Percentage Change Formula

Percentage change measures a change relative to where you started.

Formula

% change = (new − old) ÷ |old| × 100

new
the later value
old
the original value (not zero)

A positive result is an increase, a negative result a decrease.

Examples

Rent rises from 1,200 to 1,290

  1. Change: 90
  2. 90 ÷ 1,200 = 0.075

+7.5%

Visitors fall from 5,000 to 4,100

  1. Change: −900
  2. −900 ÷ 5,000 = −0.18

−18%

Chaining changes

Successive percentage changes multiply rather than add. A 20% rise followed by a 20% fall gives 1.2 × 0.8 = 0.96 — a 4% net fall. To find the single equivalent change, multiply the growth factors (1 + p₁)(1 + p₂)… and subtract 1.

Reversing a change

original = new ÷ (1 + p ÷ 100)

If a price after a 25% increase is 150, the original was 150 ÷ 1.25 = 120 — not 150 minus 25%.