A measuring instrument often produces an indication $r$ that must be related to the physical quantity of interest $x$. Calibration establishes that relationship by comparing the instrument with reference values whose properties are known well enough for the intended measurement.

A simple calibration model is affine: $$r=a+bx.$$ The intercept $a$ represents a zero offset and $b$ the sensitivity or scale factor. Measurements of several reference points allow $a$ and $b$ to be estimated rather than assuming that the nominal instrument response is exact.

Suppose a temperature sensor produces $0.52,\mathrm{V}$ at $0^\circ\mathrm C$ and $2.48,\mathrm{V}$ at $100^\circ\mathrm C$. Assuming a linear response, $$b=\frac{2.48-0.52}{100}=0.0196,\mathrm{V/^{\circ}C}.$$ A later reading of $1.50,\mathrm{V}$ corresponds to $$T=\frac{1.50-0.52}{0.0196}\approx50.0^\circ\mathrm C.$$ The calibration does not merely 'correct' a number: it defines a measurement model whose fitted parameters themselves have uncertainty.

A reference standard provides the comparison value. Traceability means that a measurement result can be related to recognized standards through a documented chain of calibrations, each contributing uncertainty. Traceability does not imply perfect accuracy; it makes the origin and uncertainty of the measurement scale explicit.

Calibration should cover the range and conditions in which the instrument will be used. Extrapolating far beyond calibration points, ignoring hysteresis or temperature dependence, or fitting an unnecessarily complicated curve can all make the numerical correction look more trustworthy than the evidence supports.