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What do "tolerance, accuracy, coefficient of variation, and precision" mean in volumetric measurements?

Graphic illustration of precision and accuracy

The dart board simulates the volume range around the centred nominal value, the white dots simulate the different measured values of a specified volume.

Accuracy 1

Good accuracy: All hits are near the centre, i.e., the nominal value.

Good precision: All hits are close together.

Result: The manufacturing process is well controlled by an accompanying quality assurance program. Minimal systematic deviations and a narrow variance in products. The permissible limits are not exceeded. There are no rejects.

Accuracy 2

Good accuracy: On average, the hits are evenly distributed around the centre.

Poor precision: No substantial errors, but hits widely scattered.

Result: All deviations are "equally probable". Instruments exceeding the permissible tolerance should be rejected.

Accuracy 3

Poor accuracy: Although all hits are close together, the centre (nominal value) is still missed.

Good precision: All hits are close together.

Result: Improperly controlled production, with systematic deviation. Instruments exceeding the permissible tolerance should be rejected.

Accuracy 4

Poor accuracy: The hits are far removed from the centre.

Poor precision: The hits are widely scattered.

Result: These volumetric instruments are of inferior quality.

Calculation formulae

The accuracy of glass volumetric instruments is commonly defined by “Tolerance Limits”, whereas for liquid handling instruments the statistical terms “Accuracy [%]” and “Coefficient of Variation [%]” have been established.


Calculation formulae Tolerance
The term “tolerance” (tol.) in the corresponding standards defines the maximum permissible deviation from the nominal value.


Calculation formulae Accuracy
Accuracy (A) indicates the closeness of measured mean volume to the nominal value, i.e., systematic measurement deviation. Accuracy is de- fined as the difference between the measured mean volume () and the nominal value (Vnom.), related to the nominal value in percent.

Coefficient of Variation

Calculation formulae Coefficient of Variation
The coefficient of variation (CV) indicates the closeness of values from repeated measurements, i.e., random measurement deviation. The coefficient of variation is defined as standard deviation in percent, related to the mean volume.

Partial volumes

Calculation formulae Partial volumes
(analogous to CVT %)
Generally, A and CV are based on the actual volume (Vact.). These data in percent must be converted to partial volumes (Vpart.). By contrast, there is no conversion for partial volumes if A and CV are stated in volume units (e.g. ml).

Tolerance from A and CV

Calculation formulae Tolerance from A and CV

To a good approximation, the tolerance, e.g. for the actual volume (Vact.), can be calculated from the accuracy and coefficient of variation.


If the variance in the individual measurement results about the mean volume is given in units of volume, this relates to precision.