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Percentage Calculator

Solve every common percentage question - what is X% of Y, X is what percent of Y, and the percentage change between two numbers.

Percentage Calculator

What is X percent of Y?

Result

50

25% of 200 is 50.

Quick reference

The three calculations, and the traps that catch people out.

QuestionFormulaExample
What is 25% of 200?(X ÷ 100) × Y50
30 is what percent of 150?(X ÷ Y) × 10020%
Change from 80 to 100?((Y − X) ÷ X) × 100+25%
Change from 100 to 80?((Y − X) ÷ X) × 100−20%
20% off, then 10% off?0.8 × 0.928% off, not 30%

How the percentage calculation works

Percent means "per hundred" — a percentage is just a fraction with 100 on the bottom. Almost every percentage question people actually ask is one of three calculations, and they are easy to mix up because the wording is so similar.

1. What is X% of Y?

Result = (X ÷ 100) × Y

What is 25% of 200? (25 ÷ 100) × 200 = 50. This is the calculation behind discounts, tips, and sales tax. A 20% discount on an $80 jacket is (20 ÷ 100) × 80 = $16 off, so you pay $64.

2. X is what percent of Y?

Result = (X ÷ Y) × 100

30 is what percent of 150? (30 ÷ 150) × 100 = 20%. This is the one to use for test scores, completion rates, and shares of a total. Getting 43 out of 50 on an exam is (43 ÷ 50) × 100 = 86%.

3. What is the percentage change from X to Y?

Result = ((Y − X) ÷ X) × 100

From 80 to 100? ((100 − 80) ÷ 80) × 100 = 25% increase. The critical detail is the denominator: you always divide by the starting value, which is why the next point catches people out.

Percentage changes are not symmetric. Going from 100 to 80 is a 20% decrease, but going from 80 back to 100 is a 25% increase. Same two numbers, different percentages, because the base changed. A stock that falls 50% needs to rise 100% to recover.

Two more distinctions worth knowing:

  • Percentage points are not percentages. If a rate rises from 4% to 5%, that is a one percentage point increase but a 25% relative increase. News reports frequently blur this and the two figures are wildly different.
  • Percentages do not stack. A 20% discount followed by a further 10% off is not 30% off. It is 0.8 × 0.9 = 0.72, so 28% off. Order does not matter, but the multiplication does.

Pick a mode above, enter your numbers, and the calculator states the result as a plain sentence so you can check it says what you meant.

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. For 15% of 240: 15 divided by 100 is 0.15, and 0.15 times 240 is 36. A quick check is that 10% is just the number with the decimal point moved one place left.

How do I work out what percentage one number is of another?

Divide the part by the whole and multiply by 100. If you scored 43 out of 50, that is 43 divided by 50, which is 0.86, times 100 - so 86%.

How do I calculate percentage increase or decrease?

Subtract the old value from the new value, divide by the old value, and multiply by 100. From 80 to 100 that is 20 divided by 80, times 100, which is a 25% increase. A negative result means a decrease.

Why is a 20% decrease not reversed by a 20% increase?

Because the base changes. Reducing 100 by 20% gives 80. Increasing 80 by 20% gives 96, not 100 - the second calculation is 20% of 80, not of 100. To return from 80 to 100 you need a 25% increase.

What is the difference between percent and percentage points?

If an interest rate moves from 4% to 5%, it has risen by one percentage point, but by 25% in relative terms. Percentage points describe the arithmetic difference between two percentages; percent describes the proportional change.

Can I stack two percentage discounts?

Not by adding them. A 20% discount followed by 10% off leaves you paying 0.8 times 0.9, which is 0.72 - a 28% total discount, not 30%. Multiply the remaining fractions rather than summing the discounts.

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