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SOP 13 

Standard Operating Procedure 

for 

Calibration of Volumetric Ware, Gravimetric Method1

1 Introduction 

 1.1 Purpose of Test 

Volumetric flasks, pipets, graduated cylinders, burets, and similar glass and 

plastic volumetric ware, such as those used in chemical and clinical laboratories, 

need to be calibrated to ensure accuracy of measurement. This SOP describes 

procedures for calibration of such ware with capacities ranging from 0.1 cm3 to 

2000 cm3. The method is extendable, in principle, to larger volumes, limited only 

by the capacity and physical dimensions of the weighing apparatus. It is not 

recommended for volumetric ware with capacities less than 0.1 cm3. This 

procedure makes use of a single pan mechanical balance. For calibrations with an 

electronic balance see SOP 14. 

1.2 Prerequisites 

1.2.1 Verify that valid calibration certificates are available for the standards 

used in the test. 

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

uncertainties for the intended level of calibration. Reference standards 

should not be used for gravimetric calibration. 

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

sufficiently small process standard deviation, as verified by a valid control 

chart or preliminary experiments, to ascertain its performance quality 

when a new balance is put into service. The accuracy of the balance and 

weighing procedures should be evaluated to minimize potential bias in the 

measurement process. 

1.2.4 Verify that the operator is experienced in precision weighing techniques 

and has had specific training in SOP 2, SOP 4, SOP 29, GMP 3, GMP 10, 

and gravimetric calibrations. 

1.2.5 Verify that the laboratory facilities meet the minimum conditions shown 

in Table 1 to meet the expected uncertainty that is achievable with this 

procedure. 

1.2.6 Verify that an adequate supply of distilled or deionized water (see GLP 

10) is available. 

 

1 Based on the work of J. Lembeck "The Calibration of Small Volumetric Glassware," NISTIR 74-461 (1974). 
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Table 1. Laboratory environmental conditions 

Procedure Temperature Relative Humidity 

Gravimetric 20 °C to 23 °C, a set point ± 2 °C, 

maximum change 1 °C/h 

40 % to 60 % 

± 10 % max change / 4 h 

 

2 Methodology 

2.1 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 balance used. The precision of 

calibration will depend on the care exercised in adjusting the various volumes and 

strict adherence to the various steps of the procedure. The accuracy attainable 

will depend on the uncertainties of the standard weights and the air buoyancy and 

thermal expansion corrections that are made. 

2.2 Summary 

This procedure is based on a determination of the mass of water contained in or 

delivered from the vessel that is calibrated. The volumetric determination is 

calculated from the above measurements and a knowledge of the temperature, 

pressure, and relative humidity of the air, and the temperature of the water that is 

weighed. 2.3 Equipment and Standards 

2.3.1 Balance having sufficient capacity to weigh the loaded vessel. The 

sensitivity of the balance will be a limiting factor in the accuracy of the 

measurement. 

2.3.2 Mass standards or built-in weights calibrated with adequate accuracy and 

valid calibration certificates traceable to NIST. Ordinarily, meeting 

ASTM Class 2 or 3 weight specifications are required. 

2.3.3 Calibrated thermometer accurate to ± 0.1 °C with recent calibration values 

that are traceable to NIST to determine water temperature. 

2.3.4 Calibrated thermometer accurate to ± 0.5 °C with recent calibration values 

that are traceable to NIST to determine air temperature.2

2.3.5 Calibrated barometer accurate to ±135 Pa (1 mm Hg) with recent 

calibration values that are traceable to NIST to determine the air pressure. 

2.3.6 Calibrated hygrometer accurate to ± 10 % with recent calibration values 

that are traceable to NIST to determine relative humidity. 

 

2 Values from the thermometer, barometer and hygrometer are used to calculate the air density at the time of the 

measurement. The air density is used to make an air buoyancy correction. The accuracies specified are 

recommended for high precision calibration. Less accurate equipment can be used with only a small degradation in 

the overall accuracy of the measurement. 
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2.3.7 Distilled or deionized water (See GLP 10). 

2.3.8 Stopwatch or other suitable timing device (does not require calibration). 

2.4 General Considerations 

2.4.1 All glassware must be meticulously cleaned, prior to calibration. When 

clean, the walls will be uniformly wetted. Instructions for cleaning are 

given in 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. 

2.4.2 Volumetric calibrations are critically dependent on the setting of a 

meniscus. See GMP 3 for guidance in reading a meniscus. 

2.4.3 Use water that is temperature-equilibrated with the laboratory 

environment. Equilibration can be achieved by storing the water in clean 

containers in the laboratory. 

2.4.4 All weighings ( I L, I E ) performed in this SOP should be determined with 

a mechanical balance that has verified calibration data available. A double 

substitution procedure(SOP 4) with air buoyancy correction may also be 

used. Equations must be modified if SOP 4 is used!

2.5 Calibration Procedure for Burets 

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

test tube, large enough to hold a thermometer, in the vicinity of the buret. 

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

stopcock.

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

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

open.

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

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

temperature.

2.5.5 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. 

2.5.6 Fully open the stopcock and discharge contents of buret into a previously 

weighed flask. The tip 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.

2.5.7 Stopper and weigh the flask. 

2.5.8 Measure and record the temperature of water in the test tube. 
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2.5.9 Test the next interval in the same manner - from the zero mark to the next 

interval of test.

2.5.10 For burets with a specified waiting time, empty as in 2.5.6 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 2.5.6.

2.5.11 Make a duplicate determination.

2.5.12 Calculate the volume for each interval as described in Section 3.

2.6 Calibration Procedure for Pipets (One-Mark) 

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

in contact with the internal surface of a beaker.

2.6.2 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 a beaker while this setting is being 

made. Do not remove any water remaining on tip at this time.

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

weighed weighing flask, with the tip in contact with the inside wall or 

neck.

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

contact with the flask.

2.6.5 Stopper the flask and weigh with its contained load. 

2.6.6 Make a duplicate determination. 

2.6.7 Calculate the volume as described in Section 3. 2.7 Calibration of Flasks (To Contain) 

2.7.1 Clean and dry flask as described in GLP 13, then stopper and weigh the 

flask. Record the Empty Flask value. 

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

reference graduation while maneuvering the flask to wet the entire neck 

below the stopper. 

2.7.3 Let stand for two minutes then adjust the meniscus to the reference 

graduation line. 

2.7.4 Determine the temperature of the water by putting some in a beaker or test 

tube containing a thermometer. 

2.7.5 Weigh the filled flask and record the Filled Flask mass value. 

2.7.6 Make a duplicate determination. 
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2.7.7 Perform volume calculations as described in Section 3. 

2.8 Calibration of Flasks (To Deliver) 

2.8.1 Clean but do not dry flask. 

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

below the reference graduation while maneuvering the flask to wet the 

entire neck below the stopper. 

2.8.3 Let the flask stand for two minutes, then adjust the meniscus to the 

reference graduation line, then weigh the full vessel, with cap or stopper. 

2.8.4 Empty the flask over a 30-second period by gradually inclining it so as to 

avoid splashing. When the main drainage has ceased, hold the flask in 

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

touch off the drop of water adhering to the top of the flask. 

2.8.5 Place a stopper or cap on the flask and reweigh. 

2.8.6 Make a duplicate determination. 

2.8.7 Calculate the volume of the flask as described in Section 3. 2.9 Calibration of Other Volumetric Glassware. 

2.9.1 Measuring Pipets - Calibrate in a manner similar to that used to calibrate 

burets (2.5). 

2.9.2 Graduated Cylinders - Calibrate in a manner similar to that used for flasks 

(2.7, 2.8). 

 

3 Calculations 

 

3.1 Calculate the volume at 20 °C from the weight of water, contained or delivered, 

for each run, as follows: 

[ 1 ( 20)] ( )

1

20 ( )( ) 1 t V I I Q 

B w a

a

L E ⎥ − −

⎦

⎤ ⎢

⎣

⎡

− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − − α

ρ ρ ρ

ρ
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Table 2. Variables for volume equation 

Variable Description 

 IL - IE the difference, in grams, obtained from the balance indications 

associated with the loaded vessel and the empty vessel. 

Q 

the apparent mass correction factor defined by the expression 

( )

( ) .0012

0.0012

20

20

−

− =

B

B

D

D Q

ρ

ρ

where ρB is the density of the balance weights in g/cm3, 0.0012 is the 

density of normal air in g/cm3 and D20 is the apparent mass to which 

the weights are adjusted. The factor has a maximum value of 

1.000013 so it may be considered as unity for most calibrations. 

ρB density of the balance weights in g/cm3

ρw density of water at the temperature of measurement in g/cm3

ρa density of air at the conditions of calibration in g/cm3

 α the thermal cubical coefficient of expansion for the vessel being 

calibrated (in per degree units that match temperature units) 

t water temperature of calibration, °C 

3.2 Air density should be calculated using formula provided in SOP 2. Water density 

should be calculated as described in GLP 10. Look up the cubical coefficient of 

expansion for the vessel material in NIST IR 6969, Table 9.10 or obtain it from 

the manufacturer. Calculations of these intermediate values are preferred. 

However, values for the density of water and air, and for the cubical coefficient of 

expansion may be found in Tables 9.8, and 9.9 in NISTIR 6969. These values are 

used in connection with equation 3.1. 

3.3 Calculate the average volume at 20 °C. If a reference temperature other than 

20 °C is needed, the equation provided in 3.1 must be appropriately modified. 

4 Measurement Assurance 

4.1 Duplicate the process with a suitable check standard (See GLP 1, SOP 30, and 

NISTIR 6969, Sec. 7.4) 

4.2 Plot the check standard value and verify that it is within established limits OR a ttest may be incorporated to check the observed value against an accepted value. 

4.3 The mean of the check standard is used to evaluate bias and drift over time. 

4.4 Check standard observations are used to calculate the standard deviation of the 

measurement process, sp. 

5 Assignment of Uncertainty 

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

the mass standards used, us, plus the uncertainty of measurement, sp, at the 95 percent 
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level of confidence. See SOP 29 for the complete standard operating procedure for 

calculating the uncertainty. 

5.1 The standard uncertainty for the standard, us, is obtained from the calibration 

report. The combined standard uncertainty, uc, for the standard 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. 

5.2 Standard deviation of the measurement process from control chart performance 

(See SOP 17 or 20.). 

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

estimated based on the range of duplicate measurements over time. This value 

will incorporate a repeatability factor related to the precision of the weighings and 

the setting of the meniscus, but not related to the uncertainty of internal weights 

in the balance or errors in reading the meniscus. 

5.3 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 standards used, improper observance of drainage times, viscosity or 

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

and the lack of internal cleanliness. 

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, (2006).