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Percentage calculator

Choose the kind of percentage question, enter the two numbers, and read off the answer with the working. Six calculations cover almost every percentage problem, from a tip to a price before tax.

15% of 80 12
Result12
As a decimal multiplier× 0.15
The other 85%68
80 + 15%92

15%: 12 (15%)   rest: 68 (85%)

Show the working, step by step

  1. Percent means “per hundred”, so turn the percentage into a decimal by dividing by 100.

    15% = 15 ÷ 100 = 0.15

  2. Multiply the number by that decimal.

    0.15 × 80 = 12

Shortcut: X% of Y equals Y% of X, so 15% of 80 is the same as 80% of 15.

The formulas

QuestionFormulaDefault example
What is X% of Y?X ÷ 100 × Y15% of 80 = 12
X is what % of Y?X ÷ Y × 10018 of 72 = 25%
Change from X to Y(Y − X) ÷ |X| × 100250 → 310 = +24%
Y increased by X%Y × (1 + X ÷ 100)1,200 + 8% = 1,296
Original before an X% risefinal ÷ (1 + X ÷ 100)126 after +20% → 105
Percentage difference|X − Y| ÷ ((X + Y) ÷ 2) × 10040 and 60 → 40%

“Per cent” means per hundred, so every formula either divides by 100 to turn a percentage into a decimal, or multiplies by 100 to turn a decimal into a percentage.

A worked example

The calculator opens on 15% of 80. Divide 15 by 100 to get 0.15, then multiply: 0.15 × 80 = 12. The other 85% is 68, and 80 increased by 15% is 92.

Multipliers make chains easy

An increase of 8% is the same as multiplying by 1.08; a decrease of 8% is multiplying by 0.92. Thinking in multipliers helps with several changes in a row: a price that rises 10% and then falls 10% ends at 1.10 × 0.90 = 0.99 of where it started, a 1% loss, not zero. It also explains reverse percentages: to undo “× 1.20” you divide by 1.20.

Which number is the base?

Nearly every percentage mistake comes from dividing by the wrong number. The base is the value the percentage is “of”: the old value for a change, the whole for a share, the original price for a discount. When a question says “a 20% increase gave 126”, the base is the unknown original, not 126.

Percentages, fractions and decimals

PercentageDecimalFraction
1%0.011/100
12.5%0.1251/8
20%0.21/5
25%0.251/4
33.33…%0.333…1/3
75%0.753/4
150%1.53/2

Knowing a few of these makes mental estimates quick: 25% of 72 is a quarter of 72, which is 18, the reverse of the “18 is what percent of 72?” example.

Common mistakes

  • Subtracting the percentage to reverse it. 126 − 20% = 100.8, but the original was 105.
  • Adding successive percentages. +10% then +10% is +21%, not +20% (1.1 × 1.1 = 1.21).
  • Dividing by the new value for a change. 250 → 310 is +24% of 250, not 60 ÷ 310 = 19.35%.
  • Mixing up percent and percentage points. See the FAQ below.

Common questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply: 15% of 80 = 0.15 × 80 = 12. A handy check is that X% of Y equals Y% of X, so 15% of 80 is also 80% of 15, which is 12.

How do I work out a percentage increase or decrease?

Subtract the old value from the new one, divide by the old value, and multiply by 100. From 250 to 310: (310 − 250) ÷ 250 × 100 = 24%, an increase. A negative answer is a decrease.

Why is a 24% rise not undone by a 24% fall?

Because each percentage is taken of a different base. 250 up 24% is 310, but 310 down 24% is 235.6. To get back from 310 to 250 you need a fall of 60 ÷ 310 = 19.35%.

How do I find the original price before a percentage change?

Divide by the multiplier rather than subtracting the percentage. If a price is 126 after a 20% rise, the original is 126 ÷ 1.20 = 105. Taking 20% off 126 gives 100.8, which is wrong because the 20% was 20% of 105, not of 126. The same applies to removing sales tax or VAT from a price.

What is the difference between percentage change and percentage difference?

Percentage change measures from a starting value: 40 to 60 is a 50% increase. Percentage difference compares two values with neither as the base, dividing by their average: |40 − 60| ÷ 50 = 40%. Use change for before-and-after, difference for two measurements side by side.

What is the difference between percent and percentage points?

A rate going from 4% to 5% has risen by 1 percentage point but by 25 percent, because 1 is a quarter of 4. News reports mix these up often, so check which one is meant.

Written and reviewed by our editorial team. Last updated . Method and sources: how these numbers are computed.