Instrumentation calibration is the operation to obtain under specified conditions, the relationship between the values of a measurand and the corresponding output indications of the instrument in calibration.


By calibration we mean

  • according to ISO-IMV (International Metrology Vocabulary): “operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication”;
  • or we could deduce the following practical example from the previous one:  “operation performed to establish a relationship between the measured quantity and the corresponding output values of an instrument under specified conditions”.

Calibration should not be confused with the adjustment, which means: “set of operations carried out on a measuring system so that it provides prescribed indications corresponding to given values of a quantity to be measured (ISO-IMV);

Hence, the adjustment is typically the preliminary operation before the calibration, or the next operation when a de_calibration of the measuring instrument is found.

Calibration should be performed on 3 or 5 equidistant measuring points for increasing (and decreasing) values in the case of instruments with hysteresis phenomena: eg manometers):

Figure 1 presents the calibration setup, while Table 1 presents the calibration results.

Manometer setup calibration
Manometer setup calibration

Figure 1 – Calibration setup of a manomete








Relieved Values


Relieved Errors


















0 0.05 0.05  




2 1.95 2.05 – 0.05 0.05
4 3.95 4.05 – 0.05 0.05
6 5.95 6.00 – 0.05 0.00
8 7.95 8.00 – 0.05 0.00
10 10.00   0.00
Table 1 – Calibration Results

From the calibration results shown in Table 1, the metrological characteristics of the manometer     (or pressure gauge) can be obtained in terms of:

  • Measurement Accuracy: that is, maximum positive and negative error: ± 0.05 bar
  • Measurement Uncertainty: or instrumental uncertainty that takes into account the various factors related to the calibration, namely:

Iref    Uncertainty of the reference standard                  0.01 bar (supposed)

Emax  Max error of measurement relieved                       0.05 bar

Eres  Error of resolution of the manometer                     0.05 bar

from which the composed uncertainty uc can be derived from the following relation:

Instrument calibration formula

and then the extended uncertainty (U), at 95% confidence level (ie at 2 standard deviations):


Calibration formula instruments 


Obviously, the measurement uncertainty of the manometer (usually called instrumental uncertainty) is always higher than the measurement accuracy (because it also takes into account the error of resolution of the instrument in calibration and the uncertainty of the reference standard used in the calibration process).


Author: Eng. Alessandro Brunelli

Book: Manuale di Strumentazione