Steven’s Power Law

Steven’s Power Law, also known as Steven’s Law, is a mathematical principle that describes the relationship between the strength of a physical stimulus and the perceived intensity or magnitude of the resulting sensation.


Steven’s Power Law was first proposed by psychologist Stanley Smith Stevens in 1957. Stevens conducted experiments to investigate how individuals perceive the intensity of various sensory stimuli, such as brightness, loudness, and weight.


According to Steven’s Power Law, the perceived intensity of a stimulus (S) is proportional to the physical magnitude (M) of the stimulus raised to an exponent (b):

S = k * M^b

Where S represents the perceived intensity, M represents the physical magnitude, k is a constant factor, and b is an exponent that characterizes the specific sensory modality being studied.

Exponent Values

The value of the exponent (b) can vary depending on the type of sensory modality being examined:

  • For brightness perception, the exponent (b) is typically around 0.4-0.5.
  • For loudness perception, the exponent (b) is usually around 0.6-0.7.
  • For weight perception, the exponent (b) typically ranges from 1.2-1.5.


Steven’s Power Law has implications for various fields, including psychology, neuroscience, and industrial design. It suggests that our subjective perception of sensory stimuli does not necessarily correspond to their physical properties in a linear manner.

Understanding Steven’s Power Law helps in designing stimuli that accurately evoke desired sensations or experiences, such as creating the right level of brightness for a visual display or adjusting the loudness of an audio system to achieve optimal auditory perception.