The percentage change formula
1
Formula
(New − old) ÷ old × 100.
2
Increase
From 80 to 100: (100 − 80) ÷ 80 = 25% increase.
3
Decrease
From 100 to 80: (80 − 100) ÷ 100 = 20% decrease. The two percentages differ.
Common mistakes
Divide by the old value: Percentage change is always relative to the old value.
Up then down: +50% then −50% doesn’t bring you back: 100 → 150 → 75.
Percentage points: From 4% to 5% is one percentage point, but a 25% change.
Pay rise: From 8,000 to 8,600 is a 7.5% rise.
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FAQ
How do I work out a pay rise percentage?
Subtract the old pay from the new, divide by the old and multiply by 100: 600 ÷ 8,000 = 7.5%.
How do I calculate a percentage decrease?
Same formula; the result is negative, meaning a decrease.
Why can’t the old value be zero?
Dividing by zero is undefined; growth from zero has no percentage.