How do I calculate a percentage increase?

Subtract the old value from the new one, divide by the old value, and multiply by 100. Going from 200 to 230 is (30 ÷ 200) × 100 = 15%.

Why does a 50% rise then a 50% fall not cancel out?

Because the fall is applied to the larger number. 100 rises to 150, then 50% of 150 is 75 — so you end at 75, not 100.

Percentage Calculator

Find a percentage of a number, work out what percentage one number is of another, or calculate percentage change.

Draft — figures checked, awaiting an editorial read. Not indexed.

Result—

Direction: —
Absolute change: —

Formula: X% of Y = (X ÷ 100) × Y. X as a percentage of Y = (X ÷ Y) × 100. Change from A to B = ((B − A) ÷ |A|) × 100.

What this calculates

This handles the three percentage questions that actually come up, which are genuinely different calculations even though people describe all of them as "working out a percentage". The first is finding a portion of a number — 15% of 200. The second is expressing one number as a proportion of another — 30 out of 200 is what percent. The third is percentage change between two values, which is the one most often got wrong because it depends on which number you treat as the starting point.

How it works

Finding A% of B divides A by 100 and multiplies by B. Expressing A as a percentage of B divides A by B and multiplies by 100 — note the reversal, which is why the two get confused. Percentage change subtracts the starting value from the ending value, divides by the absolute value of the starting value, and multiplies by 100. Using the absolute value of the base matters when the starting figure is negative, where a naive formula flips the sign of the answer and reports a rise as a fall.

Worked example

15% of 200 is (15 ÷ 100) × 200 = 30. Turning it around, 30 is what percent of 200? (30 ÷ 200) × 100 = 15%. Now change: going from 200 to 230 is ((230 − 200) ÷ 200) × 100 = 15% increase. But going from 230 back to 200 is ((200 − 230) ÷ 230) × 100 = −13.04%, not −15%. The base changed, so the percentage did too.

Common mistakes

Assuming a percentage increase and the matching decrease cancel out. A 50% rise followed by a 50% fall does not return you to where you started — it leaves you at 75% of the original, because the second percentage applies to a larger base. Second, confusing percentage points with percent: a rate moving from 4% to 6% has risen two percentage points, but that is a 50% increase. Third, averaging percentages that have different bases, which is rarely valid.

Common questions

How do I calculate a percentage increase?: Subtract the old value from the new one, divide by the old value, and multiply by 100. Going from 200 to 230 is (30 ÷ 200) × 100 = 15%.
Why does a 50% rise then a 50% fall not cancel out?: Because the fall is applied to the larger number. 100 rises to 150, then 50% of 150 is 75 — so you end at 75, not 100.