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GMP 3 

Good Measurement Practice

for

Method of Reading a Meniscus Using Water or Other Wetting Liquid

1 Meniscus Reading in Calibrations

The meniscus of most liquids used in volumetric calibrations is concave-up, with the lowest 

point in the center that is used to determine the meniscus reading. The curvature of a 

meniscus is related to the surface tension of the liquid and inversely related to the diameter 

of the tubing in which it is formed. When reading any meniscus, it is important to ascertain 

that it is in an equilibrium position. Tapping of sight glasses and/or small motions of 

containers may be used to induce slight displacements of the meniscus. Return to the same 

reading is evidence of a stable meniscus.

The meniscus formed by a non-wetting liquid, such as mercury (Hg), is convex with the 

highest point in the center and is no longer regularly used for volumetric calibrations. In 

the case of a convex meniscus, the highest point is used to make the reading. The reading 

of a mercury barometer or thermometer is a classic example of this kind.

In all apparatus where the volume is defined by a concave-up meniscus, the setting or 

reading is made on the lowest point of the meniscus. In order that the lowest point may be 

observed, it is necessary to place a shade of some dark material immediately below the 

meniscus, which renders the profile of the meniscus dark and clearly visible against a light 

background. A convenient device for this purpose is a collar-shaped section of thick black 

rubber tubing, cut open at one side and of such size as to clasp the tube firmly. 

2 Types of Meniscus Readers

Several types of meniscus readers are available. These include black/white meniscus card 

readers, magnifying glasses with cross-hairs, and collar shaped tubes that may be placed 

around the graduated neck of the volumetric container. Black/ white meniscus card readers 

are simple to create as shown in the figure below. 

This type of meniscus reader is generally preferred for the Option A method of reading the 

meniscus. More elaborate card readers may be purchased that allow placement around the 

neck of a flask.

Figure 1. Example meniscus reader.
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Another type of meniscus reader consists of a clear lens (plastic or glass) with etched lines 

on the front and back that are aligned to prevent parallax errors in reading. This type may 

or may not include magnification. This type of reader is preferred for Option B.

3 Methods for Meniscus Reading

Two common methods are used for setting and visually reading a meniscus: Options A and 

B. The method used in calibration should be consistent with the intended use of the 

volumetric standard. For interlaboratory comparisons, the method to be used should be 

defined during the planning stages of the comparison. The width of the graduation on the 

neck scale will affect the readability of the meniscus and should be estimated to the nearest 

1/10 of a division when using either Option A or Option B.

Option A

Option A is suitable when graduation lines extend more than 75 percent of the 

circumference of the sight gage area, for example with graduated neck type flasks 

or single mark flasks.

The position of the lowest point of the meniscus with reference to the graduation 

line is such that it is in the plane of the middle of the graduation line. This position 

of the meniscus is obtained by making the setting in the center of the ellipse formed 

by the graduation line on the front and the back of the tube as observed by having 

the eye slightly below the plane of the graduation line. This is illustrated below. 

The setting is accurate if, as the eye is raised and the ellipse narrows, the lowest 

point of the meniscus remains midway between the front and rear portions of the 

graduation line. By this method it is possible to observe the approach of the 

meniscus from either above or below the line to its proper setting. 
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Figure 2. Front and side view of reading a meniscus (Option A).

Option B

Option B, is typically used with opaque liquids or when the graduation mark does 

not extend around the circumference of the volumetric standard. (Option B is also 

referenced in several ISO and OIML standards for glassware, thus it is important 

to review meniscus reading practices with the user.) 

In setting the meniscus or taking a reading, the observer's eye should be normal to 

and in the same horizontal plane as the meniscus. The illumination is adjusted to 

get a sharp definition of the meniscus. Elimination of parallax error is very 

important and can be judged by slight fluctuations of eye level that do not affect 

the reading.

The position of the lowest point of the meniscus with reference to the graduation 

line is horizontally tangent to the plane of the upper edge of the graduation line. 

The position of the meniscus is obtained by having the eye in the same plane of the 

upper edge of the graduation line as shown below. Offsets from reading in the same 

plane will produce parallax errors. 

Front Side of Index Line

Meniscus Surface

Rear Side of 

Index Line

FRONT VIEW

Observer’s View from Slightly Below the 

Horizontal Level of the Graduation Line.

SIDE VIEW

Exaggerated Curvature 

Meniscus Surface

Circumferential 

Graduation Line

Line-of-Sight to Front 

Side of Index

Observer’s Eye

Line-of-Sight to Rear 

Side of Index Line-of-Sight to 

Meniscus

Black Rubber Opaque Screen Placed a 

Fraction of a Millimeter Below the 

Graduation Line (or a Card Reader with the 

Black Side on the Bottom.)
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Comparison of Option A and Option B Methods 

For most practical applications, the difference between these two methods is 

insignificant compared to the tolerances of the volumetric standards. However, a 

component for measurement uncertainty should be included as appropriate. When 

performing calibrations, using the glassware as precision standards with clear 

liquids, or when comparing results among laboratories the difference in meniscus 

setting is directly related to the visible thickness of the meniscus and the volume of 

liquid contained in the neck between the top of a graduation line and the middle of 

the graduation line as shown in the following diagram as 1) which results with 

Option B when clear liquids are used and 2) which results with Option A and is 

only possible when clear liquids are used. 

When opaque liquids are used, an additional error or correction factor based on the 

volume contained between the upper and lower edges of the meniscus may need to 

be considered. The curve of the meniscus and impact of this error is dependent on 

the diameter of the meniscus and surface tension of the liquid being used. 

4 Uncertainty and Error Analysis in Meniscus Readings

The standard deviation of replicate meniscus readings of volumetric measures provides an 

estimate of precision that can be used in the uncertainty analysis. However, potential errors 

in reading a meniscus may be caused by poor eye alignment, using Option A or B, by lack 

of cleanliness on material surfaces, by variations in visual acuity, by lighting, using 

cameras or other optical tools, and by the thickness of the graduation line and 

characteristics of the meniscus itself. Repeatability, or precision, provides an estimate of 

the process variability, but the potential errors may result in systematic inaccuracies or 

biases. 

Potential systematic errors (inaccuracies) in meniscus readings are included as an 

uncertainty component in volume calibrations. An estimate of the meniscus error and 

variability may be captured as part of the process standard deviation only when multiple 

staff perform measurements where a check standard is maintained. Potential systematic 

Observer’s Eye Graduation Line

Graduation Line

Graduation Mid

Figure 3. View of reading the meniscus (Option B).

Figure 4. Comparison of Option A (left) and Option B (right) with visible meniscus location.
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variability is not captured using standard deviation or range charts alone because the 

process for each person may be repeatable, but accuracy of meniscus reading cannot be 

assessed without using a check standard or making special efforts to capture meniscus 

reading differences among staff.

“Precision” in the following graphic illustrates the repeatability of the measurement 

process and “Accuracy” demonstrates the possible systematic inaccuracy of the mean value 

versus a reference value, due to uncorrected errors. 

The sensitivity of the volume measurement to the meniscus reading uncertainty may be 

calculated using the equation for the volume of a cylinder and the neck diameter.

2 Vol r h = π where r is the radius of the internal diameter and h is the height of the line or 

meniscus reading uncertainty. Units will be determined based on the dimensional units that 

are used. For example, radius in cm2 and height in cm, will provide results in cm3 or mL. 

The meniscus itself often has an observed “thickness” that is larger than the graduation 

lines, so this should be considered as well. The potential error in meniscus reading is 

usually treated as a triangular distribution.

Example for a Glass Flask

If the internal diameter of a flask is 1.5 cm (15 mm) and the 

height of the graduation line is 0.50 mm, the volume associated 

with the line can be calculated as follows: 15 2 ( ) 0.5 2

Vol = π = 

88.36 mm3 (0.088 mL). 

These values are rounded for illustrative purposes only; 

significance must be evaluated based on measuring 

instruments and flask resolution. Experimental data 

obtained by reading a meniscus 

among multiple laboratory staff 

Figure 5. Accuracy and precision in meniscus reading.

Figure 6. Meniscus error 

analysis for a glass flask.
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members may also be used to incorporate an estimate of uncertainty in meniscus 

reading. 

Example for a Test Measure or Prover

In a test measure or prover, the volume inside the gauge also represents the volume 

inside the neck. So, two volumes can be calculated and added together to determine 

the impact. 

If the internal diameter of the gauge tube 

is 13 mm (0.5 in) and the height of the 

graduation line is 0.50 mm, the volume 

associated with the line inside the gauge 

tube can be calculated as follows: 

13 2 ( ) 0.5 2

Vol = π = 66.4 mm3

(0.066 mL). This amount alone is 

generally not readable on the test 

measure or prover. But, the equivalent 

amount of volume that this gauge tube 

volume represents in the neck (given a 3 

in neck) can be calculated as follows: 

76.2 2 ( ) 0.5 2

Vol = π = 2.28 mL. These 

two volumes are added together, giving a 

sum of 2.346 mL, or about 0.143 in3. In 

the case of a 5 gal test measure, the 

typical calibration uncertainty is about 0.35 in3, 

so this potential error is significant. 

Using the example for the test measure or prover, and a triangular distribution, two 

examples for estimating the uncertainty of meniscus reading are shown. The values 

are based on the estimate of error in reading the meniscus, em. When the pooled 

standard deviation of the process is less than the calculated triangular distribution 

estimates, use the calculated values shown below as a minimum value. Note that 

this value is unrelated to graduation size.

Estimate 1, with multiple staff and check standard available:

1 3 3 0.20 0.143 in 0.0286 in

2 6 me =× = Eqn. (1)

Estimate 2, in a one person lab or with no check standard available:

1 3 3 0.41 0.143 in 0.05863 in

6 me =× = Eqn. (2)

Figure 7. Meniscus error analysis for 

a test measure or prover.
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These values are rounded for illustrative purposes only; actual significance must be 

evaluated based on measuring instruments and resolutions. Experimental data 

obtained by reading a meniscus among multiple laboratory staff members may also 

be used to incorporate an estimate of uncertainty in meniscus reading provided the 

examples and assessments are fully documented. 
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