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 

  