# Using & Understanding a Calibration Certificate

When a measuring instrument is sent to be calibrated, it is returned to the user with a calibration certificate. But what exactly is a calibration certificate? What information does it tell us? And how is this information used?

### What is calibration?

In order to understand a calibration certificate, we must first be familiar with what the term ‘calibration’ means. The BIPM defines ‘calibration’ as the

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

This is a slightly cumbersome definition, but in simple terms ‘calibration’ can be defined as

the process which establishes, under specific conditions, the relationship between the values of quantities indicated by a measurement instrument and the corresponding certified values of standards – accompanied by an associated statement of uncertainty.

A ‘calibration’ takes a measuring instrument and uses it to measure a known quantity (be this a mass, temperature, length, density, pressure etc.) whose value is traceable to international standards (and certified as such).

#### Density Calibration

To use an example from our own field, to calibrate a density meter one would take a certified density standard, put it into the density meter, and note the result. If the value of the standard was, say 998.200kg/m³, and the value indicated by the density meter was 998.305kg/m³, we would know that the meter was +0.095kg/m³ adrift from reality.

#### Calibration Certificate

Once a calibration has been performed, the results are summarised in a calibration certificate.

## What is a calibration certificate?

A calibration certificate is a statement of the results of a calibration. It also contains information about the laboratory which carried out the calibration, and about the calibration method used.

For ISO 17025 accredited calibrations, the form of the calibration certificate is standardised, meaning that regardless of the type of instrument being calibrated, or the laboratory performing the calibration, the resultant certificate will be in a widely recognisable format.

The diagram below explains the different elements of the calibration certificate.

### Using a calibration certificate to apply a calibration correction

The calibration certificate tells us the ‘calibration correction’ (ie. the number that must be added to the indicated value to obtain the true value) displayed by the instrument and the certified value of the standard) at a number of different points across the instrument’s range. The calibration correction is equal to the difference between the value displayed by the instrument during calibration, and the certified value of the standard.

This means that if a test sample being measured has a similar indicated value to that of a given calibrant, then it is reasonable to assume that the calibration correction which applies to that particular calibrant also applies to the sample being measured.

### Using a calibration certificate – Worked example 1

With reference to the example certificate 12345 as shown above. Let us say that we are using the density meter to measure the density of a sample ‘A’, and the instrument shows an indicated density of 0.6870g/cm³. This value is very close to the 2,2,4-trimethylpentane calibration point. Therefore we can assume that the correction which applies to 2,2,4-trimethylpentane can also be applied to sample ‘A’. Therefore to calculate the true density of sample ‘A’, we take the indicated value (0.687g/cm³), and apply the relevant correction (+ 0.0003g/cm³). Therefore the true density of sample ‘A’ is 0.6870 + 0.0003 = 0.6873g/cm³

### Using a calibration certificate – Worked example 2

We have seen how to apply a calibration correction when the indicated value is near to one of the calibration points stated on the certificate. But what do we do when the indicated density of a sample is not particularly near any of the calibration points on the certificate? The answer is that we can use the data on the calibration certificate to interpolate between the calibration points and determine a correction at the density we require. This is done by drawing a graph of indicated density vs correction.

Consider the following example certificate, which shows the results of a three point density calibration performed on a bench top density meter at a nominal 20°C. The density meter has been set to read in kg/m³.