Weber - Fechner law

The Weber-Fechner law characterizes the relationship between the physical intensity of a stimulus acting on a receptor and the subjective perception of intensity (sensation) that this action causes. It is named after the German physician E. H. Weber (1795–1878) and the German psychologist G. Th. Fechner (1801–1887).

The Weber-Fechner law can be mathematically described, for example, by the following relation:


 * $$\mathrm{d}S = k\cdot\frac{\mathrm{d}I}{I}$$

This relation can be modified by solving the relevant differential equation to the known formula:


 * $$S = k\cdot\ln\frac{I}{I_0}$$


 * S – intensity of subjective perception;
 * k – constant;
 * I – the physical intensity of the stimulus acting on the receptor;
 * I0 – threshold intensity, i.e. the absolute lowest possible intensity that an individual is capable of perceiving.

It helps to illustrate the mathematical description if we replace the differential in the first equation with a small change Δ:


 * $$\Delta S = k\cdot\frac{\Delta I}{I}$$

The relationship can then be understood in such a way that a subjectively perceived small change in sensation is directly proportional to a small change in the intensity of the stimulus and inversely proportional to the intensity of the sensation. This means that, for example: The reason for this behavior of the receptors is apparently primarily the fact that a high range of perceived physical intensities and a high discrimination ability at least at low intensities are possible at the same time.