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SOP 31

Standard Operating Procedure for

Scale Plate Calibration for Volumetric Field Standards

1 Introduction 

Purpose 

This procedure is used for conformity assessment to verify the accuracy and 

linearity of scale plates used on volumetric field standards per NIST Handbook 

105-3: Specifications and Tolerances for Graduated Neck Type Volumetric Field 

Standards (2010) and NIST Handbook 105-4: Specifications and Tolerances for 

Liquefied Petroleum Gas and Anhydrous Ammonia Liquid Volumetric Provers 

(2016). Neck scale plate calibrations are generally conducted only for new or 

damaged volumetric measures or those that have not been calibrated by the 

laboratory in the past.

Prerequisites 

Verify that prerequisites listed in SOP 18, SOP 19, or SOP 21 (as applicable) are

met prior to the scale plate calibration. 

2 Methodology 

Scope, Precision, Accuracy

This procedure is applicable for the calibration of scale plates on field standard test 

measures and provers. The scale plate is evaluated according to requirements 

published in Handbook 105-3 or Handbook 105-4 (as applicable) where the 

uncertainty of the calibration process is considered as a part of the compliance 

assessment. 

Summary 

The neck volume of the test measure or prover is evaluated across the range of the 

scale plate graduations using calibrated volumetric standards to assess accuracy and 

linearity of the scale plate for 4 to 6 calibration intervals. Temperature 

measurements and volumetric corrections are not performed during the neck 

calibration. 
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Required Standards and Equipment

The test measure or prover being evaluated. 

A funnel to aid in transferring water from calibrated volumetric standards 

into the unknown prover. 

Calibrated volumetric standards of suitable sizes to fill the prover body and 

neck to the nominal volume.

Calibrated volumetric standards of suitable sizes to verify the scale plate for 

the test measure or prover. Volumetric standards used for this purpose must 

be calibrated to or corrected for the appropriate reference temperature. An 

ideal standard is approximately one-fourth of the volume of the scale plate 

on the test measure or prover (or reasonable sub-multiples). 

Note: For example, per NIST Handbook 105-3, the minimum neck volume 

on the scale of a 100 gal prover is 1.5 gal (347 in3). For the sake of simplicity 

in an example, if the neck volume noted on the scale plate is 2.0 gal, four 

calibration points of 0.5 gal (115.5 in3) provides good calibration points 

with the nominal volume mid-range in the calibration process. 

Meniscus reading devices (See GMP 3).

Procedure 

Preliminary Operations

2.4.1.1 Prepare and level the test measure or prover according to the 

applicable calibration procedure.

2.4.1.2 Fill the unknown prover with water from the laboratory working 

standard that will be used to perform the calibration of the prover to 

nominal volume. The neck scale calibration is conducted during this 

prover wet-down run.

2.4.1.3 Check the prover level condition in the same way in which it will be 

used by placing a precision spirit or electronic digital level vertically 

on the neck on at least two locations, 90 degrees apart around the 

circumference of the neck and adjust the orientation of the unknown 

prover until the neck is as close to vertical (plumb or perpendicular 

to the horizontal plane) as possible. Adjust the prover orientation as 

necessary.

2.4.1.4 Check the prover system for leaks. 
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Cleanliness check

The standard(s) and the unknown prover must be internally clean and should 

have been verified during preliminary operations. The gauge tube and scale 

plate must be clean and clear to enable proper scale plate readings. 

Scale plate calibration

2.4.3.1 The number of calibration points used is determined by the neck 

volume and the size of the standard from which water will be 

delivered to conduct the calibration. Typically, 4 to 6 calibration

points are distributed across the range of the volume on the neck 

scale plate. Select the number of neck scale calibration points and 

the bottom scale reading, sri, so that one of the neck scale calibration

points is near the prover nominal volume line. This is most easily 

accomplished by using an even number of neck scale calibration

points.

Note: A higher number of calibration points increases the time 

required for the calibration, increases the uncertainty due to the 

number of meniscus reading components, and provides limited 

value.

2.4.3.2 Select the volume of the standard, VSn, to use for the neck calibration 

intervals by dividing the total volume of the neck scale plate that 

will be calibrated by the number of calibration points, keeping in 

mind that the value of VSn may be the sum of multiple deliveries 

from the actual standard used (see Eqn. 1).

Note: For example, a prover with scale plate volume of 2 gal and 4 

calibration points will result in the VSn of 0.5 gal, but each interval 

may be measured with two deliveries of a 0.25 gal calibrated 

standard.

Total neck scale plate volume

# calibration points

VSn =

Eqn. (1)

2.4.3.3 The best starting point for the initial scale reading, sri, for a 

prover having the nominal volume graduation near the 

midpoint of the neck can be calculated using Eqn. 2:

# calibration p ints o

2 i prover Sn sr Nom = − V

Eqn. (2)

2.4.3.4 Offsetting from the nominal value is permitted for older provers 

where the nominal volume is offset from the middle of the neck 

scale. In those cases, the value of ssssii may be calculated and set 

based on a full multiple of VSn, but offset, where the number of neck 

scale calibration points is not centered around the nominal prover 

volume graduation. 
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2.4.3.5 Decrease the liquid level to an easily read graduation mark near the 

value calculated for sri above. "Rock" the prover to "bounce" the 

liquid level, momentarily, to ensure that it has reached an 

equilibrium level. Read and record this setting to be used as the 

initial scale reading, sri.

2.4.3.6 Remove any fill hoses or pipes obstructing the top opening and 

insert a wetted funnel, if needed. 

2.4.3.7 Verify the sri scale reading, then add water in a quantity equal to the 

volume of the first calibration point from a suitable calibrated 

standard. Record the scale reading as sr1.

2.4.3.8 Continue verifying each interval by successive additions from the 

calibrated standard until the selected number of calibration points 

have been recorded.

2.4.3.9 Record scale readings after each addition. The last reading is the 

final scale reading, srf. Be aware that as the water level approaches 

the top of the neck, it will become harder to "bounce" the liquid in 

the gauge. 

2.4.3.10A plot of scale readings with respect to the total volume of water 

added to reach that reading should be linear and is a gross check of 

the validity of this calibration. Calculate and assess the accuracy 

(Deviation between volume added and observed scale plate reading) 

of the neck scale for each interval using Eqn. 3: 

∆= − + sr sr sr xV x x i Sn ( ) Eqn. (3)

2.4.3.11A neck scale correction factor may be calculated using Eqn. 4:

( ) w

f i

V NSCF

sr sr = − Eqn. (4)

Note: When a neck scale correction factor is provided to a 

user, a description of how they should use the neck scale 

correction factor to correct their measurements must also be 

provided. The NSCF is a multiplier by which the indicated 

deviation from the prover nominal volume must be 

multiplied to calculate the actual volume indicated by the 

reading and applies only to that portion of the prover volume 

indicated by the scale deviation from the prover nominal. 

The NSCF is NOT multiplied by the total prover volume and 

is only a correction factor for the volume deviation from 

nominal for the scale plate readings!
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Table 1. Variables for neck scale calibration and Neck Scale Correction Factor equation.

Variable Description

NSCF Neck scale correction factor

# calibration

points Total number of intervals making up the neck scale calibration

VSn

‘To Deliver’ volume of water added for each interval of the neck scale 

calibration, may be multiples of actual volume of standard used. The 

calibrated volume at the prover reference temperature must be used (typically 

60 °F for test measures and provers used for petroleum products). If glassware 

is used, an additional calibration value for the flask is needed as they are 

normally calibrated to 20 °C.

Vw Total volume of water added to neck to increase the water level from sri to srf

x number assigned to each increasing neck scale calibration point; x = f for final 

calibration point

sri Initial scale reading

srx ... srf

Scale reading for each interval of the neck scale calibration (1 through f) ‘f ‘= 

# calibration points

Δsrx Deviation between volume added and observed scale plate reading

3 Measurement Assurance

The process for scale plate calibration does not need to be duplicated unless the data, 

accuracy, and linearity appear questionable or fail to comply with the published 

requirements. In the case where questionable data are observed or a scale plate calibration

fails compliance, a replicate calibration should be conducted for confirmation. Typically, 

the process standard deviation, sp, will be dominated by the operator’s ability to read the 

meniscus and thus the component(s) for the meniscus reading are deemed sufficient to 

cover the process standard deviation.

4 Assignment of Uncertainties

Uncertainties associated with the neck scale calibration include the setting of the 

meniscus on the standard used (with each delivery), the reading of the meniscus on 

the unknown prover (at each volume reading), and the calibration uncertainty of the 

standard used and are used in compliance assessments and are included in the test 

measure or prover calibration uncertainty. The uncertainty for the standard, us, used 

will be treated as a dependent uncertainty and combined in summation prior to the 

root sum square combination of the meniscus reading uncertainties for the standard, 

umS, and meniscus reading uncertainties for the field standard, umX, in question. 

Follow the guidance provided in NISTIR 7383, GMP 3 for methods to estimate the 

uncertainty of the meniscus readings in each prover. The calibration uncertainty for 

four neck scale calibration intervals comprised of one delivery from the standard 

per interval, with a meniscus reading on both the standard and unknown measure 

might look like the following equation:

22 2 ( 4) 4 ( ) 4 ( ) n S mS mX uu u u = × +× × + Eqn. (5)
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The calibration uncertainty for four neck scale calibration intervals comprised of 

two deliveries from the standard for each interval with a meniscus reading on both 

the standard and unknown measure might look like the following equation:

22 2 ( 8) 8 ( ) 4 ( ) n S mS mX uu u u = × +× +× Eqn. (6)

Uncorrected systematic errors, included in the uncertainty budget for a test measure 

or prover, must be less than the compliance limits specified in the published 

requirements, must be less than limits published in NISTIR 6969, SOP 29 (i.e., less 

than the expanded uncertainty when all other components are combined) and may 

be included as a rectangular distribution in the test measure or prover calibration 

uncertainties. The mean (average) deviation of all calibration points may be 

calculated from the deviation for each calibration point and used as the value for an 

uncorrected systematic error. 

Table 2. Example Uncertainty Budget Table.

Uncertainty Component 

Description Symbol Source Typical Distribution

Uncertainty of the standard us

Calibration certificate; may 

be multiplied or added 

based on dependencies

Expanded divided 

by coverage factor

Ability to read the Meniscus in S um

None if using a slickerplate type standard; GMP 3 Triangular

Ability to read the Meniscus in X um GMP 3 Triangular

5 Compliance Assessments

The maximum capacity tolerance between the nominal volume line and any other 

line on the scale must be less than the published specifications or the scale plate 

should be replaced. Alternatively, if the scale readings are determined to be in error 

but proportional to the calibration points, a Neck Scale Correction Factor (NSCF) 

may be issued with instructions to the user for its use if it is anticipated that this 

correction factor will be used. For use of the NSCF to be valid, all corrected scale 

plate readings must fall within the applicable tolerance after the NSCF is applied to 

the actual scale plate reading. If the linearity and proportionality errors are 

sufficiently large that the NSCF does not bring all corrected neck scale readings 

within the tolerance limits, use of the NSCF correction is not appropriate. 

Neck scale errors less than the limits provided in published requirements should be 

included in the uncertainty estimate associated with the prover calibration as 

uncorrected errors. 

Uncertainties must be considered when evaluating the acceptability of the neck 

scale plate. If uncertainties for the scale plate calibration exceed the published 

compliance limits, the laboratory may not reject the scale plate. The application of 

scale plate tolerances must allow for the uncertainty of the neck scale calibration

measurements. The neck scale capacity error must exceed the value of one division 
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plus the uncertainty of the neck scale calibration to be rejected by the weights and 

measures enforcement agency.

Per NIST Handbook 105-3 for field standard test measures and provers: 

Capacity Tolerances also apply to the scale intervals marked on both sides of 

the scale mark corresponding to the nominal capacity of a volumetric field 

standard (test measure or prover). This means that the volume represented by 

each scale mark over the entire range of the scale plate must be accurate within 

the maximum permissible error of 0.05 % of the nominal capacity.

The maximum capacity error between the nominal volume line and any other 

line on the scale must be less than one (1) maximum subdivision as defined in 

the handbook. If smaller subdivisions are used, the maximum allowed 

subdivision is the tolerance applied to the neck uniformity. 

Per NIST Handbook 105-4 for field standard LPG and anhydrous provers:

Capacity Tolerances apply to the scale intervals marked on both sides of the 

scale mark corresponding to the nominal capacity of a volumetric field 

standard (test measure or prover). This means that the volume represented by 

each scale mark over the entire range of the scale plate must be accurate within 

the maximum permissible error of 0.2 % of the nominal capacity.

The maximum capacity tolerance between the nominal volume line and any 

other line on the scale must be less than two (2) major scale divisions as defined 

in the handbook. If smaller divisions or subdivisions are used, two (2) times 

the maximum allowed division listed in the handbook is the tolerance applied 

to the neck uniformity. 

6 Calibration Certificate

A supplemental statement on the test measure or prover calibration certificate may be 

generated and include supporting measurement calibration results or may include the neck 

scale correction factor along with instructions as to its use. 

Conformity Statement

Evaluate and report compliance to applicable tolerances as needed or required by 

the customer or by legal metrology requirements as described in Section 5. 

Compliance assessments must note the applicable documentary standard and which 

portions of the standard were or were not evaluated. 
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Appendix A

Scale Plate Calibration Data Form

(One needed for each scale plate calibrated)

Laboratory data and conditions:

Laboratory Date Calibrated

Location

Temperature

Barometric Pressure

Date Received Relative Humidity

Unknown Standard Description:

Owner Neck Scale calibrated (Right or Left)

Unique Identifier Neck Inside Diameter

Model/Type Gauge Tube Inside Diameter

Material Neck scale graduations 

Nominal Volume Maximum allowed subdivision 

Cubical Coefficient of Expansion (β) Applicable scale plate accuracy limit

Total Neck Scale Plate volume Applicable scale plate linearity limit

Reference temperature Reason for Neck Scale Calibration

Volume standard(s) data:

ID (Note ID of 

Standards) Nom. Vol. Ref. Temp. Cal. Vol.

VSn

Exp. Unc. Unc.

k factor

# Del. per 

interval

Cubical 

Coef. of Exp.

(α)

S

S

S

Volumes delivered from the standards into the neck:

Interval # Vol. Added 

________ units

Scale Plate Reading srx

________ units

Dev. between 

volume added and 

observed scale 

plate reading

∆ssssxx

Passes Scale Plate 

Accuracy Limit? 

(Yes/No)

Initial Scale 

Reading, sri

1

2

3

4

5

6

Average (absolute) deviation for uncorrected systematic uncertainty:

Neck Scale Correction Factor (NSCF) if appropriate