Ladabo

Percentage Calculator

All four percentage questions, answered at once.

Results update as you type. Nothing is sent anywhere.

First as a percentage of second —
First % of second —
Change from first to second —
Second increased by first % —
Second decreased by first % —
First plus first % of itself —

How this is worked out

Most percentage pages make you choose a mode from a dropdown before you can see anything. There are only four common questions, so this page answers all of them from the same two numbers and lets you read off the one you wanted.

With A = 25 and B = 200:

Question Sum Answer
What percentage of B is A? 25 ÷ 200 × 100 12.5%
What is A% of B? 25 ÷ 100 × 200 50
What is the change from A to B? (200 − 25) ÷ 25 × 100 +700%
B increased by A% 200 × 1.25 250
B decreased by A% 200 × 0.75 150

The one that trips people up is percentage change, because it depends on which number you start from. Going from 25 to 200 is a 700% increase. Going from 200 back down to 25 is an 87.5% decrease. Same two numbers, very different percentages, because the base changed.

A worked example

A price rises from 80 to 100.

Enter A = 80, B = 100. The change reads +25%.

Now the price falls from 100 back to 80. Enter A = 100, B = 80. The change reads −20%.

A 25% rise followed by a 20% fall returns you exactly where you started. This is why a stock that drops 50% needs to rise 100% to recover, and why "up 30% then down 30%" leaves you down 9%, not level. Percentage moves do not cancel out, because each one is measured against a different base.

What this doesn't cover

  • Percentage change is undefined when the starting number is zero — there is nothing to measure against. The field shows a dash in that case.
  • The difference between percent and percentage point matters in news and finance. A rate going from 4% to 5% has risen by one percentage point, but by 25 per cent. Both statements are true and they mean different things.

Common questions

How do I add tax or a tip to a bill?

Put the percentage in the first box and the bill in the second, then read the "increased by" line. For 19% on 84.50, enter 19 and 84.50 to get 100.56.

How do I work backwards from a price that already includes tax?

Divide rather than subtract. A price of 119 including 19% tax was 119 ÷ 1.19 = 100 before tax. Subtracting 19% from 119 gives 96.39, which is wrong — a mistake worth knowing about, because it appears on a lot of invoices.

Two discounts of 20% and 10% — is that 30% off?

No, it is 28%. The second discount applies to the already-reduced price: 0.8 × 0.9 = 0.72. Stacked discounts are always worth slightly less than their sum.

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