when using a Microscope 

1. The microscope furnished to State laboratories with the length bench has a reticle on which 

each graduation represents 0.002 inch which must have a suitable calibration from an 

accredited supplier to ensure metrological traceability to the International System of Units 

(SI). The difference in length between two tapes is measured from the center of the 

graduations of interest. The tape should be placed on the length bench such that the reading 

edge of the tape partially covers the graduations marked on the length bench. Place the 

microscope so that both the edges of the tape and the edge of the bench graduations are in the 

field-of-vision of the microscope, preferably near the center, and within reading range of the 

graduated reticle. Position the microscope so that part of the graduations on the reticle 

overlaps the bottom portion of the graduation on the tape and part overlaps the graduation on 

the length bench. See Figure 1 for illustration. Do not move or refocus the microscope once 

the comparison between the unknown, X, and standard, S, has begun. 

Figure 1. Graduated reticle overlapping tape and bench graduations. 

2. Determine the center of a graduation by first determining the width of the graduation, 

dividing the width by two and adding this value to the reticle reading for the left edge of the 

graduation. In the illustration above, let the length bench be the standard, S, and the tape be 

the unknown, X. The left edge of the tape graduation is at 206 (0.206 inch); the right edge is 

at 216 (0.216 inch). The width of the graduation is 0.010 inch. Adding half this value to 206 

(0.206 inch), gives the center of the graduation at 211 (0.211 inch). Following the same 

procedure for the length bench graduation shows the left edge of the graduation at 190 (0.190 

inch) and the right edge at 197 (0.197 inch). The center of the graduation is 193.5 (0.193 5 

inch). The difference between the two tapes is 211 – 193.5, which is 17.5 (0.211 inch – 0.193 

5 inch = 0.017 5 inch). Since X is longer than S, d is positive. Using the equation X – S = d, 

X – S = 0.017 5 inch or X = S + 0.017 5 inch 

 
October 2014 

GMP 2 Page 2 of 2 

3. If it is necessary to calibrate a rigid rule to the end of the rule, the edge of ends of the rule are 

reference points for the measurement. In these cases, there will be only a single value read 

from the microscope reticle for each end of the rule since the center of graduation is assumed 

to be the end of the rules. 
October 2014 

GMP 8 Page 1 of 4 

GMP 8 

Good Measurement Practice 

for 

Reporting Tape Calibrations 

Tape calibration results should be reported as described in SOP 1, Preparation of 

Calibration Certificates. The use of the Calibration Certificate and Test Report Review Checklist, 

(SOP 1, Appendix B), is highly recommended. 

Information pertinent to this type of calibration should include: 

1. A note that reported lengths may be converted to catenary suspension support 

lengths by use of the “Equations for Metallic Tapes” (GMP 9); 

2. Description of the procedure, and the position of the test artifact relative to the 

observer; 

3. Tension applied to the tape during the test; 

4. Type of support, e.g., continuous, catenary (include information regarding 

spacing); 

5. The assumed linear coefficient of expansion for the tape material; 

6. The relationship between the International System of Units (SI) and US 

customary units; 

7. The degrees of freedom (effective) associated with the coverage factor k;

8. AE value, if requested by customer; and 

9. Weight per Unit Length, if requested by customer. 

An example of a Calibration Certificate follows in the Appendix. 
October 2014 

GMP 8 Page 2 of 4 

Appendix – Example 

COMPLIANT CALIBRATION LABORATORY 

123 Some Ave. 

City, State 12312-1231 

CALIBRATION CERTIFICATE 

FOR 

25 foot Iron-Nickel Alloy Tape 

Maker: LUFSTARTOYO Lab Test No.: TI-14-056

Serial No.: C917R NMI Test No.: 822/1234 

SUBMITTED BY 

YOUR CUSTOMER, INC. 

Customer’s Address 

City, State 

This tape has been compared to the standards of Compliant Calibration Laboratory. The 

horizontal distances between the centers of graduations of the indicated intervals have the 

following lengths at 20 °C (68 °F) when the tape is subjected to 10 pound horizontally applied 

tension and supported on a horizontal flat surface. The terminal points of the indicated intervals 

are the centers of the graduations at the edge of the tape ribbon nearest the observer when the 

zero graduation is to the left. 

Interval 

(feet) 

Length 

(inches) 

Uncertainty 

(inches) 

Interval 

(feet) 

Length 

(inches) 

Uncertainty 

(inches) 

0 to 1 12.000 3 0.001 0 0 to 14 167.999 4 0.001 0 

0 to 2 24.000 5 0.001 0 0 to 15 180.000 1 0.001 0 

0 to 3 36.000 3 0.001 0 0 to 16 192.000 4 0.001 0 

0 to 4 48.000 2 0.001 0 0 to 17 204.000 3 0.001 0 

0 to 5 59.999 8 0.001 0 0 to 18 216.000 2 0.001 0 

0 to 6 71.999 6 0.001 0 0 to 19 220.000 4 0.001 0 

0 to 7 84.000 2 0.001 0 0 to 20 239.999 8 0.001 0 

0 to 8 96.000 1 0.001 0 0 to 21 252.000 4 0.001 0 

0 to 9 108.000 2 0.001 0 0 to 22 264.000 1 0.001 0 

0 to 10 120.000 4 0.001 0 0 to 23 275.999 7 0.001 0 

0 to 11 132.000 4 0.001 0 0 to 24 287.999 6 0.001 0 

0 to 12 144.000 2 0.001 0 0 to 25 300.000 7 0.001 0 

0 to 13 155.999 6 0.001 0 

The data in the above table only applies to those items specifically listed on this report. 

This document does not represent or imply endorsement by Compliant Calibration Laboratory, NMI, or any agency of the State and/or national 

governments. This document may not be reproduced, except in full, without the written permission of Compliant Calibration Laboratory. 

Page 1 of 3 
October 2014 

GMP 8 Page 3 of 4 

Reported lengths may be converted to catenary suspension support lengths by use of the 

“Equations for Metallic Tapes” (GMP 9).

The exact relationship between the International System of Units (SI) and the US customary 

units of length is one foot equals 0.304 8 meter. 

Uncertainty statement: 

The combined standard uncertainty includes the standard uncertainty reported for the standard, 

the standard uncertainty for the measurement process, the standard uncertainty of the coefficient 

of expansion, the standard uncertainty of the tension weights, the standard uncertainty of the 

graduated reticle, and a component of uncertainty to account for any observed deviations from 

NIST values that are less than surveillance limits. The combined standard uncertainty is 

multiplied by a coverage factor of 2.07, for 35 effective degrees of freedom, to provide an 

expanded uncertainty, which defines an interval having a level of confidence of approximately 

95 percent. The expanded uncertainty presented in this report is consistent with the ISO/IEC 

Guide to the Expression of Uncertainty in Measurement (2008). The expanded uncertainty is not 

to be confused with a tolerance limit for the user during application. 

Traceability statement: 

The Standards of the Compliant Calibration Laboratory are traceable to the International System 

of Units (SI) through the National Institute of Standards and Technology, and are part of a 

comprehensive measurement assurance program for ensuring continued accuracy and 

measurement traceability within the level of uncertainty reported by this laboratory. The 

laboratory test number identified above is the unique report number to be used in referencing 

measurement traceability for artifacts identified in this report only. 

Supplemental Information 

Description of artifacts submitted for testing: 

25 foot, iron-nickel alloy (invar), tape. A linear coefficient of thermal expansion of 

0.000 000 4 /°C (0.000 000 22 /°F) was assumed. 

Conditions of artifacts submitted for testing: 

Artifact showed evidence of proper handling. No bents or kinks were observed. A light film of 

oil covered the tape ribbon. 

Treatment of artifacts prior to testing: 

Artifact was cleaned with cheesecloth and alcohol to remove the protective oil film. The artifact 

was kept in the length laboratory, next to the standard, for 36 h to allow for thermal equilibrium. 

Equipment & Standards 

Standard: Length bench Calibrated: August 2014 

Tension weights: 10 pound, Class F

Microscope: B&L, 0.002 inch graduated reticle 

This document does not represent or imply endorsement by Compliant Calibration Laboratory, NMI, or any agency of the State and/or national 

governments. This document may not be reproduced, except in full, without the written permission of Compliant Calibration Laboratory.

Page 2 of 3 
October 2014 

GMP 8 Page 4 of 4 

Procedure used: NISTIRXXXX, SOP 11, Calibration of Metal Tapes, Bench Method 

Environmental conditions at time of test: 

Temperature: 20.1 C to 20.2 C Barometric Pressure: 752.7 mm Hg 

Relative Humidity: 43.35 % to 43.40 % 

Date artifact was received: September 15, 2014 

Date of test: September 17, 2014 

Due date per customer’s request: September 17, 2016 

Date of report preparation: September 18, 2014 

 Josh Balani, Jr. 

Test performed by: Josh Balani, Jr. 

 Metrology Expert 

Member: 

NCSLI 

NCWM 

ASQ 

ASTM 

This document does not represent or imply endorsement by Compliant Calibration Laboratory, NMI, or any agency of the State and/or national 

governments. This document may not be reproduced, except in full, without the written permission of Compliant Calibration Laboratory.

Page 3 of 3 
October 2014 

GMP 9 Page 1 of 2 

GMP 9 

Good Measurement Practice 

for 

Equations for Metallic Tapes 

Table 1. Symbols used in this practice. 

Symbol Description 

L Horizontal straight-line distance 

LS Calibrated length of the tape interval on a flat surface at TS and PS

Ln Designated nominal length of the tape interval 

P Applied tension 

PS Standard tension applied to the tape interval for LS

AE Average cross-sectional area times Young’s Modulus of Elasticity 

T Temperature 

TS Standard temperature of the tape interval for LS, 20 °C (68 °F) 

α Coefficient of thermal expansion of the tape ribbon 

W Average weight per unit length of the tape ribbon 

N Number of equidistant catenary suspensions 

PO Tension of accuracy (Tension of accuracy is defined as that tension which must be 

applied to the tape interval to produce its designated nominal length at the observed 

temperature of the tape.) 

PC Tension of accuracy while the tape is supported in catenary suspensions 

The horizontal straight-line distance, L, of a tape interval can be computed by the following 

equation for an applied tension, P, and temperature, T, when the tape is supported for N, number 

of equidistant catenary suspensions. When both a standard tape and a tape to be calibrated are 

placed in a catenary suspension condition, the horizontal straight line distance for the compared 

intervals for each tape must be calculated. Intervals can be compared only at the supported 

points along the tape length. 

24

( * * ) ( ) ( ) 2 L W L N P

L T T

AE

L P P

L L n n

n S

n S

S        (1) 

For simplicity, it is recommended to entirely support the tape on a horizontal flat surface for 

calibration. When the tape is supported entirely on a horizontal flat surface, N = ∞, and the 

general equation is reduced to: 

( ) ( ) n S

n S

S L T T

AE

L P P

L L      (2) 

The distance, L, of the tape interval can be set to the designated nominal length, Ln, for 

determining the tension of accuracy, PO, while the tape is supported on a flat surface, by writing 

equation (2) as follows: 
October 2014 

GMP 9 Page 2 of 2 

( ) ( ) n S

n O S

n S L T T

AE

L P P

L L      (3) 

from which the following equations are developed: 

( ) ( )

S

n

n S

O S AE T T

L

AE L L

P P      (4) 

or 

( ) ( )

S

n

n S

S O AE T T

L

AE L L P P      (5) 

Substituting equation (5) for PS in the general equation (1), we have 

24

( ) ( * * )

2

n O n n C

n

L W L N P

AE

L P P

L L     (6) 

The distance, L, of the tape interval again can be set to the designated nominal length, Ln, for 

determining the tension of accuracy, PC, while the tape is supported in catenary suspensions, by 

writing this equation as follows 

24

( ) ( * * )

2

n C O n n C

n n

L W L N P

AE

L P P

L L     (7) 

from which: 

24

( * ) ( )

2

2 AE W L N P P P n

C C  O  (8) 

or 

24

( * ) ( ) ( ) 2

2 AE W L N AE T T

L

AE L L P P P n

S

n

n S

C C S  



 





      (9) 

The value of PC can be solved by first determining the right side of the equal signs in equations 

(8) or (9), then substituting various values for PC until the left side approaches the right side 

within the desired limits. If the value is greater than the right side, reduce the value of PC. 
Standard Operating Procedures 

 
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October 2014 

SOP 10 Page 1 of 9 

SOP No. 10 

Recommended Standard Operating Procedure 

for 

Calibration of Rigid Rules 

1. Introduction 

1.1. Purpose 

This SOP describes the procedure to be followed for the calibration of rigid rules 

by comparison to the 18 inch metal rule issued to each State as the State reference 

standard which is calibrated in the interval from 1 inch to 13 inches. Equations 

provided here assume that the rigid rules being compared have the same 

coefficient of expansions. If rigid rules having different coefficients of expansion 

are compared at a temperature other than 20 °C the procedure and equations of 

SOP 11 must be used. 

The maximum length of rule that can be directly compared to the standard rule is 

12 inches. However, longer lengths can be calibrated in segments of 12 inches 

with reference to the standard rule. 

1.2. Prerequisites 

1.2.1. Valid calibration certificates with appropriate values and uncertainties 

must be available for all of the standards used in the calibration. All 

standards must have demonstrated metrological traceability to the 

international system of units (SI), which may be to the SI through a 

National Metrology Institute such as NIST. 

1.2.2. The ocular microscope used in measuring differences in lengths must be in 

good operating condition and must be equipped with a graduated reticle 

having established traceability. 

1.2.3. The operator must be trained and experienced in precision measuring 

techniques with specific training in GMP 2, GMP 8, GMP 9, SOP 10, and 

SOP 29. 

1.2.4. Laboratory facilities must comply with following minimum conditions to 

meet the expected uncertainty possible with this procedure. Equilibration 

of supporting surface, standard rule and rule to be calibrated requires 

environmental stability of the laboratory within the stated limits for a 

minimum of 24 hours before a calibration. 
October 2014 

SOP 10 Page 2 of 9 

Table 1. Environmental conditions. 

Temperature Requirements During a Calibration Relative Humidity 

(%) 

Lower and upper limits: 18 °C to 22 °C 

Maximum changes: < ± 1 °C / 24 h and ± 0.5 °C / 1 h 40 to 60 ± 10 / 4 h 

2. Methodology 

 2.1. Scope, Precision, Accuracy 

The accuracy of calibration of standard rules is possible to within 0.000 1 inch, 

provided suitable calibration of standards are obtained. The precision of 

intercomparison and the accuracy of the standard limit the uncertainty of 

calibration to 0.002 inch under optimum conditions. 

2.2. Summary 

A rigid rule (test rule) is calibrated by comparing intervals on it with intervals of 

the standard rule. A reticle eye piece (ocular micrometer) is used for this purpose. 

Test rules longer than the standard rule may be calibrated in segments, using the 

last calibrated graduation as the zero graduation mark for the succeeding 

segments. Deviations from nominal that are calculated for each successive 

interval are cumulative. 

2.3. Apparatus/Equipment Required 

2.3.1. Length bench or similar flat surface on which to lay the test rule and the 

standard rule. 

2.3.2. Calibrated standard rule. 

2.3.3. Microscope with calibrated graduated reticle having graduations spaced at 

intervals no greater than 0.002 inch. 
October 2014 

SOP 10 Page 3 of 9 

2.4. Symbols 

Table 2. Symbols used in this procedure. 

Symbol Description 

A, B, C, D Calculated centers of graduations 

S Standard 

X Unknown 

X0L Left edge of zero on unknown 

X0R Right edge of zero on unknown 

S0L Left edge of zero on standard 

S0R Right edge of zero on standard 

Xm Center of graduation of unknown 

Sm Center of graduation of standard 

di Difference between X and S. The subscript i, designates the trial number, 1 or 2. 

LS Calibrated length of standard 

LX Calibrated length of test rule 

2.5. Procedure 

2.5.1. Both the test rule and the standard rule must be in temperature equilibrium 

with the environment of the length laboratory. 

2.5.2. Place the test rule and the standard rule on the length bench or similar flat 

surface, parallel to one another with the reading edges adjacent. It is not 

necessary to have the “zero” graduations in coincidence. 

 Ordinarily, this will require that one rule reads left-to-right (increasing 

units) while the other reads right-to-left (decreasing units). In this case, for 

convenience of calculation, the standard rule is placed in the right-to-left 

position. A worksheet to reverse the calibration on the standard rule is 

provided at the end of this SOP. Place shims under the rules as necessary 

so that the upper surfaces of both are in the same plane. 

2.5.3. Place the microscope on the bench in the vicinity of the zero position and 

align it so that its reticle scale is parallel to the scales under test. (See 

GMP No. 2 for instructions on reading graduations with the microscope.) 

2.5.3.1. Observe readings of left and right sides of the corresponding 

graduation of the standard rule and record to the nearest 

0.001 inch. The average of these readings will give a value for A. 

2.5.3.2. Observe readings of left and right sides of the corresponding 

graduation of the test rule and record to the nearest 0.001 inch. 

The average of these readings will give a value for B. If the 
October 2014 

SOP 10 Page 4 of 9 

“zero” graduation is the end of the rule, only the reading for the 

end of the rule is taken. 

2.5.4. Move the microscope successively to each graduation to be calibrated and 

record readings as described in 2.5.3.1 and 2.5.3.2 identifying the readings 

for the standard rule as C and for the unknown as D. CAUTION! Be 

certain that the rules are not disturbed during movement of the 

microscope. 

2.5.5. Return the microscope to the zero graduation and repeat readings (2.5.3.1. 

and 2.5.3.2.) to verify that the rules have not been disturbed. Accept all 

previous data if the initial zero readings do not disagree with the final zero 

readings by more than 0.002 inch; otherwise, discard all previous data and 

repeat entire sequence of readings until a satisfactory set of zero readings 

are obtained. 

2.5.6. Repeat 2.5.3. thru 2.5.5. for every additional segment of the test rule 

requiring calibration. This will require repositioning the rules, aligning the 

last measured interval graduation on the test rule with the initial 

graduation of the standard rule. Deviations from nominal for successive 

segments are cumulative. 

2.5.7. Move the rules and reposition, making a second set of measurements as 

directed in 2.5.3, 2.5.4, and 2.5.5 for Trial 2. 

. 

3. Calculations 

3.1. Calculate the difference between the Initial (A, B) and Final (A1, B1) zero 

measurements to ensure that the initial and final readings agree within 0.002 inch. 

(2.5.5.) 

 |A – B – A1 + B1| (1) 

3.2. Calculate the center of graduation for unknown, Xm, and standard, Sm, for each set of 

measurements and each scale interval. The center of the “starting” graduation on the 

standard rule is A; for the test rule it is B. The subsequent centers of graduations for the 

standard and the test rule are recorded as C and D, respectively, for each interval 

measured. For each trial, the values for A and B will remain constant for all measured 

intervals on that trial, and will be used to compute the measured differences between 

the test rule and the standard. 

A C S S S L R

m , 2

( )    (2) 
October 2014 

SOP 10 Page 5 of 9 

B D X X X L R

m , 2

( )    (3) 

3.3. Calculate the differences, d1, and d2 between X and S for each scale interval and 

each trial. (The subscript i is associated with the trial number.) 

di  A  B Ci  Di (4) 

3.4. Obtain the calibrated length of the standard, LS, for the measured interval from the 

calibration certificate for the standard rule. 

3.5. Calculate the length of the test rule, LX, for each interval measured using the mean 

of the measured differences. 

 

X LS

d d L   2

1 2 (5) 

4. Measurement Assurance 

4.1. Duplicate the process with a suitable check standard or have a suitable range of 

check standards for the laboratory. See NISTIR 7383 SOP 17, SOP 20 and 

NISTIR 6969 SOP 30. Plot the check standard length and verify it is within 

established limits OR a t-test may be incorporated to check the observed value 

against an accepted value. The mean of the check standard observations is used to 

evaluate bias and drift over time. Check standard observations are used to 

calculate the standard deviation of the measurement process which contributes to 

the Type A uncertainty components. 

4.2 If a standard deviation chart is used for measurement assurance, the standard 

deviation of each combination of Trial 1 and Trial 2 is calculated and the pooled 

(or average) standard deviation is used as the estimate of variability in the 

measurement process. Note: the pooled or average standard deviation over time 

will reflect varying conditions of test items that are submitted to the laboratory. A 

standard deviation chart will be needed for each interval calibrated so that the 

variability resulting from transfers will be measured (the number of charts may be 

adjusted through analysis using F-tests). 

5. Assignment of Uncertainty 

5.1. The limits of expanded uncertainty, U, include estimates of the standard 

uncertainty of the length standards used, us, estimates of the standard deviation of 

the measurement process, sp, and estimates of the effect of other components 

associated with this procedure, uo. These estimates should be combined using the 

root-sum-squared method (RSS), and the expanded uncertainty, U, reported with 

a coverage factor to be determined based on degrees of freedom, which if large 
October 2014 

SOP 10 Page 6 of 9 

enough will be 2, (k = 2), to give an approximate 95 percent level of confidence. 

See NISTIR 6969, SOP 29 (Standard Operating Procedure for the Assignment of 

Uncertainty) for the complete standard operating procedure for calculating the 

uncertainty. 

5.1.1 The expanded uncertainty for the standard, U, is obtained from the 

calibration report. The combined standard uncertainty, uc, is used and not 

the expanded uncertainty, U, therefore the reported uncertainty for the 

standard will usually need to be divided by the coverage factor k. When 

transfers are used, us for values after the transfer are dependent and 

cumulative. See NISTIR 6969, SOP 29 for handling of dependent 

uncertainties. 

5.1.2. The standard deviation of the measurement process, sp, is taken from a 

control chart for a check standard or standard deviation charts. See 

NISTIR 7383, SOP 17, SOP 20, and NISTIR 6969, SOP 30. 

5.1.3. Uncertainty associated with bias, ud. Any noted bias that has been 

determined through analysis of control charts and round robin data must 

be less than limits provided in SOP 29 and included if corrective action is 

not taken. See SOP 29 for additional details 

5.1.4. Other standard uncertainties usually included at this calibration level 

include uncertainties associated with the ability to read the graduated 

reticle, only part of which is included in the process variability due to 

parallax and visual capabilities, and uncertainties associated with the 

graduations of the reticle. 

 Table 3. Example uncertainty budget table. 

Component Description Reference 

us Standard uncertainty for standards Calibration report, divide by k 

sp Standard uncertainty for the process Measurement assurance process; 

range charts 

ugr Standard uncertainty for graduated 

reticle 

Must be assessed experimentally or 

from a calibration certificate 

ud Standard uncertainty for disparity due 

to drift/bias 

Rectangular distribution and 

reasons, 0.577 d, 0.29 d; 

SOP 29 (NISTIR 6969) 

ures Standard uncertainty due to resetting of 

the rules 

Must be assessed experimentally; if 

an interval based standard deviation 

chart is used ures will be included in 

the control chart standard deviation 

value. 

uo Standard uncertainty for other factors 

6. Report 

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

 
October 2014 

SOP 10 Page 7 of 9 

Appendix A 

Rigid Rule Calibration Data Sheet 

Date Environmental parameters 

Metrologist Before After Unc/ability to measure 

Test No. Temperature °C °C 

sp in Pressure mmHg mmHg 

df Humidity % % 

Based on NISTIR 6969, SOP 29, Appendix A at 95.45 % probability distribution: k factor 

 ID Range 

S 

X 

 Trial 1 Trial 2 

Rule Graduation Left Right Center of 

graduation 

Left Right Center of 

graduation 

S A = A = 

X B = B = 

S1 C1 = C1 = 

X1 D1 = D1 = 

d1 = A – B – C1 + D1 = d2 = A – B – C1 + D1 = 

 Average d = (d1 + d2) / 2 = LS = 

 Length of X, LX = average d + LS = 

S2 C2 = C2 = 

X2 D2 = D2 = 

d1 = A – B – C2 + D2 = d2 = A – B – C2 + D2 = 

 Average d = (d1 + d2) / 2 = LS = 

 Length of X, LX = average d + LS = 

S3 C3 = C3 = 

X3 D3 = D3 = 

d1 = A – B – C3 + D3 = d2 = A – B – C3 + D3 = 

 Average d = (d1 + d2) / 2 = LS = 

 Length of X, LX = average d + LS = 

S A1 = A1 = 

X B1 = B1 = 

Trial 1: Absolute difference between initial 

and final zero measurements = |A – B – A1 + B1|= 

Is result ≤ 0.002 inch? Yes/No If YES, accept all data. 

Trial 2: Absolute difference between initial 

and final zero measurements =|A – B – A1 + B1|= 

Is result ≤ 0.002 inch? Yes/No If YES, accept all data. 

 
October 2014 

SOP 10 Page 8 of 9 

Form A-2. Worksheet to Reverse the Calibration of the Rigid Rule Standard 

Nominal 

Length of 

Interval 

(inches) 

Calculations to be performed Length of Interval 

(inches) 

1 L1 = C13 – C12 = - 

2 L2 = C13 – C11 = - 

3 L3 = C13 – C10 = - 

4 L4 = C13 – C9 = - 

5 L5 = C13 – C8 = - 

6 L6 = C13 – C7 = - 

7 L7 = C13 – C6 = - 

8 L8 = C13 – C5 = - 

9 L9 = C13 – C4 = - 

10 L10 = C13 – C3 = - 

11 L11 = C13 – C2 = - 

12 L12 = C13 – C1 = - 

To reverse the calibration on the State standard rigid rule, subtract the lengths for each calibrated 

interval from the length from the 1 inch to the 13 inch graduation. 

Example: 

Length from 13 to 12 = Length from 1 to 13 – Length from 1 to 12 

Length from 13 to 12 = 11.999 8 – 10.999 7 = 1.000 1 inch 

 
October 2014 

SOP 10 Page 9 of 9 

Appendix B 

Calibration of a Metric Rule Using a Standard Indicating in Inches 

A. Work with the customer to determine the intervals they wish to have calibrated. 

Convert those interval to inches (E.g., 10 mm / 25.4 mm/in = 0.3937 in). It is helpful 

to make the conversions for all the interested intervals at one time. Round these 

conversions to the nearest 0.01 in. 

B. For the first calibration interval “a”, refer to the group of intervals from 1 in to 12.5 in 

and 1 in to 13 in on the calibration report for the lab’s standard rule. Select the 

report’s interval with the same numbers after the decimal point as the selected 

customer interval “a”. (E.g., for the customer’s 2.94 in interval, refer to the 1 in to 

12.94 in interval on the report.) An interval “a” which ends in a number less than 0.5 

should have a report interval selected which is 0.5 more than the listed value. (E.g., 

for the customer’s 0.39 in interval, refer to the 1 in to 12.89 in interval on the report.) 

The 12.xx value which has been selected will be the point on the standard which is 

lined up with the 0 calibration point on the customer’s rule. Record the appropriate 

standard length value for the referred to interval. (E.g., 11.888 4 for the 1 in to 12.89 

in interval.) 

C. Subtract the desired interval “a” from the 12.xx figure which was selected in step B. 

This difference “b” is the point on the standard rule which will be lined up with the 

desired calibration point on the customer’s rule. Refer to the calculated difference “b” 

on the calibration report for the laboratory 18 in standard rule. Record the appropriate 

standard length value for the interval “b”. (E.g., for the interval 0.39 in, subtract 

0.39 in from 12.89 in to obtain a difference of 12.50 in. The 12.5 in mark on the 

standard rule will be lined up with an interval which is 0.39 in (10 mm) from the 0 

point on the customer’s rule. Refer to the 1 in to 12.50 in interval on the data sheet 

and record a value of 11.498 1.) 

D. Subtract the value recorded in step C from the one recorded in step B to obtain the 

standard’s length for the interval “a” which will be observed. (E.g., subtract 11.498 1 

from 11.888 4 and you get a standard length of 0.390 3 in.) Use this value as your LS

in your calculations. 

E. Repeat steps B through D for all of the intervals to be calibrated. 

F. Set up the rules, take readings, and make calculations for each interval in accordance 

with this SOP. After calculating LX in inches, convert it to metric, and report the 

metric values to the customer. 
This page intentionally made blank. 
October 2014 

SOP 11 Page 1 of 15 

SOP No. 11 

Recommended Standard Operating Procedure 

for 

Calibration of Metal Tapes 

Bench Method 

1. Introduction 

1.1. Purpose 

Metal tapes are used by contractors, surveyors, and others for building layouts, 

measurement of land areas, establishment of land boundaries, and similar 

purposes. Inaccuracies in such measurements can cause structural misalignments, 

boundary controversies, and other problems. The test method described here 

provides a procedure to calibrate such tapes to four decimal places in the case of 

measurements in customary units (inches), and to 6 decimal places for 

measurements expressed in SI units (meters). The calibrated length bench is used 

as the standard. This procedure may also be used to compare rigid rules having 

different coefficients of expansion when compared at temperatures other than 

20 °C. 

1.2. Prerequisites 

1.2.1. Valid calibration certificates with appropriate values and uncertainties 

must be available for all of the standards used in the calibration. All 

standards must have demonstrated metrological traceability to the 

international system of units (SI), which may be to the SI through a 

National Metrology Institute such as NIST. 

1.2.2. The ocular microscope used in measuring differences in lengths must be in 

good operating condition and must be equipped with a calibrated 

graduated reticle having established traceability. 

1.2.3. The operator must be trained and experienced in precision measuring 

techniques with specific training in GMP 2, GMP 8, GMP 9, SOP 11, and 

SOP 29. 

1.2.4. Laboratory facilities must comply with following minimum conditions to 

meet the expected uncertainty possible with this procedure. Equilibration 

of length bench and tapes requires environmental stability of the 

laboratory within the stated limits for a minimum of 24 hours before a 

calibration. 
October 2014 

SOP 11 Page 2 of 15 

Table 1. Environmental conditions. 

Temperature Requirements During a Calibration Relative Humidity 

(%) 

Lower and upper limits: 18 °C to 22 °C 

Maximum changes: < ± 1 °C / 24 h and ± 0.5 °C / 1 h 40 to 60 ± 10 / 4 h 

2. Methodology 

 2.1. Scope, Precision, Accuracy 

The precision and accuracy attainable depend upon the care exercised in aligning 

the tape on the length bench, and the skill acquired in the use of an optical 

micrometer to measure scale differences. 

2.2. Summary 

The tape to be calibrated is laid over the bench scale and sufficient tension is 

applied to insure that it lies flat on the bench. Differences between the graduation 

on the tape and that of the bench scale are measured using an ocular micrometer. 

The temperature of the tape is observed, and corrections applied, to calculate the 

length at the reference temperature of 20 °C using formulae or tables which are in 

Appendix B. Tapes longer than the length bench may be calibrated in segments, 

using the last calibrated graduation as the zero graduation mark for the succeeding 

segments. Typical lengths to be tested on a 100 foot tape when using the 16 foot 

length bench are: every foot through 10 feet and then 15, 20, 30, 40, 45, 50, 60, 

70, 75, 80, 90, and 100 foot lengths. 

2.3. Apparatus/Equipment Required 

2.3.1. Calibrated thermometers with sufficiently small resolution, stability, and 

uncertainty, capable of indicating temperatures in the range of 15 °C to 

30 °C, and accurate to ± 0.5 °C. 

2.3.2. Calibrated 5 meter (16 foot) length bench. 

2.3.3. Microscope with calibrated graduated reticle having graduations spaced at 

intervals no greater than 0.002 inch. 

2.3.4. Clamps, fabric tape in lengths required to connect tension weights to the 

tape being calibrated, and weights to apply an appropriate tension to the 

tape under calibration. (See C.3.) 
October 2014 

SOP 11 Page 3 of 15 

2.4. Symbols 

Table 2. Symbols used in this procedure. 

Symbol Description 

S Standard 

X Unknown 

d0i Initial zero difference 

d0f Final zero difference 

X0L Left edge of zero on unknown 

X0R Right edge of zero on unknown 

S0L Left edge of zero on standard 

S0R Right edge of zero on standard 

Xm Center of graduation of unknown 

Sm Center of graduation of standard 

d Difference of interval between X and S

t Average of initial and final temperatures 

tcorr Temperature correction 

Ln Nominal length of tape interval under test in inches 

LX Calibrated length of tape interval under test in inches 

α Linear coefficient of thermal expansion for the standard bench (0.00001063 / oC) 

β Linear coefficient of thermal expansion for the tape (0.00001160 / oC) 

AE Cross-sectional area times Young’s modulus of elasticity 

Q0 Lower load (tension) applied to the tape 

Q1 Higher load (tension) applied to the tape 

L0 Length of tape under load Q0

L1 Length of tape under load Q1

2.5. Procedure 

2.5.1. Inspect the tape to ensure that no kinks, dents, or other damage are present 

that will affect the accuracy of the tape 

2.5.2. Clean the tape and bench by first wiping with a soft cloth, and then with a 

soft cloth saturated with alcohol to remove protective oil film. (See 

Appendix C, Section C.1.) 

2.5.3. Place the tape, under the clamp, at the zero end of the bench, and adjust so 

the starting mark on the tape is near the zero graduation on the length 

bench. When the ring is part of the measuring tape, a special clamp must 

be used. See Appendix C.5 for further information on this matter. 

2.5.4. Lay the tape flat on the bench. The tape should extend well beyond the end 

roller of the bench to permit tension to be applied. Slide one end of a fabric 

strap onto another tape clamp. Fasten this tape clamp to the tape on the 

portion that extends below the end roller. Hang the tension weight from the 
October 2014 

SOP 11 Page 4 of 15 

bottom of the fabric strap. Check to see that the tape is lying straight on the 

bench and parallel to the bench scale. Adjust, if necessary. Apply tension 

using a weight of 10 pounds, unless other tension is required (See Appendix 

C.3.) When a tape is shorter than the 5 m length bench, a fabric strap is used 

to effectively lengthen the tape so that the tension weight is properly 

suspended below the rollers of the length bench. 

2.5.5. Lay two thermometers (See 2.3.1.) on the bench and tape at intervals of 

1/3 and 2/3 of the length of the bench to determine its initial and final 

temperatures at the time of the test. 

2.5.6. Adjust the tape clamp on the zero end of the bench so that the starting 

graduation on the tape coincides with the center of the zero graduation of 

the bench. Note: Some tapes are calibrated using the one foot mark as the 

reference point, rather than the zero graduation. In this case, align the 

1 foot mark of the tape with the zero graduation mark of the bench. 

2.5.7. Check all alignments and coincidence of the graduations down the length 

of the bench before proceeding with calibration. Use the lateral 

adjustments at the left end of the bench to facilitate alignment. Caution! 

Take care that tape is not touched or disturbed during the following 

sequence of measurements. Record all observations on a suitable data 

sheet. 

2.5.8. Record the temperatures indicated by the two thermometers. 

2.5.9. Place the microscope on the bench in the vicinity of the zero position and 

align it so that its reticle scale is parallel to the tape under test. (See GMP 

No. 2 for instructions on reading graduations with the microscope.) 

2.5.9.1. Observe readings of left and right sides of zero graduation of 

tape and record to the nearest 0.001 inch. 

2.5.9.2. Observe readings of left and right sides of zero graduation of 

bench and record to the nearest 0.001 inch. 

2.5.10. Move the microscope successively to each graduation that needs to be 

calibrated and record readings similarly as in 2.5.9.1 and 2.5.9.2. 

2.5.11. Return the microscope to the zero graduation and repeat readings (2.5.9.1. 

and 2.5.9.2.) to verify that the tape has not moved. Accept all previous 

data if the zero readings have not changed by more than 0.001 inch; 

otherwise, discard all previous data and repeat entire sequence of readings 

until a satisfactory set of zero readings are obtained. 

2.5.12. Loosen the tape by removing the tension weights, move the tape, hang the 
October 2014 

SOP 11 Page 5 of 15 

tension weights back on the fabric strap, and realign the zero marks on the 

tape and the bench to coincidence. 

2.5.13. Repeat 2.5.8 thru 2.5.12 for every 15 foot (5 meter) section of the tape 

requiring calibration. This will require repositioning the tape, aligning the 

last measured interval graduation on the tape with the zero graduation of 

the bench. 

2.5.14. Make a second set of measurements as directed in 2.5.8 to 2.5.13. 

. 

2.5.15. After the final measurement is taken and accepted, record the temperatures 

indicated by the two thermometers. 

2.5.16. After all measurements are completed; apply a thin film of oil to the tape. 

3. Calculations 

 3.1. Calculate the Initial Zero Difference, d0i (2.5.8.) 

 2

( ) 0 0 0 0

0

L R L R

i

X X S S d     (1) 

 3.2. Calculate the Final Zero Difference, d0f (2.5.10.) 

2

( ) 0 0 0 0

0

L R L R

f

X X S S d     (2) 

3.3. Calculate the center of graduation for unknown, Xm, and standard, Sm, for each set of 

measurements and each scale interval. 

2

( ) L R

m

X X X   (3) 

2

( ) L R

m

S S S   (4) 

3.4. Calculate the difference, d, between X and S for each scale interval. 

m m d  X  S (5) 

3.5. Obtain the correction to the standard, CS, for the measured interval from the 

calibration certificate for the length bench scale. 
October 2014 

SOP 11 Page 6 of 15 

 3.6. Calculate the temperature correction, tcorr. 

t L     t  20 (  ) corr n (6)

3.7. Calculate a correction, CX, for each trial and each scale interval. 

X S corr C  d  C  t (7A) 

Be sure to include cumulative errors from previous intervals when transfers are 

made. (For example, corrections for two prior intervals added for the case when a 

third interval is calibrated.) 

X S corr Cx' Cx" C  d  C  t   (7B) 

3.8. Calculate and report the mean,CX of the two corrections for each interval. 

3.9. Calculate the length of tape under the 10 pound load. 

LX  Ln  CX (8)

 

4. Measurement Assurance 

4.1. Duplicate the process with a suitable check standard or have a suitable range of 

check standards for the laboratory. See NISTIR 7383 SOP 17, SOP 20 and 

NISTIR 6969 SOP 30. Plot the check standard length and verify it is within 

established limits OR a t-test may be incorporated to check the observed value 

against an accepted value. The mean of the check standard observations is used to 

evaluate bias and drift over time. Check standard observations are used to 

calculate the standard deviation of the measurement process which contributes to 

the Type A uncertainty components. 

4.2 If a standard deviation chart is used for measurement assurance, the standard 

deviation of each combination of Trial 1 and Trial 2 is calculated and the pooled 

(or average) standard deviation is used as the estimate of variability in the 

measurement process. Note: the pooled or average standard deviation over time 

will reflect varying conditions of test items that are submitted to the laboratory. A 

standard deviation chart will be needed for each interval calibrated (at least 

initially) so that the variability resulting from transfers will be measured. 

5. Assignment of Uncertainty 

5.1. The limits of expanded uncertainty, U, include estimates of the standard 

uncertainty of the length standards used, us, estimates of the standard deviation of 

the measurement process, sp, and estimates of the effect of other components 

associated with this procedure, uo. These estimates should be combined using the 
October 2014 

SOP 11 Page 7 of 15 

root-sum-squared method (RSS), and the expanded uncertainty, U, reported with 

a coverage factor to be determined based on degrees of freedom, which if large 

enough will be 2, (k = 2), to give an approximate 95 percent level of confidence. 

See NISTIR 6969, SOP 29 (Standard Operating Procedure for the Assignment of 

Uncertainty) for the complete standard operating procedure for calculating the 

uncertainty. 

5.1.1 The expanded uncertainty for the standard, U, is obtained from the 

calibration report. The combined standard uncertainty, uc, is used and not 

the expanded uncertainty, U, therefore the reported uncertainty for the 

standard will usually need to be divided by the coverage factor k. When 

transfers are used, us for values after the transfer are dependent and 

cumulative. See NISTIR 6969, SOP 29 for handling of dependent 

uncertainties. 

5.1.2. The standard deviation of the measurement process, sp, is taken from a 

control chart for a check standard or standard deviation charts. (See SOP 

17, SOP 20, and SOP 30) 

5.1.3. Uncertainty associated with bias, ud. Any noted bias that has been 

determined through analysis of control charts and round robin data must 

be less than limits provided in SOP 29 and included if corrective action is 

not taken. See SOP 29 for additional details 

5.1.4. Uncertainty associated with temperature correction includes values for the 

linear coefficients of expansion for the Standard and Unknown, the 

accuracy of temperature measurements, and factors associated with 

potential gradients in measuring the temperature on the length bench and 

tape. 

5.1.5. Other standard uncertainties usually included at this calibration level 

include uncertainties associated with the ability to read the graduated 

reticle, only part of which is included in the process variability due to 

parallax and visual capabilities, and uncertainties associated with the 

graduations of the reticle. 
October 2014 

SOP 11 Page 8 of 15 

 Table 3. Example uncertainty budget table. 

Component Description Reference 

us Standard uncertainty for standards Calibration report, divide by k 

sp Standard uncertainty for the process Measurement assurance process; 

range charts 

ugr Standard uncertainty for graduated reticle Must be assessed experimentally 

or from a calibration certificate 

utc Standard uncertainty for temperature 

correction 

Calibration certificate 

 ut Standard uncertainty for temperature HB 143 accuracy guideline, 

0.1 C 

 ulce (,) Standard uncertainty for linear coefficient 

of expansion 

5 % to 10 % of the coefficient of 

expansion value 

utw Standard uncertainty for tension weights Calibration certificate 

ud Standard uncertainty for disparity due to 

drift/bias 

Rectangular distribution and 

reasons, 0.577 d, 0.29 d; 

SOP 29 (NISTIR 6969) 

ures Standard uncertainty due to resetting of 

the tape 

Must be assessed 

experimentally; may be included 

in the control chart standard 

deviation where present 

uo Standard uncertainty for other factors 

6. Report 

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

 
October 2014 

SOP 11 Page 9 of 15 

Appendix A 

Bench Method Data Sheet 

Date Environmental parameters 

Metrologist Before After Unc/ability to measure 

Test No. Temperature °C °C 

sp in Pressure mmHg mmHg 

df Humidity % % 

Based on NISTIR 6969, SOP 29, Appendix A at 95.45 % probability distribution: k factor 

 ID Range Linear coefficient of thermal expansion 

S Bench 16 ft (5 m) α 0.000 010 63 /°C 

X Tape β 0.000 011 60 /°C 

Tension lb Support 

Initial temperatures Final temperatures 

t1 °C t3 °C Average temperature °C 

t2 °C t4 °C 

Interval, ft Trial Initial Zero Graduations 

Bench Tape Tape Bench 

0 0 

1 X0L X0R S0L S0R

 

Initial zero, difference between X and S, d0i in 

2 X0L X0R S0L S0R 

 

Initial zero, difference between X and S, d0i in 

Intervals after zero 

Tape Bench 

 

 X1L X1R Xm S1L S1R Sm d CS tcorr CX Range 

1 

2 

Average CX in 

 

 X1L X1R Xm S1L S1R Sm d CS tcorr CX Range 

1 

2 

Average CX in 

Final Zero Graduations 

Tape Bench 

0 0 

1 

X0L X0R S0L S0R

 

Final zero, difference between X and S, d0f in 

Difference between Initial Zero and Final Zero, d0i - d0f in 

| d0i - d0f | ≤ 0.001 in? If YES, accept previous data. 

2 

X0L X0R S0L S0R 

 

Final zero, difference between X and S, d0f in 

 Difference between Initial Zero and Final Zero, d0i - d0f in 

| d0i - d0f | ≤ 0.001 in? If YES, accept previous data. 

t L     t  20 (  ) corr n X S corr C  d  C  t LX  Ln  CX 

 X S corr Cx' Cx" C  d  C  t   
October 2014 

SOP 11 Page 10 of 15 

Appendix B 

Table B-1. Temperature Correction Factors for Calibration of Steel Tapes graduated in feet 

when linear coefficient of thermal expansion for the tape is 0.00001160 / oC. 

All values in inches x 10-4

Ln

Feet 

Temperature, °C 

19 20 21 22 23 24 25 26 27 28 29 30 

1 0.1 0.0 -0.1 -0.2 -0.3 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0 -1.2 

2 0.2 0.0 -0.2 -0.5 -0.7 -0.9 -1.2 -1.4 -1.6 -1.9 -2.1 -2.3 

3 0.3 0.0 -0.3 -0.7 -1.0 -1.4 -1.7 -2.1 -2.4 -2.8 -3.1 -3.5 

4 0.5 0.0 -0.5 -0.9 -1.4 -1.9 -2.3 -2.8 -3.3 -3.7 -4.2 -4.7 

5 0.6 0.0 -0.6 -1.2 -1.7 -2.3 -2.9 -3.5 -4.1 -4.7 -5.2 -5.8 

6 0.7 0.0 -0.7 -1.4 -2.1 -2.8 -3.5 -4.2 -4.9 -5.6 -6.3 -7.0 

7 0.8 0.0 -0.8 -1.6 -2.4 -3.3 -4.1 -4.9 -5.7 -6.5 -7.3 -8.1 

8 0.9 0.0 -0.9 -1.9 -2.8 -3.7 -4.7 -5.6 -6.5 -7.4 -8.4 -9.3 

9 1.0 0.0 -1.0 -2.1 -3.1 -4.2 -5.2 -6.3 -7.3 -8.4 -9.4 -10.5 

10 1.2 0.0 -1.2 -2.3 -3.5 -4.7 -5.8 -7.0 -8.1 -9.3 -10.5 -11.6 

15 1.7 0.0 -1.7 -3.5 -5.2 -7.0 -8.7 -10.5 -12.2 -14.0 -15.7 -17.5 

20 2.3 0.0 -2.3 -4.7 -7.0 -9.3 -11.6 -14.0 -16.3 -18.6 -21.0 -23.3 

30 3.5 0.0 -3.5 -7.0 -10.5 -14.0 -17.5 -21.0 -24.4 -27.9 -31.4 -34.9 

40 4.7 0.0 -4.7 -9.3 -14.0 -18.6 -23.3 -27.9 -32.6 -37.2 -41.9 -46.6 

45 5.2 0.0 -5.2 -10.5 -15.7 -21.0 -26.2 -31.4 -36.7 -41.9 -47.1 -52.4 

50 5.8 0.0 -5.8 -11.6 -17.5 -23.3 -29.1 -34.9 -40.7 -46.6 -52.4 -58.2 

60 7.0 0.0 -7.0 -14.0 -21.0 -27.9 -34.9 -41.9 -48.9 -55.9 -62.9 -69.8 

70 8.1 0.0 -8.1 -16.3 -24.4 -32.6 -40.7 -48.9 -57.0 -65.2 -73.3 -81.5 

75 8.7 0.0 -8.7 -17.5 -26.2 -34.9 -43.7 -52.4 -61.1 -69.8 -78.6 -87.3 

80 9.3 0.0 -9.3 -18.6 -27.9 -37.2 -46.6 -55.9 -65.2 -74.5 -83.8 -93.1 

90 10.5 0.0 -10.5 -21.0 -31.4 -41.9 -52.4 -62.9 -73.3 -83.8 -94.3 -104.8 

100 11.6 0.0 -11.6 -23.3 -34.9 -46.6 -58.2 -69.8 -81.5 -93.1 -104.8 -116.4 

For example: For Ln = 20 feet at 25 °C, the temperature correction is -0.001 16 inches. 

 
October 2014 

SOP 11 Page 11 of 15 

Table B-2. Temperature Correction Factors for Calibration of Steel Tapes graduated in meters 

when linear coefficient of thermal expansion for the tape is 0.00001160 / oC. 

 All values in meters x 10-6

Ln

Meters 

Temperature, °C 

19 20 21 22 23 24 25 26 27 28 29 30 

0.1 0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0 

0.2 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6 -1.7 -1.9 

0.3 0.3 0.0 -0.3 -0.6 -0.9 -1.2 -1.5 -1.7 -2.0 -2.3 -2.6 -2.9 

0.4 0.4 0.0 -0.4 -0.8 -1.2 -1.6 -1.9 -2.3 -2.7 -3.1 -3.5 -3.9 

0.5 0.5 0.0 -0.5 -1.0 -1.5 -1.9 -2.4 -2.9 -3.4 -3.9 -4.4 -4.8 

0.6 0.6 0.0 -0.6 -1.2 -1.7 -2.3 -2.9 -3.5 -4.1 -4.7 -5.2 -5.8 

0.7 0.7 0.0 -0.7 -1.4 -2.0 -2.7 -3.4 -4.1 -4.8 -5.4 -6.1 -6.8 

0.8 0.8 0.0 -0.8 -1.6 -2.3 -3.1 -3.9 -4.7 -5.4 -6.2 -7.0 -7.8 

0.9 0.9 0.0 -0.9 -1.7 -2.6 -3.5 -4.4 -5.2 -6.1 -7.0 -7.9 -8.7 

1 1.0 0.0 -1.0 -1.9 -2.9 -3.9 -4.8 -5.8 -6.8 -7.8 -8.7 -9.7 

2 1.9 0.0 -1.9 -3.9 -5.8 -7.8 -9.7 -11.6 -13.6 -15.5 -17.5 -19.4 

3 2.9 0.0 -2.9 -5.8 -8.7 -11.6 -14.6 -17.5 -20.4 -23.3 -26.2 -29.1 

4 3.9 0.0 -3.9 -7.8 -11.6 -15.5 -19.4 -23.3 -27.2 -31.0 -34.9 -38.8 

5 4.8 0.0 -4.8 -9.7 -14.6 -19.4 -24.3 -29.1 -34.0 -38.8 -43.6 -48.5 

10 9.7 0.0 -9.7 -19.4 -29.1 -38.8 -48.5 -58.2 -67.9 -77.6 -87.3 -97.0 

15 14.6 0.0 -14.6 -29.1 -43.6 -58.2 -72.7 -87.3 -101.9 -116.4 -131.0 -145.5 

20 19.4 0.0 -19.4 -38.8 -58.2 -77.6 -97.0 -116.4 -135.8 -155.2 -174.6 -194.0 

25 24.3 0.0 -24.3 -48.5 -72.7 -97.0 -121.3 -145.5 -169.8 -194.0 -218.3 -242.5 

30 29.1 0.0 -29.1 -58.2 -87.3 -116.4 -145.5 -174.6 -203.7 -232.8 -261.9 -291.0 

For example: For Ln = 4 meters at 25 °C, the temperature correction is -0.000 019 4 meters. 

 
October 2014 

SOP 11 Page 12 of 15 

Appendix C 

Supplemental Information 

C.1. Cleaning 

To clean a steel tape before calibration, first wipe the tape with a soft cloth; then with a 

soft cloth saturated with alcohol to remove the film of oil used to protect the tape. 

After calibration, a thin film of light oil, such as sewing machine oil, should be applied to 

the tape for protection. 

C.2. Tolerances 

 The tolerances for measuring tapes are those stated below. 

 Table C-1. Tolerances for a 30 meter tape. 

Length Interval Tolerances 

0 through 15 meters 1.27 mm (0.050 inch) 

15 through 22 meters 1.91 mm (0.075 inch) 

22 through 30 meters 2.54 mm (0.100 inch) 

C.2.1. The inaccuracy in the length of the ribbon, when supported on a horizontal 

surface with a tension of 10 pounds at a temperature of 20 °C (68 °F) shall not exceed 

0.050 inch for the 75 foot length, and 0.100 inch for the 100 foot length. 

C.3. Tension Specifications 

The length of a tape will be affected by the temperature of the tape, the tension applied to 

the tape, and the manner in which the tape is supported. The tape will stretch when 

tension is applied and will return to its normal length when the tension is removed, 

provided the tape has not been permanently deformed when it was stretched. The 

tensions, at which steel tapes are to be calibrated, expressed in terms of the load in 

kilograms (or pounds) to be applied to obtain the tension, are stated below. The loads 

should be accurate within 45 g (0.01 lb). 

Table C-2. Tension to be applied, in terms of load. 

Length Interval Tension 

Less than 10 m (25 ft) 2 kg (3.5 lb) 

10 m through 30 m (25 ft through 100 ft) 5 kg (10 lb) 

Greater than 30 m (100 ft) 10 kg (20 lb) 

C.4. Methods of Support and Tension Considerations 

Tapes calibrated in a State laboratory are normally supported on a horizontal surface 
October 2014 

SOP 11 Page 13 of 15 

throughout the entire length of the tape. Also, tapes may be calibrated and used when 

supported in catenary types of suspension. In these cases, the tape is supported at 

equidistant points because the weight of the tape affects its length. The weight of the tape 

increases the tension and the “sag” causes the horizontal length to be shorter than when 

the tape is supported throughout its length. Equations are given in GMP No. 10 to 

compute the horizontal straight-line distance of a tape supported at N number of 

equidistant catenary suspensions and for computing the tension of accuracy, defined as 

the tension that must be applied to the tape interval to produce its designated nominal 

length at the observed temperature of the tape. 

It is sufficient to provide the user of a steel tape with the calibrated length of the tape 

under standard temperature and tension conditions, the weight per unit-length of the tape, 

and the AE value for the tape, as might be requested. This information will enable the 

user to compute the values desired using the equations cited above. 

C.5. Zero Reference Point 

Metal measuring tapes submitted to a State laboratory for calibration normally will be 

made of steel. Generally, these tapes will have a ring on the end of the tape. For 

maximum calibration and measurement accuracy, a tape should have a blank end 

between the ring and the zero graduation. The zero graduation is then more precisely 

defined and more easily referenced for calibration and use. 

Tapes that have the ring as part of the measuring portion of the tape are more difficult to 

calibrate than a tape with a blank end. When the ring is part of the measuring portion of 

the tape, the zero reference point shall be the outside end of the ring unless otherwise 

specified. It is more difficult to obtain a good zero reference setting on the ring due to its 

curvature and to parallax in reading the edge of the ring against a reference mark. 

Additionally, the ring may become permanently deformed in use and change the length of 

the tape. For these tapes the NIST normally calibrates from the 1-foot mark over the 

length of the tape, and then calibrates from the ring to the 1-foot mark. These values are 

reported separately so the user can obtain maximum measurement accuracy by using the 

1-foot graduation as the zero reference point. 

When the ring is part of the measuring range of the tape, a special holder for the ring is 

needed to clamp the tape to the length bench. A strap with an open area in the middle is 

needed to permit the end of the ring to be seen. The strap is slipped through the ring and 

the strap is clamped to the length bench. See example below. 

 Figure C-1. Strap, holder, and tape ring. 

 The edge of the tape to be calibrated (the reading edge) is the edge nearest the observer 
October 2014 

SOP 11 Page 14 of 15 

when the zero graduation is to the observer’s left. When viewed through a microscope, 

some graduations will appear to have irregular edges. The portion of the graduation to be 

used for calibration is the portion of the graduation at the bottom of the reading edge of 

the tape. This provides a reference point that can be repeated and referenced by others. 

Do not attempt to estimate the ‘best overall’ edge of a graduation because this is not 

easily repeatable and cannot be accurately reproduced by other. If the graduations to be 

calibrated do not reach to the edge of the tape, the tape should not be calibrated. 

C.6. Temperature Considerations 

The reference temperature for length calibrations is 20 °C. The length of the tape can be 

determined at any other temperature T by using the following equation. 

  1 ( 20) LT  L20  T  (C-1) 

Since α is always positive, it can be seen that for temperatures above 20 °C, the tape is 

longer than it is at 20 °C. For temperatures below 20 °C, the tape is shorter than it is at 

20 °C. 

If two length standards have different coefficients of expansion because they are made of 

different materials, the lengths of the tapes will change at different rates as the 

temperature changes. If two tapes are being compared at a temperature other than 20 °C, 

these lengths must be corrected back to 20 °C for calibration. 

If two length standards are being compared and they have the same coefficient of 

expansion, then as the temperature changes the lengths will change by the same amount. 

Hence, if the standards are compared at a temperature other than 20 °C, the relationship 

between the two standards will be the same as if they were being compared at 20 °C; 

thus, no temperature correction is needed. 

Table C-3. Coefficient of expansion of various length standards. 

Type /°C /°F 

Steel tape 11.60 x 10-6 6.45 x 10-6

Length bench 10.63 x 10-6 5.91 x 10-6

Invar tape 4.0 x 10-7 2.2 x 10-7

C.7. Invar tapes 

Invar is an alloy of nickel and steel. Invar tapes are used to obtain measurements of 

greater accuracy than can be made with steel tapes, because invar has a very low 

coefficient of expansion. It has the added benefit of being very slow to tarnish from 

exposure to the atmosphere. However, invar tapes require very careful handling to 

prevent twists and kinks. 

The load to be applied to an invar tape to maintain the desired tension is normally 20 lb. 

A load of 40 lb is used for the higher tension to determine the AE value (see C.8.). For 
October 2014 

SOP 11 Page 15 of 15 

metric tapes, the normal load is 5 kg. A load of 10 kg is used to determine the AE value. 

C.8. AE Value 

The AE Value (area elongation value) for a tape is determined by first calibrating the tape 

under its normal tension. The load is then increased by10 lb or 20 lb and one length 

interval is recalibrated to determine the length of the tape under the increased tension. 

The AE factor is computed with the following equation. 

Ln L L

Q Q AE

1 0

1 0



  (C-2) 

For example, a 100 foot tape is calibrated from 0 feet to 100 feet with a load of 10 lb 

applied to the tape with a resulting length of 99.992 feet. The load is increased to 20 lb 

and the new length is found to be 100.004 feet. The AE value is: 

lb

feet

lb feet feet lb lb AE 83333

0.012

1000 100 (100.004 99.992)(20 10 )    

It is recommended that the AE value be determined over the longest interval that is 

convenient to measure. This minimizes the error in the AE value because of the better 

readability of the change in length 

C.9 Weight per Unit Length 

The weight per unit length of a tape can be determined as follows: 

C.9.1. Weigh the tape and reel (or case). 

C.9.2. Remove the tape from the reel or case and weigh the empty reel (or case). 

C.9.3. Measure the length of any blank ends on the tape and add this to the measuring 

length. 

C.9.4. Correct for the weight of the loop on the tape. The weight of the loop that is 

normally used on steel tapes is approximately 2.5 grams. 

The weight per unit length is the computed as follows. 

length of tape length of blank ends

Weight of loaded reel weight of empty reel weight of loop Weight per Unit Length 

  
This page intentionally made blank. 
October 2014 

SOP 12 Page 1 of 12 

SOP No. 12 

Recommended Standard Operating Procedure 

for 

Calibration of Metal Tapes1

Tape-to-Tape Method 

I. Introduction 

1.1. Purpose 

Metal tapes are used by contractors, surveyors, and others for building layouts, 

measurement of land areas, establishment of land boundaries, and similar 

purposes. The accuracy of the measurement often must be provable to 0.000 1 

meter on a 100 meter tape (0.000 1 foot on a 100 foot tape), sometimes in a court 

of law. A significant feature of such proof is the knowledge of the accurate length 

of the tape used. Inaccuracies in such measurements can cause structural 

misalignments, boundary controversies, and other problems. The test method 

described here provides a procedure to calibrate such tapes by comparison to a 

calibrated standard tape. 

1.2. Prerequisites 

1.2.1. Valid calibration certificates with appropriate values and uncertainties 

must be available for all of the standards used in the calibration. All 

standards must have demonstrated metrological traceability to the 

international system of units (SI), which may be to the SI through a 

National Metrology Institute such as NIST. 

1.2.2. The operator must be trained and experienced in precision measuring 

techniques with specific training in GMP 8, GMP 9, SOP 12, and SOP 29. 

1.2.3. Laboratory facilities must comply with following minimum conditions to 

meet the expected uncertainty possible with this procedure. Equilibration 

of tapes requires environmental stability of the laboratory within the stated 

limits for a minimum of 24 hours before a calibration. 

 

1

 Many references are provided in in-pound units due to common use in U.S. weights and measures requirements. 

The International System of Units, SI, is the official system of units for metrological traceability. 
October 2014 

SOP 12 Page 2 of 12 

Table 1. Environmental conditions. 

Temperature Requirements During a Calibration Relative Humidity 

(%) 

Lower and upper limits: 18 °C to 22 °C 

Maximum changes: < ± 1 °C / 24 h and ± 0.5 °C / 1 h 40 to 60 ± 10 / 4 h 

2. Methodology 

 2.1. Scope, Precision, Accuracy 

The method is applicable to the calibration of metal tapes such as used by 

surveyors, builders, and contractors. The overall length and specified intermediate 

lengths may be checked by the technique. The accuracy is limited by the accuracy 

of the calibration of the standard tape and by the precision of intercomparison. 

The latter should be within ± 0.001 foot, corresponding to 10 parts per million in 

a 100 foot tape. The method is limited to calibration of steel tapes (because the 

tension is specified as the result of a 10 pound load). 

2.2. Summary 

This procedure is based upon the method developed by C. Leon Carroll Jr., 

National Bureau of Standards, NBSIR 74-451, “Field Comparisons of Steel 

Surveyors’ Tapes.” 

The tape to be calibrated is stretched out parallel to a standard tape on a 

reasonably flat surface. Paper scales (graph paper), graduated in millimeters are 

used at the zero and at each specified interval of calibration to measure any 

difference between the two tapes. The length of the tape undergoing calibration is 

computed from the known length of the standard tape and the observed 

differences between the test tape and the standard. 

Calibrations are usually made at each 1 foot interval for the first 10 feet, and at 

each 10 foot interval to the full length of the tape. 

2.3. Apparatus/Equipment Required 

2.3.1. Standard tape, calibrated to within ± 0.001 foot. 

2.3.2. Pieces of graph paper (10 x 10 to the centimeter, i.e., millimeter 

graduations), approximately 5 cm in width by 15 cm in height. Number 

the horizontal centimeter graduations, 0, 1, 2, etc.. Evaluate and document 

the range of use to within 0.1 mm using a calibrated rigid rule or a 

microscope with calibrated reticles to ensure that the graph paper has 

sufficient accuracy. 
October 2014 

SOP 12 Page 3 of 12 

2.3.3. Equipment, see Figure 1, to apply tension to the tapes under test, 

consisting of the following. 

2.3.3.1. Spring scales (two); one capable of indicating a load of 

10 pounds and the other capable of indicating a load of 

20 pounds. The scales should be calibrated with an 

accuracy of ± 0.1 lb. This may be done by the arrangement 

shown in Figure 2 with results internally documented. 

2.3.3.2. Turnbuckles, suitable for adjusting tension on the tapes. 

2.3.3.3. Swivel connectors to prevent axial twisting of the tapes. 

2.3.3.4. Magnifying glass to aid in reading the graph paper values. 

2.3.3.5. Small weights (< 5 lb) to hold the tapes down flat to the 

paper. 

Figure 1. Experimental Arrangement. 

 

 
October 2014 

SOP 12 Page 4 of 12 

Figure 2. Calibration of Spring Scales. 

2.4. Symbols 

Table 2. Symbols used in this procedure. 

Symbol Description 

S Length of the Standard Tape at the calibration interval 

LX Length of the Test Tape at the calibration interval 

cf Conversion factor, 

0.032 808 ft/cm for tapes graduated in feet 

0.010 000 m/cm for tapes graduated in meters 

Ln Nominal length of tape interval under test 

AE Cross-sectional area times Young’s modulus of elasticity 

Q0 Lower load (tension) applied to the tape 

Q1 Higher load (tension) applied to the tape 

L0 Length of tape under load Q0

L1 Length of tape under load Q1

2.5. Procedure 

2.5.1. Inspect the tapes to ensure that no kinks, dents, or other damage are 

present which will affect the accuracy of the calibration. 

2.5.2. Clean the tapes by first wiping with a soft cloth, and then with a soft cloth 

saturated with alcohol to remove protective oil film. 
October 2014 

SOP 12 Page 5 of 12 

2.5.3. Stretch the test tape and standard tape parallel to each other on a 

reasonably flat surface. The evenness of the surface is less important than 

the parallelism of the tapes. The two tapes should be separated by a 

constant distance of about 1 to 3 centimeters. The zero and test intervals of 

the two tapes should not be in coincidence but rather displaced by one or 

two centimeters, as indicated in the detail of Figure 1. 

2.5.4. Use the turnbuckles to apply equal loads of 10 pounds to the two tapes as 

indicated by the spring scales. (Note the use of swivels to prevent axial 

twisting.) 

2.5.5. Place a piece of graph paper under the zero interval and each interval to be 

calibrated as shown in the detail in Figure 1. Adjust the tapes and the 

paper so that the former are precisely aligned with the lateral rulings of the 

paper. It is convenient but not necessary for these to be the bold centimeter 

rulings of the paper. Note the amount of separation of the tapes at the zero 

interval and make corresponding adjustments at each calibration interval 

of interest. In this way, parallelism of the two tapes is easily verified. 

2.5.6. Make final adjustment of tensions on the tapes and recheck for parallelism 

at all test points before taking the readings described in 2.5.7. Do not 

disturb during the measurement sequence. 

2.5.7 Read the distances A, B, C, and D as indicated in the detail of Figure 1. 

Note that A and B are for the zero (or first) interval and are the same for 

all test intervals. C and D have subscripts 1, 2, etc. corresponding to the 

interval, i, calibrated. Make all readings to the center of the graduation 

mark tested and estimate to the closest 0.1 mm. Record all readings in 

centimeters. 

2.5.8. Record all measurements as Trial 1. 

2.5.9. Release the tension to the tapes and reapply it. 

2.5.10. Displace each piece of graph paper a few millimeters, then readjust the 

load, check for parallelism, and record a second series of measurements as 

Trial 2. 

2.5.11. Release the tension to the tapes and reapply it. 

2.5.12. Displace each piece of graph paper a few millimeters, then readjust the 

load, check for parallelism, and record a second series of measurements as 

Trial 3. 

2.5.13. After all measurements are completed; apply a thin film of oil to the tapes. 
October 2014 

SOP 12 Page 6 of 12 

3. Calculations 

 3.1. Calculate and record A – B – C + D for each trial, then record the value of R, the 

range of these values (difference of highest and lowest) for each scale interval. 

The range should not exceed 0.15 cm. Sum the values for A, B, C, D for the three 

trials to use when calculating the length, L, of each interval. 

 

 3.2. The value obtained from ƩA – ƩB – ƩC + ƩD must equal the sum of the column 

A – B – C + D, otherwise an error has been made in the calculations. 

 3.3. Calculate the length of the test tape at each calibration interval according to the 

following equation. 

 ( ) 3 A B C D cf LX  S      (1) 

 

4. Measurement Assurance 

4.1. Duplicate the process with a suitable check standard or have a suitable range of 

check standards for the laboratory. See NISTIR 7383 SOP 17, SOP 20 and 

NISTIR 6969 SOP 30. Plot the check standard length and verify it is within 

established limits OR a t-test may be incorporated to check the observed value 

against an accepted value. The mean of the check standard observations is used to 

evaluate bias and drift over time. Check standard observations are used to 

calculate the standard deviation of the measurement process which contributes to 

the Type A uncertainty components. 

4.2 If a standard deviation chart is used for measurement assurance, the standard 

deviation of each combination of 3 Trials is calculated and the pooled (or 

average) standard deviation is used as the estimate of variability in the 

measurement process. Note: the pooled or average standard deviation over time 

will reflect varying conditions of test items that are submitted to the laboratory. A 

standard deviation chart will be needed for each interval calibrated (at least 

initially) so that the variability resulting from transfers will be measured. 

5. Assignment of Uncertainty 

5.1. The limits of expanded uncertainty, U, include estimates of the standard 

uncertainty of the length standards used, us, estimates of the standard deviation of 

the measurement process, sp, and estimates of the effect of other components 

associated with this procedure, uo. These estimates should be combined using the 

root-sum-squared method (RSS), and the expanded uncertainty, U, reported with 

a coverage factor to be determined based on degrees of freedom, which if large 

enough will be 2, (k = 2), to give an approximate 95 percent level of confidence. 

See NISTIR 6969, SOP 29 (Standard Operating Procedure for the Assignment of 
October 2014 

SOP 12 Page 7 of 12 

Uncertainty) for the complete standard operating procedure for calculating the 

uncertainty. 

5.1.1 The expanded uncertainty for the standard, U, is obtained from the 

calibration report. The combined standard uncertainty, uc, is used and not 

the expanded uncertainty, U, therefore the reported uncertainty for the 

standard will usually need to be divided by the coverage factor k. 

5.1.2. The standard deviation of the measurement process, sp, is taken from a 

control chart for a check standard or standard deviation charts. (See SOP 

17, SOP 20, and SOP 30) 

5.1.3. Uncertainty associated with bias, ud. Any noted bias that has been 

determined through analysis of control charts and round robin data must 

be less than limits provided in SOP 29 and included if corrective action is 

not taken. See SOP 29 for additional details 

5.1.4. Other standard uncertainties usually included at this calibration level 

include uncertainties associated with the ability to read the graph paper, 

only part of which is included in the process variability due to parallax and 

visual capabilities, and uncertainties associated with the graduations of the 

graph paper. 

 Table 3. Example uncertainty budget table. 

Component Description Reference 

us Standard uncertainty for standards Calibration report, divide by k 

sp Standard uncertainty for the process Measurement assurance process; 

range charts 

ugp Standard uncertainty for graph paper Must be assessed experimentally 

utw Standard uncertainty for the spring scales Must be assessed experimentally 

or from a calibration certificate 

ud Standard uncertainty for disparity due to 

drift/bias 

Rectangular distribution and 

reasons, 0.577 d, 0.29 d; 

SOP 29 (NISTIR 6969) 

ures Standard uncertainty due to resetting of 

the tapes 

Must be assessed experimentally 

uo Standard uncertainty for other factors 

6. Report 

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

 
October 2014 

SOP 12 Page 8 of 12 

Appendix A 

Tape-to-Tape Method Data Sheet 

Date Environmental parameters 

Metrologist Before After Unc/ability to measure 

Test No. Temperature °C °C 

sp in Pressure mmHg mmHg 

df Humidity % % 

Based on NISTIR 6969, SOP 29, Appendix A at 95.45 % probability distribution: k factor 

 ID Range 

S 

X 

Tension lb 

Interval Trial A B C D A-B-C+D 

 1 

( ) 3A B C D cf 2     S L 

3 

Ʃ 

 Range 

 1 

( ) 3A B C D cf 2     S L 

3 

Ʃ 

 Range 

 1 

( ) 3A B C D cf 2     S L 

3 

Ʃ 

 Range 

 1 

( ) 3A B C D cf 2     S L 

3 

Ʃ 

 Range 

 1 

( ) 3A B C D cf 2     S L 

3 

Ʃ 

 Range 

 1 

( ) 3A B C D cf 2     S L 

3 

Ʃ 

 Range 

 
October 2014 

SOP 12 Page 9 of 12 

Appendix B 

Supplemental Information 

B.1. Cleaning 

To clean a steel tape before calibration, first wipe the tape with a soft cloth; then with a 

soft cloth saturated with alcohol to remove the film of oil used to protect the tape. 

After calibration, a thin film of light oil, such as sewing machine oil, should be applied to 

the tape for protection. 

B.2. Tolerances 

 The tolerances for measuring tapes are those stated below. 

 Table B-1. Tolerances for a 30 meter tape. 

Length Interval Tolerances 

0 through 15 meter 1.27 mm (0.050 inch) 

15 through 22 meter 1.91 mm (0.075 inch) 

22 through 30 meter 2.54 mm (0.100 inch) 

B.2.1. The inaccuracy in the length of the ribbon, when supported on a horizontal 

surface with a tension of 10 pounds at a temperature of 20 °C (68 °F) shall not exceed 

0.050 inch for the 75 foot length, and 0.100 inch for the 100 foot length. 

B.3. Tension Specifications 

The length of a tape will be affected by the temperature of the tape, the tension applied to 

the tape, and the manner in which the tape is supported. The tape will stretch when 

tension is applied and will return to its normal length when the tension is removed, 

provided the tape has not been permanently deformed when it was stretched. The 

tensions, at which steel tapes are to be calibrated, expressed in terms of the load in 

kilograms (or pounds) to be applied to obtain the tension, are stated below. The loads 

should be accurate within 45 g (0.01 lb). 

Table B-2. Tension to be applied, in terms of load. 

Length Interval Tension 

Less than 10 m (25 ft) 2 kg (3.5 lb) 

10 m through 30 m (25 ft through 100 ft) 5 kg (10 lb) 

Greater than 30 m (100 ft) 10 kg (20 lb) 

B.4. Methods of Support and Tension Considerations 

Tapes calibrated in a State laboratory are normally supported on a horizontal surface 
October 2014 

SOP 12 Page 10 of 12 

throughout the entire length of the tape. Also, tapes may be calibrated and used when 

supported in catenary types of suspension. In these cases, the tape is supported at 

equidistant points because the weight of the tape affects its length. The weight of the tape 

increases the tension and the “sag” causes the horizontal length to be shorter than when 

the tape is supported throughout its length. Equations are given in GMP No. 10 to 

compute the horizontal straight-line distance of a tape supported at N number of 

equidistant catenary suspensions and for computing the tension of accuracy, defined as 

the tension that must be applied to the tape interval to produce its designated nominal 

length at the observed temperature of the tape. 

It is sufficient to provide the user of a steel tape with the calibrated length of the tape 

under standard temperature and tension conditions, the weight per unit-length of the tape, 

and the AE value for the tape, as might be requested. This information will enable the 

user to compute the values desired using the equations cited above. 

B.5. Zero Reference Point 

Metal measuring tapes submitted to a State laboratory for calibration normally will be 

made of steel. Generally, these tapes will have a ring on the end of the tape. For 

maximum calibration and measurement accuracy, a tape should have a blank end 

between the ring and the zero graduation. The zero graduation is then more precisely 

defined and more easily referenced for calibration and use. 

Tapes that have the ring as part of the measuring portion of the tape are more difficult to 

calibrate than a tape with a blank end. When the ring is part of the measuring portion of 

the tape, the zero reference point shall be the outside end of the ring unless otherwise 

specified. It is more difficult to obtain a good zero reference setting on the ring due to its 

curvature and to parallax in reading the edge of the ring against a reference mark. 

Additionally, the ring may become permanently deformed in use and change the length of 

the tape. For these tapes the NIST normally calibrates from the 1 foot mark over the 

length of the tape, and then calibrates from the ring to the 1 foot mark. These values are 

reported separately so the user can obtain maximum measurement accuracy by using the 

1 foot graduation as the zero reference point. 

When the ring is part of the measuring range of the tape, a special holder for the ring is 

needed to clamp the tape to the length bench. A strap with an open area in the middle is 

needed to permit the end of the ring to be seen. The strap is slipped through the ring and 

the strap is clamped to the length bench. See example below. 

 Figure B-1. Strap, holder, and tape ring. 

 The edge of the tape to be calibrated (the reading edge) is the edge nearest the observer 
October 2014 

SOP 12 Page 11 of 12 

when the zero graduation is to the observer’s left. When viewed through a microscope, 

some graduations will appear to have irregular edges. The portion of the graduation to be 

used for calibration is the portion of the graduation at the bottom of the reading edge of 

the tape. This provides a reference point that can be repeated and referenced by others. 

Do not attempt to estimate the ‘best overall’ edge of a graduation because this is not 

easily repeatable and cannot be accurately reproduced by other. If the graduations to be 

calibrated do not reach to the edge of the tape, the tape should not be calibrated. 

B.6. Temperature Considerations 

No temperature correction is required, provided the test tape and the standard tape are at 

the same temperature and of the same material. This will be the case when the 

measurements are made inside a building. Tapes of the same color would be expected to 

attain the same temperature, even in sunlight. However, black and white tapes have 

shown temperature differences of as much as 8 °C when exposed to direct sunlight. In 

such cases, the temperature differences, even when measured, would be uncertain due to 

variability of exposure along the length of the tape. Accordingly, calibrations in the 

laboratory are preferred, when possible. 

B.7. Invar tapes 

Invar is an alloy of nickel and steel. Invar tapes are used to obtain measurements of 

greater accuracy than can be made with steel tapes, because invar has a very low 

coefficient of expansion. It has the added benefit of being very slow to tarnish from 

exposure to the atmosphere. However, invar tapes require very careful handling to 

prevent twists and kinks. 

The load to be applied to an invar tape to maintain the desired tension is normally 20 lb. 

A load of 40 lb is used for the higher tension to determine the AE value (see C.8.). For 

metric tapes, the normal load is 5 kg. A load of 10 kg is used to determine the AE value. 

B.8. AE Value 

The AE Value (area elongation value) for a tape is determined by first calibrating the tape 

under its normal tension. The load is then increased by10 lb or 20 lb and one length 

interval is recalibrated to determine the length of the tape under the increased tension. 

The AE factor is computed with the following equation. 

Ln L L

Q Q AE

1 0

1 0



  (B-1) 

For example, a 100 foot tape is calibrated from 0 feet to 100 feet with a load of 10 lb 

applied to the tape with a resulting length of 99.992 feet. The load is increased to 20 lb 

and the new length is found to be 100.004 feet. The AE value is: 
October 2014 

SOP 12 Page 12 of 12 

lb

feet

lb feet feet lb lb AE 83333

0.012

1000 100 (100.004 99.992)(20 10 )    

It is recommended that the AE value be determined over the longest interval that is 

convenient to measure. This minimizes the error in the AE value because of the better 

readability of the change in length 

B.9 Weight per Unit Length 

The weight per unit length of a tape can be determined as follows: 

B.9.1. Weigh the tape and reel (or case). 

B.9.2. Remove the tape from the reel or case and weigh the empty reel (or case). 

B.9.3. Measure the length of any blank ends on the tape and add this to the measuring 

length. 

B.9.4. Correct for the weight of the loop on the tape. The weight of the loop that is 

normally used on steel tapes is approximately 2.5 grams. 

The weight per unit length is the computed as follows. 

length of tape length of blank ends

Weight of loaded reel weight of empty reel weight of loop Weight per Unit Length 

  
October 2014 

SOP 23 Page 1 of 11 

SOP 23 

Recommended Standard Operations Procedure for 

Calibrations of PI Tapes 

Bench Method 

1. Introduction 

1.1 Purpose 

PI tapes are circumferential measuring tapes that are wrapped around a circular or 

cylindrical object and when read, indicate the diameter of the object. The tapes 

are manufactured for various diameter ranges and for either outside diameters 

(OD) or inside diameters (ID). The test method described here provides a 

procedure to calibrate such tapes to four decimal places in inches (diameter). A 

calibrated length bench (transfer standard, calibrated using SOP 11) is used as the 

standard. 

1.2 Prerequisites 

1.2.1 Valid calibration certificates with appropriate values and uncertainties 

must be available for all of the standards used in the calibration. All 

standards must have demonstrated metrological traceability to the 

international system of units (SI), which may be to the SI through a 

National Metrology Institute such as NIST. 

1.2.2. The ocular microscope used in measuring differences in lengths must be in 

good operating condition and must be equipped with a graduated reticle 

having established traceability. 

1.2.3. The operator must be trained and experienced in precision measuring 

techniques with specific training in GMP 2, GMP 8, GMP 9, SOP 11, SOP 

23, and SOP 29. 

1.2.4. Laboratory facilities must comply with following minimum conditions to 

meet the expected uncertainty possible with this procedure. Equilibration 

of length bench and tapes requires environmental stability of the 

laboratory within the stated limits for a minimum of 24 hours before a 

calibration. 

Table 1. Environmental conditions. 

Temperature Requirements During a Calibration Relative Humidity 

(%) 

Lower and upper limits: 18 °C to 22 °C 

Maximum changes: < ± 1 °C / 24 h and ± 0.5 °C / 1 h 40 to 60 ± 10 / 4 h 
October 2014 

SOP 23 Page 2 of 11 

2. Methodology 

2.1. Scope, Precision, Accuracy 

The precision and accuracy attainable depend upon the care exercised in aligning 

the tape on the length bench, and the skill acquired in the use of an optical 

micrometer to measure scale differences. 

2.2 Physical Characteristics 

2.2.1. PI tapes are manufactured with corrections built into the tape where they 

will indicate the proper diameter without using extensive mathematical 

corrections. These corrections will have to be taken into consideration 

when calibrating a PI tape on a flat horizontal surface. 

OD PI tapes are referenced to 20 °C with 2.25 kg (5 lb) tension (within ± 

0.5 percent of the load, i.e., Class F mass standards are more than 

adequate.) applied. There is concern about the proper tension to apply 

to an ID PI tape since they are normally used under some degree of 

compression. Most tapes are made of 1095 spring steel, which has a 

coefficient of thermal expansion of 0.00000633 / °F. 

Figure 1. Schematic drawing of Pi tape 

 As the tape is wrapped around the circumference of an object, the reading 

portion of the tape and the vernier come into alignment. The smallest 

graduation on the main body equals 0.5 mm (0.025 in). The line on the 
October 2014 

SOP 23 Page 3 of 11 

vernier scale which comes closest to lining up with a graduation on the 

main body is the value to be added to the reading. The vernier allows 

readings to be made to the nearest 0.001 in, as shown in Figure 2. 

 

 Figure 2. Reading the Vernier scale on a Pi tape. 

2.3. Fundamental Considerations 

2.3.1. The relationship of circumference, C, diameter, D, and pi () is C = (D), 

D = C/. See Figure 3 where  = 3.141592654 

 

 Figure 3. Circumference, diameter, pi ().

2.3.2. The thickness of the tape will affect the measurements in two locations, as 

shown in Figure 4. L1 is the outside portion of the tape, which becomes 

longer when the tape is bent. L2 is the center of the tape (neutral axis). It 

remains the same length when the tape is bent. L3 is the inside portion of 

the tape and it compresses and becomes shorter when the tape is bent. 

 Figure 4. Side view of tape.
October 2014 

SOP 23 Page 4 of 11 

2.3.3 Another point that must be taken into consideration is that the tape was 

tested for accuracy on a flat horizontal surface but now it is curved around 

an object. The tape becomes temporarily deformed but the amount of 

distortion is predictable using the modulus of elasticity. As shown in the 

diagram (Figure 4.), the outside portion of the tape stretches and the inside 

compresses but there is a point midway through the thickness of the tape 

which does not change in length and is called the neutral axis. 

For all homogeneous beams with the same modulus of elasticity in tension 

and compression, the neutral axis passes through the center of the section. 

If the tape has a thickness of 0.010 inch, the distance from the neutral axis 

to the surface of the object is 0.005 inch. Therefore, the reading we 

obtained is not the distance on the outside surface of the tape but is 

actually the distance along the neutral axis of the tape. When we calculate 

a diameter, this is actually the diameter of the neutral axis of the tape. 

Since this thickness affects the diameter in two locations, the amount of 

correction that must be taken into account is 0.010 inches. 

2.4. Summary 

The tape to be calibrated is laid over the bench scale and tension is applied to 

ensure that it lies flat on the bench. Differences between the graduation on the 

tape and that of the bench scale are measured using an ocular micrometer. The 

temperature of the tape is observed and corrections applied to the reference 

temperature of 20 °C. Tapes longer than the length bench may be calibrated in 

segments, using the last calibrated graduation as the zero graduation mark for the 

succeeding segments. PI tape graduations represent object diameters and may not 

directly coincide with length bench graduations. 

2.5. Apparatus/Equipment Required 

2.5.1. Calibrated thermometers with sufficiently small resolution, stability, and 

uncertainty, capable of indicating temperatures in the range of 15 °C to 

30 °C, and accurate to ± 0.5 °C. 

2.5.2. Calibrated 5 meter (16 foot) length bench. 

2.5.3. Microscope with graduated reticle having graduations spaced at intervals 

no greater than 0.002 inch. 

2.5.4. Clamps, fabric tape in lengths required to connect tension weights to the 

tape being calibrated, and weights to apply an appropriate tension to the 

tape under calibration. (See "Tension Specifications", in Appendix C.3 in 

SOP 11). 
October 2014 

SOP 23 Page 5 of 11 

2.6. Symbols 

Table 2. Symbols used in this procedure. 

Symbol Description 

S Standard 

X Unknown 

d0i Initial zero difference 

d0f Final zero difference 

X0L Left edge of zero on unknown 

X0R Right edge of zero on unknown 

S0L Left edge of zero on standard 

S0R Right edge of zero on standard 

Xm Center of graduation of unknown 

Sm Center of graduation of standard 

d Difference of interval between X and S

t Average of initial and final temperatures 

tcorr Temperature correction 

Ln Nominal length of tape interval under test in inches 

LX Calibrated length of tape interval under test in inches 

α Linear coefficient of thermal expansion for the standard bench (0.00001063 / oC)

β Linear coefficient of thermal expansion for the tape (0.00001160 / oC) 

Ld Diameter length of interval 

π 3.141592654 

2.7. Procedure 

2.7.1. Inspect the tape to ensure that no kinks, dents, or other damage are present 

which will affect the accuracy of the tape. 

2.7.2. Clean the tape by first wiping with a soft cloth, and then with a soft cloth 

saturated with alcohol to remove the protective oil film. (See Appendix C, 

Section C.1 for SOP 11). 

2.7.3. Place the tape, under the clamp, at the zero end of the bench, and adjust so 

the starting mark on the tape is near the zero graduation on the length 

bench. 

2.7.4. Lay the tape flat on the bench. The tape should extend well beyond the 

end roller of the bench to permit tension to be applied. Slide one end of a 

fabric strap onto another tape clamp. Fasten this tape clamp to the tape on 

the portion that extends below the end roller. Hang the tension weight 

from the bottom of the fabric strap. Check to see that the tape is lying 

straight on the bench and parallel to the bench scale. Adjust, if necessary. 

Apply tension using a weight of 2.25 kg (5 lb) unless other tension is 

specified. (See Appendix C.3 in SOP 11.) When a tape is shorter than the 
October 2014 

SOP 23 Page 6 of 11 

5 m length bench, fabric strap will be be used to effectively lengthen the 

tape so that the tension weight is properly suspended below the rollers of 

the length bench. 

2.7.5. Lay two thermometers (see 2.4.1.) on the bench at intervals of one-third 

and two-thirds of the length of the bench to determine its temperature at 

the time of test. 

2.7.6. Adjust the tape clamp on the zero end of the bench so that the tape zero 

graduation coincides with the center of the zero graduation of the bench. 

2.7.7. Check all alignments and coincidence of zero graduations before 

proceeding with the calibration. Use the lateral adjustments of the left end 

of the bench to facilitate alignment. Caution! Take care that the tape is not 

touched or disturbed during the following sequence of measurements. 

Record all observations on a suitable data sheet. (See SOP 11, Appendix 

A.) 

2.7.8. Record the temperatures indicated by the two thermometers. 

2.7.9. Place the ocular microscope on the bench in the vicinity of the zero 

position and align it so that its scale is parallel to the tape under test. (See 

GMP No. 2 for instructions on how to make readings.) 

2.7.9.1.Observe readings of left and right sides of zero graduation of tape 

and record to the nearest 0.001 inch. The mean of these values 

will be used to determine the center of the tape graduation. 

2.7.9.2.Observe readings of left and right sides of zero graduation of 

bench and record to the nearest 0.001 inch. The mean of these 

values will be used to determine the center of the bench 

graduation. 

2.7.10. Move the ocular microscope successively to each graduation that is to be 

calibrated and record readings similarly as in 2.7.9.1 and 2.7.9.2. 

2.7.11. Return the ocular microscope to the zero graduation and repeat readings to 

verify that the tape has not moved. Accept all previous data if the initial 

zero reading does not disagree with the final zero reading by more than 

0.001 inch; otherwise, discard previous data and repeat entire sequence of 

readings until a satisfactory set is obtained. 

2.7.12. Loosen the tape by removing the tension weights, move the tape, hang the 

tension weights back on the fabric strap, and realign the zero marks on the 

tape and bench to coincidence. 
October 2014 

SOP 23 Page 7 of 11 

2.7.13. Repeat 2.7.9. thru 2.7.12. for every 15 foot (5 meter) section of the tape 

requiring calibration. This will require repositioning the tape, aligning the 

last measured interval graduation on the tape with the zero graduation of 

the bench. 

2.7.14. Make a second set of measurements as directed in 2.7.9 through 2.7.13. 

2.7.15. After the final measurement is taken and accepted, record the temperatures 

indicated by the two thermometers. 

2.7.16. After all measurements are completed, apply a thin film of oil to the tape. 

3. Calculations 

3.1. Calculate the Initial Zero Difference, d0i (2.6.9.) 

 2

( ) 0 0 0 0

0

L R L R

i

X X S S d     (1) 

 3.2. Calculate the Final Zero Difference, d0f (2.6.11.) 

2

( ) 0 0 0 0

0

L R L R

f

X X S S d     (2) 

3.3. Calculate the center of graduation for unknown, Xm, and standard, Sm, for each set of 

measurements and each scale interval. 

2

( ) L R

m

X X X   (3) 

2

( ) L R

m

S S S   (4) 

3.4. Calculate the difference, d, between X and S for each scale interval. 

m m d  X  S (5) 

3.5. Obtain the correction to the standard, CS, for the measured interval from the 

calibration certificate for the length bench scale. 

 3.6. Calculate the temperature correction, tcorr. 

t L     t  20 (  ) corr n (6)

3.7. Calculate a correction, CX, for each trial and each scale interval. 
October 2014 

SOP 23 Page 8 of 11 

X S corr C  d  C  t (7) 

3.8. Calculate and report the mean,CX , of the two corrections for each interval. 

3.9. Calculate the length of tape under the 10 pound load. 

LX  Ln  CX (8)

3.10. As appropriate, convert the flat length of the tape to an outside diameter (OD) 

measurement using the following formula: 

 (tape thickness in inches) L L X

OD   

 (9) 

3.11. As appropriate, convert the flat length of the tape to an inside diameter (ID) 

measurement using the following formula: 

 (tape thickness in inches) L L X

ID  



 (9) 

4. Measurement Assurance 

4.1. Duplicate the process with a suitable check standard or have a suitable range of 

check standards for the laboratory. See NISTIR 7383 SOP 17, SOP 20 and 

NISTIR 6969 SOP 30. Plot the check standard length and verify it is within 

established limits OR a t-test may be incorporated to check the observed value 

against an accepted value. The mean of the check standard observations is used to 

evaluate bias and drift over time. Check standard observations are used to 

calculate the standard deviation of the measurement process which contributes to 

the Type A uncertainty components. 

4.2 If a standard deviation chart is used for measurement assurance, the standard 

deviation of each combination of Trial 1 and Trial 2 is calculated and the pooled 

(or average) standard deviation is used as the estimate of variability in the 

measurement process. Note: the pooled or average standard deviation over time 

will reflect varying conditions of test items that are submitted to the laboratory. A 

standard deviation chart will be needed for each interval calibrated (at least 

initially) so that the variability resulting from transfers will be measured. 

5. Assignment of Uncertainty 

5.1. The limits of expanded uncertainty, U, include estimates of the standard 

uncertainty of the length standards used, us, estimates of the standard deviation of 

the measurement process, sp, and estimates of the effect of other components 

associated with this procedure, uo. These estimates should be combined using the 

root-sum-squared method (RSS), and the expanded uncertainty, U, reported with 

a coverage factor to be determined based on degrees of freedom, which if large 
October 2014 

SOP 23 Page 9 of 11 

enough will be 2, (k = 2), to give an approximate 95 percent level of confidence. 

See NISTIR 6969, SOP 29 (Standard Operating Procedure for the Assignment of 

Uncertainty) for the complete standard operating procedure for calculating the 

uncertainty. 

5.1.1 The expanded uncertainty for the standard, U, is obtained from the 

calibration report. The combined standard uncertainty, uc, is used and not 

the expanded uncertainty, U, therefore the reported uncertainty for the 

standard will usually need to be divided by the coverage factor k. 

5.1.2. The standard deviation of the measurement process, sp, is taken from a 

control chart for a check standard or standard deviation charts. (See SOP 

17, SOP 20, and SOP 30) 

5.1.3. Uncertainty associated with bias, ud. Any noted bias that has been 

determined through analysis of control charts and round robin data must 

be less than limits provided in SOP 29 and included if corrective action is 

not taken. See SOP 29 for additional details 

5.1.4. Uncertainty associated with temperature correction includes values for the 

linear coefficients of expansion for the Standard and Unknown, the 

accuracy of temperature measurements, and factors associated with 

potential gradients in measuring the temperature on the length bench and 

tape. 

5.1.5. Other standard uncertainties usually included at this calibration level 

include uncertainties associated with the ability to read the graduated 

reticle, only part of which is included in the process variability due to 

parallax and visual capabilities, and uncertainties associated with the 

graduations of the reticle. 
October 2014 

SOP 23 Page 10 of 11 

 Table 3. Example uncertainty budget table. 

Component Description Reference 

us Standard uncertainty for standards Calibration report, divide by k 

sp Standard uncertainty for the process Measurement assurance process; 

range charts 

ugr Standard uncertainty for graduated reticle Must be assessed experimentally 

or from a calibration certificate 

utc Standard uncertainty for temperature 

correction 

Calibration certificate 

 ut Standard uncertainty for temperature Handbook 143 accuracy 

guideline, 0.1 C 

 ulce (,) Standard uncertainty for linear coefficient 

of expansion 

5 % to 10 % of the coefficient of 

expansion value 

utw Standard uncertainty for tension weights Calibration certificate 

ud Standard uncertainty for disparity due to 

drift/bias 

Rectangular distribution and 

reasons, 0.577 d, 0.29 d; 

SOP 29 (NISTIR 6969) 

ures Standard uncertainty due to resetting of 

the tape 

Must be assessed experimentally 

uo Standard uncertainty for other factors 

6. Report 

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

 
October 2014 

SOP 23 Page 11 of 11 

Appendix A 

Bench Method Data Sheet 

Date Environmental parameters 

Metrologist Before After Unc/ability to measure 

Test No. Temperature °C °C 

sp in Pressure mmHg mmHg 

df Humidity % % 

Based on NISTIR 6969, SOP 29, Appendix A at 95.45 % probability distribution: k factor 

 ID Range Linear coefficient of thermal expansion 

S Bench 16 ft (5 m) α 0.000 010 63 /°C 

X Tape β 0.000 011 60 /°C 

Tension lb Support 

Initial temperatures Final temperatures 

t1 °C t3 °C Average temperature °C 

t2 °C t4 °C 

Interval, ft Trial Initial Zero Graduations 

Bench Tape Tape Bench 

0 0 

1 X0L X0R S0L S0R

 

Initial zero, difference between X and S, d0i in 

2 X0L X0R S0L S0R 

 

Initial zero, difference between X and S, d0i in 

Intervals after zero 

Tape Bench 

 

 X1L X1R Xm S1L S1R Sm d CS tcorr CX Range 

1 

2 

Average CX in 

 

 X1L X1R Xm S1L S1R Sm d CS tcorr CX Range 

1 

2 

Average CX in 

Final Zero Graduations 

Tape Bench 

0 0 

1 

X0L X0R S0L S0R

 

Final zero, difference between X and S, d0f in 

Difference between Initial Zero and Final Zero, d0i - d0f in 

| d0i - d0f | ≤ 0.001 in? If YES, accept previous data. 

2 

X0L X0R S0L S0R 

 

Final zero, difference between X and S, d0f in 

 Difference between Initial Zero and Final Zero, d0i - d0f in 

| d0i - d0f | ≤ 0.001 in? If YES, accept previous data. 

t L     t  20 (  ) corr n X S corr C  d  C  t LX  Ln  CX
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