Weber-Fechner Sensation Calculator
Calculate just-noticeable differences using Weber's law and perceived sensation magnitude using the Fechner and Stevens power laws.
Enter stimulus intensity and Weber fraction.
Weber and Fechner established the mathematical relationship between physical stimuli and perceived sensation — the foundation of psychophysics.
Weber’s law (Ernst Heinrich Weber, 1834):
Delta_S = k x S
The just-noticeable difference (JND) is a constant fraction k of the current stimulus S. If you can just detect a 1-gram weight added to a 100-gram load, you need about a 10-gram addition to detect a change in a 1,000-gram load (k = 0.01 for lifted weights). Weber fractions for common senses: brightness ~0.02, loudness ~0.04, weight ~0.02, temperature ~0.15, taste ~0.20.
Fechner’s law (Gustav Fechner, 1860):
psi = k x ln(S / S0)
Perceived sensation psi grows as the logarithm of stimulus intensity relative to the absolute threshold S0. Doubling the intensity does not double the sensation — it adds a constant increment. This explains why a phone screen seems much brighter indoors than outdoors (where background luminance is 1,000x higher).
Stevens’ power law (S.S. Stevens, 1957):
psi = k x S^n
For most senses, the power law fits data better than the logarithmic Fechner law. Exponents n vary by modality: brightness n = 0.33 (compressed), loudness n = 0.67, vibration n = 0.95 (nearly linear), pain n = 1.5 (amplified — a small increase in painful stimulus is felt as a large change).