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CALCULATOR · SHOWS THE WORKING

Percentage calculator

Four percentage questions, each answered with the working written out so you can see where the number comes from.

What is X% of Y?

Try:

15% of 80 = 12

The working

  1. Percent means “out of 100”, so turn 15% into a decimal: 15 ÷ 100 = 0.15.
  2. Multiply that by 80: 0.15 × 80 = 12.
  3. So 15% of 80 is 12.

X is what percent of Y?

Try:

30 is 25% of 120

The working

  1. Divide the part by the whole: 30 ÷ 120 = 0.25.
  2. Multiply by 100 to turn the decimal into a percentage: 0.25 × 100 = 25.
  3. So 30 is 25% of 120.

Percentage change from one value to another

Try:

A 25% decrease

The working

  1. Find the change: 90 − 120 = −30.
  2. Divide the change by the starting value: (−30) ÷ 120 = −0.25.
  3. Multiply by 100: (−0.25) × 100 = −25.
  4. The sign is negative, so going from 120 to 90 is a 25% decrease.

Reverse percentage: find the original value

Try:

Original value = 100

The working

  1. A 20% increase means the final value is 100% + 20% = 120% of the original.
  2. Write that as a decimal: 120 ÷ 100 = 1.2.
  3. Divide the final value by it: 120 ÷ 1.2 = 100.
  4. Check by going forwards: 100 × 1.2 = 120.
  5. The increase itself was 20, which is 20% of the original and not 20% of 120.

How it works

How to work out a percentage

Percent means “out of 100”. To find a percentage of a number, divide the percentage by 100 and multiply. 15% of 80 is 0.15 × 80 = 12. In your head it is often quicker to start from 10%: 10% of 80 is 8, half of that is 4, and together they make 12.

Percentage change always uses the starting value

To find a percentage change, subtract the old value from the new one and divide by the old value. Going from 120 to 90 is a change of −30, and −30 ÷ 120 = −0.25, a 25% decrease. Dividing by the new value instead is the most common mistake.

Why reverse percentages need division

If a price is 120 after a 20% rise, the original is not 120 minus 20% of 120. The 20% was taken from the original, so 120 is 120% of it, and 120 ÷ 1.2 = 100. The calculator shows the check each time.

Inputs this calculator accepts

You can type decimals with a point or a comma, negative numbers, and a percent sign if you like. A comma followed by exactly three digits, as in 1,250, is read as a thousands separator. Numbers can be up to 15 digits long, and results are exact rather than rounded by floating-point arithmetic.

Worked examples

What is 35% of 240?

35% of 240 = 84

  1. Percent means “out of 100”, so turn 35% into a decimal: 35 ÷ 100 = 0.35.
  2. Multiply that by 240: 0.35 × 240 = 84.
  3. So 35% of 240 is 84.

45 is what percent of 60?

45 is 75% of 60

  1. Divide the part by the whole: 45 ÷ 60 = 0.75.
  2. Multiply by 100 to turn the decimal into a percentage: 0.75 × 100 = 75.
  3. So 45 is 75% of 60.

A rent rises from 800 to 860. What is the percentage increase?

A 7.5% increase

  1. Find the change: 860 − 800 = 60.
  2. Divide the change by the starting value: 60 ÷ 800 = 0.075.
  3. Multiply by 100: 0.075 × 100 = 7.5.
  4. The sign is positive, so going from 800 to 860 is a 7.5% increase.

A coat costs 84 after 30% off. What was the full price?

Original value = 120

  1. A 30% decrease means the final value is 100% − 30% = 70% of the original.
  2. Write that as a decimal: 70 ÷ 100 = 0.7.
  3. Divide the final value by it: 84 ÷ 0.7 = 120.
  4. Check by going forwards: 120 × 0.7 = 84.
  5. The decrease itself was 36, which is 30% of the original and not 30% of 84.

Common questions

How do I find 20% of a number?

Divide the number by 5, or find 10% by dividing by 10 and double it. 20% of 45 is 9.

Is a 50% rise followed by a 50% fall back where it started?

No. 100 rises to 150, and 50% of 150 is 75, so it falls to 75. The second percentage is taken from a different starting value.

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