The Weber fraction is treated as part of an information theoretical view of perception. In this theory of sensory perception, subjective magnitude is related to the information transmissible from stimulus to perceiver. The derived psychophysical law can be approximated as a power or logarithmic law, depending on conditions. The mathematical expression for the Weber fraction is obtained as a derivative of the psychophysical law. One of many interesting relationships derived here is that the product of the Stevens exponent with log10 stimulus range, for many sensory modalities, is equal to the maximum information transmitted per stimulus (in bits, measured in a test of categorical judgments) multiplied by 0.6. This number is a derived constant and is not measured from the data.