The psychophysical laws establish relationships between physical stimuli and the effectorial responses emitted by the subjects; thus, psychophysics establishes the relationship between physical stimuli and perception.

On the other hand, it also studies how external stimuli produce internal responses (subjective experiences), only accessible by the subject himself through introspective processes. In this article we will know the Law of Weber-Fechner , considered the first law of psychophysics.

Background: Weber’s Law

Fechner, a German philosopher, physician by training and professor of physics and philosophy, elaborated a law in psychophysics, specifically the first law of psychophysics , from the use of indirect methods. To do so, he based himself on Weber’s Law and the postulate that establishes the equality of justly perceptible differences.

As for Weber’s Law, it established the concept of WTP (hardly perceptible difference), as the unit of measurement of the differential threshold. According to Weber, WTP depends on the magnitude or intensity of the E (stimulus) , and its mathematical formula is as follows:

DAP = k x S (where “k” is a constant and “S” is the intensity of the stimulus.

However, Weber’s Law was only fulfilled when the stimulus tended to average values; thus, it was true for most of the senses, as long as the stimulus intensity was not very close to the threshold .

Weber-Fechner’s Law: Characteristics

Weber-Fechner’s law establishes a quantitative relationship between the magnitude of a physical stimulus and how it is perceived by the subject. This law was initially proposed by Ernst Heinrich Weber (1795-1878) (German doctor and anatomist) and later elaborated until its current form by Gustav Theodor Fechner (1801-1887), already mentioned above.

This law states that “the smallest discernible change in the magnitude of a stimulus is proportional to the magnitude of the stimulus”. This can be said in many other ways so that we can understand it; for example, that “the intensity of the sensation is proportional to the logarithm of the intensity of the stimulus”, or that “if a stimulus grows in geometric progression, perception will evolve in arithmetical progression”.


To better understand Weber-Fechner’s Law, let’s illustrate it with an example : if we hold a 100 gram ball in our hand, we may not be able to distinguish it from a 105 gram ball, but we can distinguish it from a 110 gram ball. In this case, the threshold to discern the change in mass is 10 grams.

But in the case of holding a 1,000 gram ball, 10 grams will not be enough for us to notice the difference, as the threshold is proportional to the magnitude of the stimulus. Instead, we will need to add 100 grams to notice the difference, for example.

Mathematical Formulation

The mathematical formulation of Weber-Fechner’s Law is as follows

P = k x log (l) = Fechner’s Law

Where “k” is a constant and “l” is the intensity.

Thus, Fechner argues that when the intensity of the stimulus grows according to a geometric progression the sensation grows according to an arithmetic progression (logarithmically).

Previous theories

As far as the history of psychophysics is concerned, and prior to Weber-Fechner’s Law, the first theories formulated were oriented towards the study of stimuli that were difficult to detect (of low intensity); to this end, two notable theories were formulated: the classical theory of threshold and the theory of signal detection (or response threshold theory).

1. Classical Threshold Theory

This theory encompasses and defines two types of thresholds:

1.1. Absolute threshold

This is the minimum amount of energy (E) that an observer can detect .

1.2. Differential threshold

It consists of the smallest difference between two stimuli (EE) that can be detected, or, in other words, the minimum increase in energy necessary for an increase in sensation to be perceived .

2. Signal Detection Theory (TDS) (or response threshold theory)

The TDS dispenses with the concept of threshold and assumes that at any stimulation, the result of the sensory process will consist of a sensation that can take on multiple values.

This theory considers that the sensory system of people is subject to fluctuations , so that the level of sensation can vary when presented with the same stimulus; for example, adopting different values, or, conversely, being identical when presented with different experimental conditions.

Bibliographic references:

  • Norwich, K. (2003). INFORMATION, SENSATION, and PERCEPTION. Biopsychology, University of Toronto
  • Goldstein, E.B. (2006). Sensation and perception. 6th edition. Debate. Madrid