Percentage Increase Calculator
Find the percentage increase between two values, or apply an increase to a starting figure. The working is shown so you can check the result.
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Percentage increase
+25%
- Absolute change
- 20
- From
- 80
- To
- 100
((100 − 80) ÷ 80) × 100 = +25%
The formula
Percentage increase measures growth relative to the starting value. Subtract the old value from the new one, divide by the old value, and multiply by 100.
Dividing by the old value is the part people get wrong. Dividing by the new value gives a different, smaller number that answers a different question.
Increase % = ((New − Old) ÷ Old) × 100
- From 80 to 100 → ((100 − 80) ÷ 80) × 100 = +25%
- From 100 to 250 → ((250 − 100) ÷ 100) × 100 = +150%
- Doubling is always a 100% increase, not 200%.
Why percentage changes do not cancel out
A 20% rise followed by a 20% fall does not return you to the start. 100 rises to 120, then falls by 20% of 120 — which is 24, not 20 — leaving 96.
The reason is that each percentage is taken of a different base. To undo a 20% increase you need a 16.67% decrease; to undo a 50% loss you need a 100% gain. This asymmetry is behind a great deal of misleading statistics.
100 → +20% → 120 → −20% → 96
Percent versus percentage point
When the quantity is itself a percentage, the two are different. A rate moving from 2% to 3% has risen by one percentage point, but by 50% in relative terms.
Both statements are true and they describe very different magnitudes, which is why the distinction matters in reporting on interest rates, unemployment and election polling.
Frequently asked questions
How do I calculate a percentage increase?
Subtract the old value from the new value, divide the result by the old value, then multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%.
Why is doubling a 100% increase and not 200%?
Because the increase is measured against the starting value. Going from 50 to 100 adds 50, and 50 is 100% of the original 50. The new value is 200% of the old one, but the increase is 100%.
Can a percentage increase be more than 100%?
Yes. Any growth beyond doubling exceeds 100%. Going from 10 to 50 is a 400% increase, because the gain of 40 is four times the original value.
What if the starting value is zero?
The percentage increase is undefined, because it would mean dividing by zero. Any growth from nothing is infinite in relative terms, so report the absolute change instead.
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