Percentage calculator: four modes, with the reverse one people miss

Type your numbers above and the answer appears as you go: 20% of 150 is 30, 30 is 20% of 150, 200 increased by 15% is 230, and a total of 345 after a 15% increase started at 300. The four modes cover the questions people actually ask, including the one that trips almost everyone: undoing a percentage increase is division, not subtraction.

What each mode does

X% of Y takes a portion of a number. Ask for 20% of 150 and you get 30; ask for 150% of 40 and you get 60, because a percentage can be larger than the whole.

A as a percentage of B tells you how big one number is relative to another. 30 as a share of 150 is 20%.

Percentage change measures how far a number moved from its starting point. Going from 80 to 100 is a 25% increase.

Reverse an increase works backwards from a final figure to the original. A total of 345 that already includes a 15% increase started at 300.

The mode people need without knowing it

Say a price rose by 23% and now reads 123. To find what it was before, you divide by 1.23, which gives 100. This is the mode people reach for last and need most.

The tempting shortcut is to subtract 23% from 123. That gives 94.71 — and it is wrong. Subtracting 23% takes 23% of the larger, post-increase figure, but the original increase was 23% of the smaller, pre-increase figure. The two percentages are slices of different totals, so they never cancel out. The same logic recovers any starting value: a price of 60 after 20% off began at 75, because you divide 60 by 0.8 rather than adding 20% back.

Reading percentage change

Direction changes the number, because the starting point is the base you measure against. From 80 to 100 is a 25% increase: the 20-point gain is measured against 80. But from 100 to 80 is a 20% decrease: the same 20-point gap is now measured against 100. Same two numbers, different base, different percentage.

This asymmetry has real consequences. If a value drops 20% from 100 to 80, it needs a 25% rise to get back to 100 — not another 20%. A 50% fall needs a 100% rise to recover, because you are climbing back from a smaller base. If you want a single figure that treats both numbers even-handedly, the percentage difference between 80 and 100 — measured against their average — is 22.22%, and it reads the same whichever number you start from.

Method note

This is plain arithmetic, done live in your browser as you type. There is no server call, no account, and no stored history. Nothing you enter leaves the page, and refreshing clears it. The percentage-change mode and the reverse mode are separate on purpose, because a percentage change and its reversal are different sums — one multiplies, the other divides — and merging them is exactly where the 94.71 error comes from.