The formula for percentage increase, with worked examples and common pitfalls including the asymmetry trap.
percentage increase = (new − old) ÷ old × 100Or equivalently: new ÷ old × 100 − 100.
(75 − 50) ÷ 50 × 100
= 25 ÷ 50 × 100
= 0.5 × 100
= 50%A 50% increase took 50 up to 75.
new = old × (1 + P ÷ 100)A 50% increase on 50: 50 × 1.50 = 75.
A 50% increase followed by a 50% decrease does NOT return to the start:
50 → 75 (+50%)
75 → 37.5 (−50% from 75)To return from 75 back to 50, you only need a 33.3% decrease. This is why percentage change is direction-sensitive.
If something rises from 5% to 7%:
Both are correct ways to describe the change.
(new − old) ÷ old × 100. The result is positive for increases, negative for decreases. To apply an increase, multiply by (1 + P/100).
Almost — percent change is the broader term that includes both increases (positive result) and decreases (negative result). Percentage increase is the specific case where the result is positive.
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