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Percentage calculator

Four percentage tools on one page. Each one updates as you type, so you can check a discount, a pay rise or a change in sales without a formula.

What is X% of Y?

Result–

X is what percent of Y?

Percentage–

Percentage change

Change–

Increase or decrease by a percentage

New value–

Percentage formulas

A percentage is a number out of 100. Every tool above uses one of these four formulas.

X% of Y
Result = X ÷ 100 × Y

X is what percent of Y
Percentage = X ÷ Y × 100

Percentage change from A to B
Change = (B − A) ÷ A × 100

Increase or decrease Y by X%
New value = Y × (1 ± X ÷ 100)

Examples you can check

  • Discount: 25% off a 80 jacket is 0.25 × 80 = 20, so you pay 60.
  • Test score: 42 correct answers out of 50 is 42 ÷ 50 × 100 = 84%.
  • Price change: a coffee going from 3.20 to 3.60 is a (3.60 − 3.20) ÷ 3.20 × 100 = 12.5% increase.
  • Pay rise: a 4% rise on a 2,500 monthly salary gives 2,500 × 1.04 = 2,600.

Percentage change vs percentage points

If an interest rate moves from 4% to 5%, it has risen by one percentage point, but by 25% in relative terms, because 1 is a quarter of 4. News reports mix these up often. Use percentage points when you compare two percentages directly, and percentage change when you compare the size of the move.

Why an increase and a decrease don't cancel out

Raise 100 by 20% and you get 120. Lower 120 by 20% and you get 96, not 100. The second percentage is taken from a bigger starting number, so it removes more. To undo a 20% increase you need a decrease of about 16.67%, which you can confirm with the percentage change tool.

Quick mental shortcuts

10% of any number is the number divided by 10. 5% is half of that, and 1% is the number divided by 100. Percentages also swap around: 8% of 50 is the same as 50% of 8, which is 4. That trick makes many calculations easy to do in your head.

Frequently asked questions

How do I work out a percentage of a number?

Divide the percentage by 100 and multiply by the number. 15% of 240 is 0.15 × 240 = 36.

How do I calculate a percentage increase?

Subtract the old value from the new value, divide by the old value and multiply by 100.

What is the formula for percentage decrease?

It is the same as percentage change. The result is negative, which shows a decrease.

Can a percentage be more than 100?

Yes. If sales grow from 50 to 150, that is a 200% increase. A part of a whole, though, can't be more than 100%.

Why does the percentage change tool show an error when I start from zero?

Any change from zero is infinitely large in percentage terms, so it can't be expressed as a percentage.

Last reviewed on by the Dailycaltor team.