Weber Fraction Formula and JND: Worked Examples

Weber's law: the just noticeable difference (JND) is a constant fraction of the starting stimulus. The Weber fraction is k = JND / I, where I is the original intensity.

Formula use

JND = k x I. Heavier or brighter baseline stimuli need a larger change to be noticed.

Worked examples

1. You can just tell 100 g from 102 g. k = 2 / 100 = 0.02. At 500 g the JND is 0.02 x 500 = 10 g.
2. A light must go from 40 to 44 units to be noticed. k = 4 / 40 = 0.10. A 200-unit light needs a 20-unit change.
3. A sound JND is 3 units at 60 units. At 120 units, expect 6.

Where it breaks

Weber's law holds well in the middle of the range and fails near the absolute threshold and at extreme intensities.

Common traps

• Using the new intensity in the denominator. Use the original.
• Thinking JND is constant. The fraction is constant; the JND grows with I.
• Mixing JND with absolute threshold. Absolute threshold is the minimum detectable stimulus.

One-minute recap

• k = JND / I.
• JND scales with the baseline.
• Fails at extremes.