Stevens' Power Law

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Stevens' Power Law calculator computes a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. Stevens' methods are usually applied in global psychophysics, meaning the stimuli would be discriminated correctly with nearly perfect certainty for any population.

INSTRUCTIONS: Enter the following:

(k) Proportionality Constant (based on units used)
(I) Physical Magnitude of Stimulation
(a) Exponent given to I (depends on the type of stimulation)

Magnitude of Sensation (Ψ): The calculator computes the subjective magnitude of sensation.

Stevens' Power Law Exponents (a)
Continuum	Exponent	Stimulus condition
Loudness	0.67	Sound pressure of 3000 Hz tone
Vibration	0.95	Amplitude of 60 Hz on finger
Vibration	0.6	Amplitude of 250 Hz on finger
Brightness	0.33	5° target in dark
Brightness	0.5	Point source
Brightness	0.5	Brief flash
Brightness	1	Point source briefly flashed
Lightness	1.2	Reflectance of gray papers
Visual length	1	Projected line
Visual area	0.7	Projected square
Redness (saturation)	1.7	Red-gray mixture
Taste	1.3	Sucrose
Taste	1.4	Salt
Taste	0.8	Saccharin
Smell	0.6	Heptane
Cold	1	Metal contact on arm
Warmth	1.6	Metal contact on arm
Warmth	1.3	Irradiation of skin, small area
Warmth	0.7	Irradiation of skin, large area
Discomfort, cold	1.7	Whole body irradiation
Discomfort, warm	0.7	Whole body irradiation
Thermal pain	1	Radiant heat on skin
Tactual roughness	1.5	Rubbing emery cloths
Tactual hardness	0.8	Squeezing rubber
Finger span	1.3	Thickness of blocks
Pressure on palm	1.1	Static force on skin
Muscle force	1.7	Static contractions
Heaviness	1.45	Lifted weights
Viscosity	0.42	Stirring silicone fluids
Electric shock	3.5	Current through fingers
Vocal Effort	1.1	Vocal sound pressure
Angular acceleration	1.4	5 s rotation
Duration	1.1	White noise stimuli

The Math

The formula for Stevens' Power Law is as follows:

Ψ = k•I^a

where:

ψ is the Steven's Law magnitude of sensation.
k is a proportionality constant that is based on the units used
I is the physical magnitude of the stimulation
a is the exponent given to I that depends on the type of stimulation

Ψ is the subjective magnitude of the sensation evoked by the stimulus. For your convenience, the corresponding table of exponents that Stevens reported is provided in the table.

Source

The Wikipedia page on Stevens' Power Law is located HERE.

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