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Percentage Calculator

This percentage calculator answers the three everyday percent questions. It finds a percentage of a number, works out what percent one number is of another, and calculates the percent increase or decrease between two values, showing the working each time.

What do you want to find?

Result

20% of 150 is 30

Calculation20 ÷ 100 × 150
150 + 20%180
150 − 20%120

Results update as you type.

How to Calculate Percentages

A percent is a number out of 100: 20% means 20 per 100, or 0.20 as a decimal. Every percentage question is one of three types.

1. What is X% of Y?

  • Result = X ÷ 100 × Y
  • Example: 20% of 150 = 0.20 × 150 = 30

2. X is what percent of Y?

  • Percent = X ÷ Y × 100
  • Example: 30 is 30 ÷ 150 × 100 = 20% of 150

3. Percent change from X to Y

  • Percent change = (Y − X) ÷ |X| × 100
  • Example: from 50 to 75 is (75 − 50) ÷ 50 × 100 = 50% increase
  • Example: from 75 to 50 is (50 − 75) ÷ 75 × 100 = 33.33% decrease

Worked Examples

A 25% discount on a $64 item: 25% of 64 is 0.25 × 64 = 16, so the sale price is 64 − 16 = $48. The same answer comes from 64 × 0.75.

A test score of 42 out of 48: 42 ÷ 48 = 0.875, × 100 = 87.5%.

Rent going from $1,200 to $1,320 a month: (1,320 − 1,200) ÷ 1,200 × 100 = 10% increase.

Tips and Common Mistakes

Divide by the starting value for percent change

Percent change is always measured against the old value. Dividing by the new value instead is the most common mistake, and it gives a different answer.

Percentages of percentages don’t add

Two 10% increases in a row are a 21% increase in total, not 20%, because the second 10% is taken of a bigger number: 1.10 × 1.10 = 1.21. This is how compound interest works; see the compound interest calculator.

Removing a percentage that’s already included

To find the price before a percentage was added, divide rather than subtract. A $108.25 total including 8.25% tax was 108.25 ÷ 1.0825 = $100 before tax. The sales tax calculator does this for you.

Fractions and percents

To turn a fraction into a percent, divide the top by the bottom and multiply by 100: 3/8 = 0.375 = 37.5%. For fraction arithmetic, use the fraction calculator.

Frequently Asked Questions

How do I calculate a percentage of a number?

Divide the percentage by 100 to turn it into a decimal, then multiply by the number. 20% of 150 is 0.20 × 150 = 30.

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

Divide the part by the whole and multiply by 100. 30 out of 150 is 30 ÷ 150 = 0.2, and 0.2 × 100 = 20%.

How do I calculate percent increase or decrease?

Subtract the old value from the new value, divide by the old value and multiply by 100. Going from 50 to 75 is (75 − 50) ÷ 50 × 100 = 50%. A negative answer is a decrease.

Why isn't a 50% increase undone by a 50% decrease?

Each percentage is taken of a different starting value. 100 increased by 50% is 150, but 50% of 150 is 75, so decreasing by 50% leaves 75, not 100. To get back to 100 from 150 you need a 33.33% decrease.

How do I add a percentage to a number?

Multiply the number by 1 plus the percentage as a decimal. Adding 15% to 80 gives 80 × 1.15 = 92. To subtract 15%, multiply by 0.85 instead, which gives 68.

What is the difference between percent and percentage points?

Percentage points measure the plain difference between two percentages, while percent change measures it relative to the starting percentage. A rate that rises from 4% to 5% has gone up 1 percentage point, which is a 25% increase.

Can a percentage be more than 100?

Yes. More than 100% means more than the whole. 250% of 40 is 100, and a value that grows from 20 to 50 has increased by 150%.

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