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Percentage Increase

Add a percentage to a value, or give two numbers and see the increase between them — in per cent and in absolute difference.

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Why a 50% rise and a 50% fall do not cancel out

Start at 100, add 50%, and you have 150. Take 50% off that and you have 75, not 100. The two percentages are applied to different numbers: the rise was 50% of 100, the fall was 50% of 150. This is the single most common percentage mistake, and it is why "up 50%, then down 50%" leaves you a quarter poorer.

The same asymmetry runs the other way, and it is worse. A value that falls 50% needs a 100% rise to get back. Fall 80%, and you need 400%. That is why a portfolio down 30% is not fixed by a 30% recovery — it needs about 43%.

A rise is applied by multiplying: +15% means × 1.15. That is also how you compound several rises — three consecutive 10% increases multiply to 1.1 × 1.1 × 1.1 = 1.331, a 33.1% rise, not 30%.

Frequently asked questions

How do I calculate a percentage increase between two numbers?

Subtract the old value from the new one, divide by the old value, and multiply by 100. From 40 to 44: (44 − 40) ÷ 40 × 100 = 10%. The denominator is always where you started — dividing by the new value answers a different question.

What is the difference between per cent and percentage points?

If a rate moves from 40% to 44%, that is a rise of four percentage points and of ten per cent. Both are correct and they are not interchangeable. The calculator above shows both, because reports that mix them up are the source of a great deal of confusion about interest rates and polls.

How do I add several increases together?

You multiply them, you do not add them. Two 10% increases give 1.1 × 1.1 = 1.21, so 21% — not 20%. The extra one per cent is the second increase applying to the first increase.

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