Weber's Law, formulated by Ernst Heinrich Weber in 1834, is one of the oldest and most robust quantitative laws in psychology. It states that the smallest detectable change in a stimulus (the just noticeable difference, or JND) is a constant proportion of the stimulus magnitude. This ratio, known as the Weber fraction (k), remains approximately constant across a wide range of stimulus intensities for any given sensory modality.
The Weber Fraction
The Weber fraction varies across modalities: it is approximately 0.02 for visual length discrimination, 0.05 for lifted weights, 0.08 for sound intensity, and 0.20 for taste (salt concentration). Smaller Weber fractions indicate greater sensitivity to relative changes. The constancy of the Weber fraction across intensities means that our sensory systems are tuned to proportional rather than absolute changes — a fundamental design principle of biological sensors.
ΔI = just noticeable difference (JND)
I = stimulus intensity
k = Weber fraction (modality-specific constant)
Theoretical Significance
Weber's Law served as the foundation for Fechner's Law and, through it, for the entire discipline of psychophysics. Fechner recognized that if the JND is the unit of subjective sensation, and if the Weber fraction is constant, then integration yields a logarithmic relationship between physical intensity and subjective magnitude: S = k·ln(I/I₀). Stevens later challenged this with his Power Law, but Weber's Law remains the starting point for both formulations.
Modern research has shown that Weber's Law breaks down at very low intensities (near absolute threshold) and very high intensities, and that the "near miss to Weber's Law" in many modalities shows a slightly decreasing Weber fraction at high intensities. Nevertheless, as a first approximation, it remains remarkably accurate across an enormous range of conditions and modalities.