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SOP No. 14

Recommended Standard Operating Procedure

for

Gravimetric Calibration of Volumetric Standards Using an Electronic Balance

1 Introduction

Purpose of Test 

This procedure is a precision mass calibration converting mass values to volumetric 

values using pure water as a standard reference material. The results provide 

calibration of either the "To Deliver" (TD) or "To Contain" (TC) volume of 

measuring containers that may be used as volumetric measuring standards. The 

procedure uses gravimetric calibration principles to minimize calibration 

uncertainties. Accordingly, the procedure is especially useful for high accuracy 

calibrations. The procedure references measurement control standards to ensure the 

validity of the standards and the measurement process; however, additional good 

measurement practices such as those required for precision mass calibrations must 

be used. The procedure uses an electronic balance and is suitable for all sizes of 

gravimetric calibrations only limited by the capacity and resolution of the balance 

and handling capabilities. Detailed measurement ranges, standards, equipment, and 

uncertainties for this SOP are generally compiled in a separate document in the 

laboratory. This procedure calculates the average volume based on two runs. Note: 

NIST calibrations generally make use of the average of five replicates.

Conformity Assessment

Standards that are calibrated for use in legal weights and measures applications 

should be evaluated for conformance to the appropriate specifications and 

tolerances that apply. Where compliance is required by law, conformity evaluations 

should be conducted prior to performing calibrations. See Section 6.2 for reporting 

results.

Prerequisites

Verify that valid calibration certificates with appropriate values and 

uncertainties are available for all 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.

Verify that the mass standards to be used have sufficiently small standard 

uncertainties for the level of calibration. Reference mass standards should 

not be used for gravimetric calibration due to the risk of water 

contamination. Weights of ASTM Class 2 or 3 or OIML Class F1 or F2 are 

recommended for this procedure. Working standards of other classes are 

generally not designed to maintain adequate stability needed; however, 

corrections obtained within a few days of the volume calibration may 
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provide adequate stability and may be used if the uncertainty is sufficiently 

small and the density is available for performing buoyancy corrections.

Verify that the balance used is in good operating condition with adequate 

capacity, sufficiently small resolution, and sufficiently small process 

standard deviation, as verified by a valid control chart or preliminary 

experiments using this procedure. Note: standard deviations obtained from 

mass calibrations do not reflect the process repeatability of gravimetric 

calibrations; therefore, process repeatability must be obtained using this 

procedure! The accuracy of the balance and weighing procedures should be 

evaluated to minimize potential bias in the measurement process. 

Verify that the operator is experienced in precision weighing techniques and 

has had specific training in NISTIR 6969 SOP 2, SOP 4, SOP 29, GMP 3, 

GMP 10, and gravimetric calibrations.

Verify that an adequate quality and supply of distilled or deionized water 

(see GLP 10) is available. Note: Do not use tap water for this procedure!

Verify that air currents are minimized in the laboratory when weighing is 

performed. Verify that the laboratory facilities meet the following minimum 

conditions to enable meeting the expected uncertainty that is achievable 

with this procedure:

Table 1. Laboratory environmental conditions.

Procedure Temperature Relative Humidity

Gravimetric 18 °C to 23 °C

Stable to ± 1 °C / 1 h, during the calibration

40 % to 60 %

Stable to ± 10 % / 4 h

2 Methodology

Scope, Precision, Accuracy 

The procedure is applicable for the calibration of any size of measuring container 

that, when filled with water, will not overload the electronic balance used. Typical 

containers range in capacity from 1 mL to 20 L; however, this procedure is also 

applicable for larger provers, provided facility, equipment, and standards meet the 

requirements in this SOP. When larger provers (e.g., 100 gal or more) are tested, 

also see the Test Notes in the Appendix. The procedure is generally only

appropriate for micropipettes when additional evaporation corrections are made. 

The precision of calibration depends on the care exercised in adjusting the various 

volumes and strict adherence to the various steps of the procedure. The accuracy 

attainable depends on the ability of the operator to read and set the meniscus, 

uncertainties of the standard weights, the air buoyancy corrections, and thermal 

expansion corrections that are made.
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Summary

The electronic balance used is calibrated by incorporating standard masses into the 

procedure. The volumetric vessel to be calibrated is then weighed dry or “wetted 

down,” depending on whether the calibration is to be made on a “To Contain” or 

“To Deliver” basis. The container is filled with pure water of known temperature 

and re-weighed. The difference in mass is used to calculate the capacity of the 

container at the nominal capacity and at various capacities when multiple neck 

graduations are present. Transfer vessels may be used for all procedures except for 

flasks and containers marked.

Standards and Equipment Requirements

An electronic balance having sufficient capacity to weigh the loaded vessel

is required. The balance selection affects the potential measurement errors 

associated with this procedure. Prior to use and where available, it is 

recommended to use the adjust/calibrate feature on balances. Option A 

provides a single point calibration factor for the balance. In general, 

concerns are greater for balances or mass comparators larger than 5 kg due 

to corner loading errors, non-linearity, and repeatability over the range of 

use. Option B as described in the calculation section for larger volumes 

corrects for balance non-linearity in both the filled and empty/drained 

ranges of use. Option B will also likely be required on mass comparators 

that have multiple ranges. It also provides corrections for variations in air 

density that may occur over a longer weighing process on larger volumes. 

For all procedures in this SOP, the balance should be zeroed prior to each 

measurement to minimize possible effects due to balance drift. The 

sensitivity or resolution of the balance may be a limiting factor in the 

accuracy of the measurement. The resolution and repeatability must be 

smaller than the accepted uncertainty of the calibration. Linearity errors or 

additional uncertainties may need to be considered when the mass standards 

are slightly less than the volume or container being measured. 

Sufficient quantity of calibrated mass standards. Mass standards are 

selected so that they are slightly larger than the combined mass of the 

volume and container or transfer vessel that will be weighed. When 

summations of masses are used, the summation mass is used, and the 

“effective density” must be calculated, taking care not to use “average” 

density values. 

Thermometer with resolution and uncertainty less than 0.1 °C to determine 

water temperature.

Thermometer with resolution and uncertainty less than 0.50 °C to determine 

air temperature.1

 1 See NISTIR 6969, SOP 2 for calculating air density and requirements for temperature, barometric pressure, and relative humidity.
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Barometer with resolution and uncertainty less than 135 Pa (1 mmHg) to 

determine air pressure.1

Hygrometer with resolution and uncertainty less than 10 % to determine 

relative humidity.1

Distilled or deionized water (See GLP 10) of sufficient quality and quantity 

for the calibration. Note: Do not use tap water for this procedure!

Stopwatch or another suitable timing device (does not need to be 

calibrated.)

General Considerations

Cleanliness checks

Verify that all containers to be calibrated are clean as evidenced by uniform 

drainage of water. No water droplets should remain on any interior surface 

as the water drains from the container. A reproducible “wet-down” weight 

is evidence for cleanliness in cases where it is not possible to visually check 

for uniform drainage. Use GMP 6 or 7 to clean vessels as necessary. All 

glassware must be meticulously cleaned, prior to calibration. When clean, 

the walls will be uniformly wetted. Instructions for cleaning are given in 

GMP 6 and GMP 7. An exception is plastic ware, which will not be wetted. 

Follow manufacturer's instructions for cleaning such vessels. Do not use 

cleaning agents that will attack, discolor, or swell plastic ware.

Use water that is thermally equilibrated with the laboratory environment. 

Equilibration can be achieved by storing the water in clean containers in the 

laboratory. It is important to use water that is equilibrated in the laboratory 

as much as possible to minimize potential calibration errors and convection 

currents during the calibration. Consider water to be equilibrated when 

within ± 5 °C of the laboratory temperature.

Volumetric calibrations to a marked volume (graduation line) are critically 

dependent on the setting of a meniscus. See GMP 3 for guidance in reading 

a meniscus.

Use GLP 13 as the procedure to dry any container to be calibrated on a “To 

Contain” basis.

Wet down (not used for any container calibrated “To Contain”).

For glassware and hand-held test measures: Fill the container to capacity 

with distilled or deionized water, then empty over a 30 s period while 

avoiding splashing. Drain for 10 s unless another drain time is specified. 

(This is commonly called a “30 s pour, 10 s drain” emptying procedure.) A 

30 s (± 5 s) pour followed by a 10 s drain, with the measure held between a 

10 degree and 15 degree angle from vertical is required during calibration 
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and use for glass flasks. A wet-down is not required for a transfer vessel 

that is used to weigh a delivered volume of water.

For stationary provers: Fill the container to capacity with distilled or 

deionized water, then empty. Time the drain once the cessation of the main 

flow is complete for 30 s and close the valve.

Calibration Procedure for Burets

Clamp the buret vertically on a support stand. Also clamp a plain glass test 

tube or beaker, large enough to hold a thermometer, near the buret.

Fill the buret with water and test for absence of leaks from the tip and 

stopcock. Drain and fill several times to condition the buret. Fill when ready 

to test.

Drain and record the delivery time, defined as the time of unrestricted flow 

from the zero mark to the lowest graduation mark with the stopcock fully 

open.

Fill the buret slightly above the zero mark with temperature-equilibrated 

water and fill the test tube that holds the thermometer. Record the water 

temperature.

Set the meniscus on the zero mark and touch the tip with the wetted wall of 

a beaker to remove any excess water. The buret tip must be full.

Measure and record the air temperature, air pressure, and relative humidity.

Zero the balance and then place a known mass standard on the balance pan 

that is slightly larger than the filled capacity of the empty transfer vessel or 

flask when filled with water. Record the reading as O1. 

Zero the balance and then weigh an empty transfer vessel or flask including 

the stopper or cover to be used. Record as O2. 

Fully open the stopcock and discharge the contents of the buret into the 

previously weighed flask or transfer vessel. The tip of the buret should be 

in contact with the wall of the flask. When the level in the buret is within a 

few millimeters above the line being calibrated, slow the discharge, and 

make an accurate setting. When the setting is completed, move the flask 

horizontally to break contact with the tip. Recheck the setting.

Stopper (or cover) the filled transfer vessel or flask. Check to make sure that 

the outside of the transfer vessel or flask is not wet. Zero the balance and 

then weigh the filled transfer vessel or flask. Record the balance reading as 

O3.

Measure and record the temperature of water in the container.
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Test the next interval in the same manner - from the zero mark to the next 

interval of test.

For burets with a specified waiting time, empty as in 2.5.9 to within a few 

millimeters of the calibration mark. Pause for the specified waiting time 

(e.g., 10 s), then adjust the meniscus to the graduation line as in 2.5.9.

Measure and record the air temperature, air pressure, and relative humidity.

Make a duplicate determination for each interval (Run 2).

Calculate the volume for each interval as described in Section 3, Option A.

Calibration Procedure for Pipets (One-Mark)

Measure and record the air temperature, air pressure, and relative humidity.

Zero the balance and then place a known mass standard on the balance pan 

that is slightly larger than the filled capacity of the empty transfer vessel or 

flask when filled with water. Record the reading as O1. 

Zero the balance and then weigh an empty transfer vessel or flask, including 

the stopper or cover that will be used. Record the balance reading as O2.

Fill the pipet to the index mark and measure the delivery time with the tip 

in contact with the internal surface of a beaker (not the transfer vessel that 

will be used.)

Refill the pipet by suction, slightly above the index line. Record the water 

temperature. Wipe tip with filter paper, then slowly lower level to the index 

line, using a stopcock or pinch clamp for fine control. The tip must be in 

contact with the wetted wall of the beaker while this setting is being made. 

Do not remove any water remaining on tip.

Hold the pipet in a vertical position and deliver water into the previously 

weighed transfer vessel or flask, with the tip in contact with the inside wall 

or neck.

After the flow has ceased, wait two seconds then remove the pipet from 

contact with the flask. Check to make sure that the outside of the transfer 

vessel or flask is not wet. 

Stopper (or cover) the filled transfer vessel or flask. Zero the balance and 

then weigh the transfer vessel or flask. Record the balance reading as O3.

Measure and record the temperature of water in the container.

Measure and record the air temperature, air pressure, and relative humidity.
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Make a duplicate determination for the pipet (Run 2).

Calculate the volume as described in Section 3, Option A. 

Calibration of Flasks (To Contain) – Transfer vessel must not be used. 

Clean and dry the flask to be calibrated as described in GLP 13. Then 

stopper the flask.

Measure and record the air temperature, air pressure, and relative humidity.

Zero the balance and then place a known mass standard on the balance pan 

that is slightly larger than the filled capacity of the flask when filled with 

water. Record the reading as O1. 

Zero the balance and then weigh the dry flask including its stopper or cover. 

Record the balance reading as O2.

Place an appropriately sized funnel in neck and fill the flask to just below 

the reference graduation while maneuvering the flask to wet the entire neck 

below the stopper. Let stand for two minutes then adjust the meniscus to the 

reference graduation line, taking care to avoid wetting the neck above the 

capacity graduation.

Check that the outside surface of the flask, and its internal surface above the 

water level are dry, and that neither bubbles or foam are present in the water. 

Remove visible water droplets if needed with a laboratory wipe. Stopper or 

cover the flask. 

Zero the balance and then weigh the filled flask and its stopper or cover, 

and record the balance reading as O3.

Measure and record the temperature of the water in the flask or another 

container.

Measure and record the air temperature, air pressure, and relative humidity.

Make a duplicate determination (Run 2) after drying the flask per GLP 13.

Perform volume calculations as described in Section 3, Option A.

Calibration of Flasks (To Deliver)

Clean but do not dry the flask to be calibrated. Condition the flask by filling 

and emptying the flask over a 30 s period by gradually inclining it to avoid 

splashing. When the main flow has ceased, hold the flask in a nearly vertical 

position for 10 seconds unless another drain time is specified, then touch 

off the drop of water adhering to the tip of the flask.
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Measure and record the air temperature, air pressure, and relative humidity.

Zero the balance and then place a known mass standard on the balance pan 

that is slightly larger than the filled capacity of the flask when filled with 

water. Record the reading as O1. 

Zero the balance and then weigh the drained (empty) flask including its 

stopper or cover. Record the balance reading as O2.

Fill the flask to just below the reference graduation. Let the flask stand for 

two minutes, then adjust the meniscus to the reference graduation line. Do 

not dry the inside of the flask above the graduation line but take care to 

ensure that the outside of the flask is dry. 

Zero the balance and then weigh the filled vessel, with cap or stopper.

Record the balance reading as O3.

Measure and record the temperature of the water in the flask.

Measure and record the air temperature, air pressure, and relative humidity.

Make a duplicate determination (Run 2).

Calculate the volume of the flask as described in Section 3, Option A.

Note: The order of weighing the filled and drained flask in Section 2.8 may 

be reversed. In that case, the filled vessel is still weighed and recorded as 

O3, the flask is drained as in 2.8.1, and the properly drained vessel is 

weighed and recorded as O2.

Calibration of Other Volumetric Glassware 

Measuring Pipets (non-single-mark) – Calibrate in a manner like that used 

to calibrate burets (2.5).

Graduated Cylinders – Calibrate in a manner like that used for flasks (To 

Deliver cylinders, use section 2.8; To Contain cylinders, use section 2.7).

Calibration of Slicker-Plate Type Standards

This calibration makes use of Option B where equivalent mass standards 

are used at both the filled and empty loads on the balance. A transfer vessel 

is recommended.

Condition the slicker-plate type standards with several wet-down runs to 

fully ensure wet down and smooth valve operation.

Measure and record the air temperature, air pressure, and relative humidity.
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Zero the balance and then place a standard mass, MS1, on the balance 

platform (MS1 should be slightly larger than the mass of the drained vessel, 

dry vessel, or empty transfer vessel.) Record reading as O1.

Zero the balance. Place the dry or “wet-down” transfer vessel on the balance 

platform, as appropriate, and record reading as O2. Caution: all containers 

must be dry on the outside for all weighing.

Fill the slicker-plate standard to just above the rim of the standard. Record 

the water temperature. Slide the slicker plate across the level top. Set the 

transfer vessel below the nozzle to ensure all volume is transferred into the 

vessel and that no splashing occurs. 

Open the slicker-plate standard valve and remove the plate simultaneously 

and smoothly to deliver the water into the transfer vessel. Time the drain for 

30 s after cessation of the main flow and close the valve. Cover the transfer 

vessel and move it from beneath the standard to ensure additional drops of 

water are not transferred. Note: Never fill the transfer vessel while it is 

sitting on the balance platform to ensure that the balance is not damaged 

with water and to avoid errors associated with balance drift and hysteresis.

Zero the balance and then place a standard mass, MS2, on the balance 

platform. MS2 should be slightly larger than the mass of the filled vessel. 

Record the balance reading as O3.

Zero the balance and then weigh the filled transfer vessel and record the 

balance reading as O4.

Immediately after weighing, check the temperature of the water in the filled 

container. Ensure that the water has not changed by more than 0.2 °C during 

the measurement process or repeat the run.

Measure and record the air temperature, barometric pressure, and relative 

humidity.

Make a duplicate determination (Run 2).

Calculate the volume as described in Section 3, Option B.

Calibration of Hand-held Graduated Neck Type Provers

A hand-held test measure is weighed empty and filled much like the 

procedure for To Deliver flasks (section 2.8). However, this calibration 

makes use of Option B where equivalent mass standards are used at both 

the filled and empty loads on the balance.

Condition the test measure by filling and draining using a 30 s pour followed 

by a 10 s drain. Take care to avoid splashing of water on the outside of the 
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measure. The wet-down will help equilibrate the test measure with the water 

temperature.

Measure and record the air temperature, air pressure, and relative humidity.

Zero the balance and then place standard masses, MS1, on the balance 

platform. MS1 should be slightly larger than the mass of the drained vessel. 

Record reading as O1. 

Zero the balance and then place the “wet-down” test measure on the balance 

platform, and record the balance reading as O2. Caution: all containers must 

be dry on the outside for all weighing.

Fill the graduated neck type test measure to just below the nominal volume 

mark. Record the water temperature. Adjust the meniscus to nominal. 

Zero the balance and then place standard masses, MS2, on the balance 

platform. MS2 should be slightly larger than the mass of the filled vessel. 

Record the balance reading as O3.

Zero the balance and then weigh the filled transfer vessel and record the 

balance reading as O4. 

Immediately after weighing, check the temperature of the water in the filled 

container. Ensure that the water has not changed by more than 0.2 °C since 

step 2.11.6 or repeat the run.

Measure and record the air temperature, barometric pressure, and relative 

humidity.

Make a duplicate determination (Run 2).

Calculate the volume as described in Section 3, Option B. You may use the 

average water temperature in calculations. If a neck scale plate verification 

is performed, additional weighings may be performed after setting the 

meniscus at each level. 

Calibration of Large Volume Graduated Neck Type Provers

This calibration makes use of Option B where approximately equivalent 

mass standards are used at both the filled and empty loads on the balance. 

A transfer vessel is recommended. The unknown vessel to be calibrated 

must be elevated to facilitate transfer of water into the transfer vessel.

Condition the prover with a wet-down run to fully ensure smooth valve 

operation, temperature equilibration, and wet-down of the delivery system.

Measure and record the air temperature, air pressure, and relative humidity.
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Zero the balance and then place standard masses, MS1, on the balance 

platform. MS1 should be slightly larger than the mass of the drained vessel, 

dry vessel, or empty transfer vessel. Record reading as O1. 

Zero the balance. Place dry or “wet-down” transfer vessel including cover 

on balance platform, as appropriate, and record reading as O2. Caution: all 

containers must be dry on the outside for all weighing.

Fill the graduated neck type prover to just below the nominal volume mark. 

Record the water temperature. Adjust the meniscus to nominal. Set the 

transfer vessel below the nozzle to ensure all volume is transferred into the 

vessel and that no splashing occurs. Use hoses and piping of minimum 

length to avoid errors associated with retention during delivery. Hoses 

should be translucent so that cessation of the main flow is visible. Care 

should be taken to ensure that there are no loops or sags in the hose that may 

hold water. When using hoses or piping, be sure to include them as part of 

the wet-down process. 

Open the unknown prover valve to deliver the water into the transfer vessel. 

Time the drain for 30 s after the cessation of the main flow and close the 

valve. Cover the transfer vessel and move it from beneath the prover to 

ensure additional drops of water are not transferred.

Zero the balance and then place standard masses, MS2, on the balance 

platform. MS2 should be slightly larger than the mass of the filled vessel. 

Record the balance reading as O3.

Zero the balance and then weigh the filled transfer vessel and its cover. 

Record the balance reading as O4.

Immediately after weighing, check the temperature of the water in the filled 

container. The temperature should not change by more than 0.2 °C if the 

prover and water have been equilibrated in the laboratory environment. 

Measure and record the air temperature, barometric pressure, and relative 

humidity.

Make a duplicate determination (Run 2).

Calculate the volume as described in Section 3, Option B. You may use the 

average water temperatures for calculations. 
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3 Calculations

Option A – One-point balance calibration. Compute the volume at the temperature 

under test, Vt, for each determination using the equation:

( 3 2 ) 1

1 1 s a

t

s wa

M V OO

O

ρ

ρ ρρ

    =− −         − Eqn. (1)

Note: The O3 value is the filled volume container or transfer vessel and O2 is the 

dry, empty, or drained value. If the order of any weighing operations were changed, 

the calculated volume may indicate a negative value.

Option B – Two-point balance calibration. Compute the volume, Vt, for each 

determination using the equation:

4 2

2 1

3 21 1

1 1 1 a a

t s s

s s wa

O O VM M

O O

ρ ρ

ρ ρ ρρ

       = −− −        −        Eqn. (2)

Table 2. Variables used in volume equations.

Variable Description

Ms, Ms1, Ms2 mass of standards (i.e., true mass, vacuum mass) (g)

ρs density of MS (g/cm3)

ρw density of water at the temperature of measurement (g/cm3)

ρa

density of air at the conditions of calibration – may be different for filled 

and empty/drained conditions (g/cm3)

Vt

represents either the “To Contain” or “To Deliver” volume (depending on 

whether O2 represents a dry or a “wet down” container at the temperature of 

the measurement) (cm3 or mL)

Glassware is typically calibrated to 20 °C. Compute V20, the volume at 20 °C, for 

each run, using the expression:

VV t 20 = −− t   1 20 α ( )   Eqn. (3)

where α is the cubical coefficient of expansion of the container being calibrated

(°C-1

), (see NISTIR 6969, Table 9.10), and, t, is the temperature (oC) of the water. 

Compute the mean V20 for the duplicate measurements.

Test measures and provers are typically calibrated to 60 °F. Compute V60, the 

volume at 60 °F, for each run, using the expression (taking care to use the cubical 

coefficient of expansion in °F-1):

VV t 60 = −− t   1 60 α ( )   Eqn. (4)
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If using a different reference temperature, use the following equation and take care 

to match the cubical coefficient of expansion units with the units of temperature:

V V tt ref t 1 α ( ref ) = −−     Eqn. (5)

Other Reference temperatures may be used. Common reference temperatures for 

other liquids follow:

Table 3. Reference temperatures for measured volumes.

Commodity Reference 

Temperature

Frozen food labeled by volume (e.g., fruit juice) -18 oC (0 oF)

Beer 3.9 oC (39.1 oF)

Food that must be kept refrigerated (e.g., milk) 4.4 oC (40 oF)

Distilled spirits or petroleum 15.56 oC (60 oF)

Petroleum (International Reference) 15 oC (59 oF)

Compressed Natural Gas (CNG) 15 °C (60 oF)

Wine 20 oC (68 oF)

Unrefrigerated liquids (e.g., sold unchilled, like soft drinks) 20 oC (68 oF)

Hydrogen (H2) 21 oC (70 oF)

Petroleum (Hawaii) 26.67 oC (80 oF)

Calculate water density for air-saturated water, using the equations provided in 

GLP 10.

Calculate the air density per NISTIR 6969, Selected Mass Calibration Procedures, 

SOP 2, Option B. 

Calculate the within process standard deviation, sw, for the replicate runs and 

determine the applicable degrees of freedom (number of replicates minus one). 

Calculate the F statistic to compare the observed within process standard deviation, 

sw, to the accepted (pooled) within process standard deviation for the measurement 

process. (See NISTIR 6969, Sections 8.4 and 8.9.2, for more information on 

pooling standard deviations and F-tests.)

2

Accepted

2

Observed

w

w

s

s F = Eqn. (6)
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The calculated F statistic must be less than the F value obtained from an F table at 

95 % confidence level (Table 9.12, NISTIR 6969) to be acceptable. The F value is 

obtained from the F table for numerator degrees of freedom and denominator 

degrees of freedom equal to the number of degrees of freedom in the accepted

(pooled) within process standard deviation. If the data fails the F-test and the source 

of the error cannot be determined conclusively, the measurement must be repeated.

Calculate and report the mean volume of the volumetric standard at its applicable 

reference temperature. 

If adjustments were made during replicate runs, report the “as found” volume or 

the mean of “as found” volumes and the “as left” volume or mean of “as left” 

volumes, as applicable, at the appropriate reference temperature. (I.e., do not 

calculate a mean value by combining “as found” and “as left” values when 

adjustments are made.)

4 Measurement Assurance

Where practical, duplicate the process with a suitable check standard (See GLP 1, 

SOP 30, in NISTIR 6969, or Sec. 7.4, in NBS Handbook 145).

Plot the calculated check standard volume and verify it is within established 

limits. A t-test may be incorporated to check the observed value against an 

accepted value.

( ) p

c c

s

S S

t − = Eqn. (7)

The t-statistic is evaluated using Eqn. 7 with a 95 % confidence level. All 

values must be entered in the control chart, even if failing this statistic to 

ensure the variability obtained for the process is truly representative of the 

process and not unduly reduced over time. The observed value of the check 

standard is compared to the accepted mean value of the check standard and 

divided by the standard deviation for the check standard observations over 

time. The limits for the t-test are based on applicable warning and action 

limits on the control chart. See SOP 20 for applicable t-test limits.

The mean of the calculated check standard values is used to evaluate bias 

and drift over time and may be used to identify or signify problems with the 

volume standard or changes in water quality.

Check standard observations may also be used to calculate the standard 

deviation of the measurement process, sp.

This procedure uses replicate measurements to monitor the measurement process 

following SOP 20 and a standard deviation chart (preferred) or a range chart 

(optional). For standards that may be and are adjusted, do not combine an “as 

found” value with an “as left” value for the two runs recorded in the chart; use the 
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adjusted value from Run 1 and the value from Run 2, both at the applicable 

reference temperature, when entering values in a standard deviation or range chart. 

Control chart run values must both be from either before adjustment or after

adjustment. A minimum of 12 replicate measurements are required to establish 

initial process limits and 25 to 30 points are required for reporting valid uncertainty 

values.

5 Assignment of Uncertainties

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

mass standards used, us, plus the measurement process repeatability, sp, and the additional 

items noted below and in the uncertainty budget table, Table 4, at approximately a 95 

percent level of confidence. See NISTIR 6969, SOP 29 for the complete standard operating 

procedure for calculating the uncertainty. 

The standard uncertainty for the standards, us, 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. Multiple mass standards are often used, so 

see SOP 29 for treatment of dependencies and correlations.

Standard deviation of the measurement process from control chart performance.

See SOP No. 17 or 20.

The value for sp is obtained from the control chart data for check standards when a 

check standard is available using this procedure. It may also be estimated based on 

replicate measurements over time. Replicate measurements over time provide a 

pooled standard deviation that may be used (alternatively, the average range is used 

to estimate the standard deviation) per SOP 17 or 20. This standard deviation value 

is a repeatability factor related to the precision of the measurement process 

weighings and the setting of the meniscus when present, but does not include 

uncertainties associated with systematic errors in reading the meniscus. See GMP 

3 for details. Use the larger of the sp from a check standard or the sw obtained from 

within process repeatability.

Include uncertainties associated with the reading of the meniscus when one is 

present. See GMP 3 for details. 

Other standard uncertainties usually included at this calibration level include 

uncertainties associated with water temperature measurements, thermometer 

accuracy, calculation of air density, standard uncertainties associated with the 

density of the mass standards, coefficients of expansion, viscosity, or surface

effects on the volume of liquid clinging to vessel walls after draining, improper 

observance of drainage times, and the lack of internal cleanliness.

Example components to be considered for an uncertainty budget table are shown in 

Table 4. Multiple values may need to be considered in some cases. 
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Table 4. Example uncertainty budget table.

Uncertainty Component Description Symbol Source Typical 

Distribution

Uncertainty of the standard mass(es) (5.1) us Calibration certificate Expanded divided 

by coverage factor

Accepted standard deviation of the 

process (5.2) sp

Control chart, standard 

deviation chart Normal

Water temperature utx

Consider accuracy, 

resolution, and gradients Rectangular

Water density uρw GLP 10 Rectangular

Cubical Coefficient of Expansion (CCE) uCCE

5 % to 10 % of the CCE

(EURAMET CG-19) Rectangular

Meniscus reading (when present) (5.3) um GMP 3 Triangular

Drain time effects (insignificant if 

following procedures) ud From experimental data Rectangular

Air temperature (for air density) ut NISTIR 6969, SOP 2 Rectangular

Air pressure (for air density) up NISTIR 6969, SOP 2 Rectangular

Air relative humidity (for air density) uRH NISTIR 6969, SOP 2 Rectangular

Air density (equation) uρa NISTIR 6969, SOP 2 Rectangular

Mass density uρm

Assumed reference 

densities or OIML R111 Rectangular

5.6 Uncertainty Evaluation

Where applicable, uncertainties for volume calibrations that are assessed for 

conformity must meet decision rule criteria in the applicable documentary 

standards.

6 Calibration Certificate

Report results as described in NISTIR 6969 SOP 1, Preparation of Calibration

Certificates, with the addition of the following:

“To Contain” or “To Deliver” volume, reference temperature, uncertainty, material, 

thermal coefficient of expansion (assumed or measured), construction, any 

identifying markings, tolerances (if appropriate), laboratory air temperature, water 

temperature(s) at time of test, barometric pressure, relative humidity, and any outof-tolerance conditions.

Conformity Assessment

Evaluate compliance to applicable tolerances as needed or required by the customer 

or by legal metrology requirements. Compliance assessments must note the 

applicable documentary standard and which portions of the standard were or were 

not evaluated. The uncertainty for volume calibrations must be less than the 

tolerances published in the applicable documentary standards. For volume 

calibrations where the unknown standard can be adjusted, it is standard practice to 
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adjust the standard or leave the scale plate in a position close enough to its nominal 

volume to ensure that the absolute value of the measurement result plus the 

uncertainty is less than the applicable tolerance. Where the unknown standard 

cannot be adjusted, and a portion of the uncertainty band from the error exceeds 

tolerance limits, it is not appropriate to state compliance with the tolerances unless 

additional decision rules are communicated with and agreed to by the end user. 

Correction values (measurement results) may need to be used by the end user in 

such cases.

7 Additional References:

Bean, V. E., Espina, P. I., Wright, J. D., Houser, J. F., Sheckels, S. D., and Johnson, A. N., 

NIST Calibration Services for Liquid Volume, NIST Special Publication 250-72, National 

Institute of Standards and Technology, Gaithersburg, MD, (2009).

EURAMET Calibration Guide 19, Guidelines on the Determination of Uncertainty in 

Gravimetric Volume Calibration, (Version 2.1, 03/2012). 
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Appendix A (Single-Point Balance Calibration)

Gravimetric Calibration Data Sheet (Option A)

Laboratory data and conditions:

Vessel Identification Operator

Material Date

Cubical Coefficient of Expansion Before After

Balance Identification Temperature

Load Pressure

Standard deviation of the process, 

from control chart, sp Relative Humidity

Degrees of Freedom Reference water 

temperature 

Mass standard(s) data:

Identification (ID)

(Note ID and for Filled or 

Empty Load)

Nominal Mass Correction* Expanded Unc:

From cal. report

Unc:

k factor

Density

g/cm3

S

S

S

S

S

*Mass Correction = True Mass values are required.

Observations:

Run 1 Weights – Zero balance before each weighing. Balance Observations, Units______

MS O1

Empty or Drained O2

Filled O3

tw

Run 2 Weights – Zero balance before each weighing. Balance Observations, Units______

MS O1

Empty or Drained O2

Filled O3

tw
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Appendix B (Two-Point Balance Calibration)

Gravimetric Calibration Data Sheet (Option B)

Laboratory data and conditions:

Vessel Identification Operator

Material Date

Cubical Coefficient of Expansion Before After

Balance Temperature

Load Pressure

Standard deviation of the process, 

from control chart, sp Relative Humidity

Degrees of Freedom Reference water 

temperature 

Mass standard(s) data:

Identification

(Note ID for Empty (MS1) 

or Filled (MS2) Loads)

Nominal Mass Correction* Expanded Unc:

From cal. report

Unc:

k factor

Density

g/cm3

S

S

S

S

S

S

S

*Mass Correction = True Mass values are required.

Observations:

Run 1 Weights – Zero balance before each weighing. Balance Observations, Units______

Ms1 O1

Empty or Drained O2

MS2 O3

Filled O4

tw in standard: tw in unknown: Temperature change is less than 0.2 °C? Y/N

Run 2 Weights – Zero balance before each weighing. Balance Observations, Units______

Ms1 O1

Empty or Drained O2

MS2 O3

Filled O4

tw in standard: tw in unknown: Temperature change is less than 0.2 °C? Y/N
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Appendix C

Test Notes for Large Provers

1. Pour and drain times.

It is impractical to completely drain a filled container because some of the contents will remain 

as a film. By strict adherence to a specified procedure, the residual contents can be held 

essentially constant so that, reproducible calibration constants can be obtained. The 

conventionally selected conditions are as follows:

For bottom-drain containers: open the drain valve fully and allow contents to discharge at 

maximum rate. When main flow ceases (flow decreases so that drain opening no longer 

runs full), wait 30 s, close the valve, and touch off any drops adhering to spout. 

For pour-type containers: pour contents by gradually tilting container to an 85o angle, so 

that virtually all liquid is delivered in 30 s. Allow to drain for an additional 10 s, then touch 

off any drops adhering to the lip. 

The instructions described above must be precisely followed during calibration and use of 

the calibrated vessels.

2. Evaporation losses.

A suitable cap should be placed on the top of open vessels to minimize evaporation losses. If 

used, the cap must be included in all weighings.

3. Slicker-plate.

When a slicker-plate standard is calibrated, the plate should be used to fix the water level in it. 

A transfer vessel is recommended for use when calibrating a slicker-plate type standard. But if 

the standard is weighed, the plate must be weighed with the standard during each such 

operation.