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Calculators

Percentage Calculator

Three different questions get called “calculating a percentage”, and mixing them up is the usual source of a wrong answer. Pick the one you mean below and the calculator shows the result along with the working.

What do you want to work out?

Enter both values to see the result.

How to use this tool

  1. Choose which question you are answering: a percentage of a value, a value as a share of a total, or the change between two values.
  2. Enter the two numbers. The labels change to match the question you picked, so you always know which number goes where.
  3. Read the result underneath. It updates as you type — there is nothing to submit.
  4. Use Reset to clear both fields before starting a different calculation.

Formula and method

What is X% of Y?

result = (X ÷ 100) × Y
X
— the percentage you want
Y
— the value you are taking it from

Dividing by 100 turns the percentage into a plain multiplier: 20% becomes 0.2, and multiplying by that gives the part you asked for.

X is what percent of Y?

percent = (X ÷ Y) × 100
X
— the part
Y
— the whole

This is the reverse of the first formula. It is undefined when the total is zero, because nothing can be a share of nothing — the calculator says so rather than returning a number.

Percentage increase or decrease

change = ((new − old) ÷ |old|) × 100
old
— the starting value
new
— the ending value

The change is always measured against the starting value, which is why a rise from 50 to 100 is a 100% increase but the fall back from 100 to 50 is only a 50% decrease. Using the absolute value of the starting figure keeps the sign meaningful when the starting value is negative.

Worked examples

What is 20% of 150?

  1. Convert the percentage to a multiplier: 20 ÷ 100 = 0.2
  2. Multiply by the value: 0.2 × 150 = 30

20% of 150 is 30.

A £40 shirt now costs £52. What is the increase?

  1. Find the difference: 52 − 40 = 12
  2. Divide by the starting price: 12 ÷ 40 = 0.3
  3. Multiply by 100: 0.3 × 100 = 30

The price rose by 30%.

You scored 34 out of 40. What percentage is that?

  1. Divide the part by the whole: 34 ÷ 40 = 0.85
  2. Multiply by 100: 0.85 × 100 = 85

34 out of 40 is 85%.

Notes and limitations

  • Percentage change is measured against the starting value, so an increase and the decrease that undoes it are different percentages. Going up 50% then down 50% leaves you below where you started.
  • A percentage change from zero has no meaning and the calculator will tell you so instead of showing infinity.
  • Results are shown to six decimal places at most. For money, round to the currency's smallest unit yourself — the calculator does not assume you are working in a particular currency.
  • Percentage points and percent are not the same thing. A rate moving from 4% to 6% has risen by two percentage points, which is a 50% increase.

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percentage by 100 to get a multiplier, then multiply it by the number. For 15% of 80: 15 ÷ 100 = 0.15, and 0.15 × 80 = 12.

How do I calculate percentage increase?

Subtract the old value from the new one, divide the result by the old value, then multiply by 100. From 200 to 250: (250 − 200) ÷ 200 = 0.25, which is a 25% increase.

How do I calculate percentage decrease?

The method is identical to an increase — the result simply comes out negative. From 250 to 200: (200 − 250) ÷ 250 = −0.2, a 20% decrease. Note that this is not the same 25% that took you up.

What is 20% of 150?

30. Twenty percent is one fifth, and a fifth of 150 is 30.

How do I work out the original price before a discount?

Divide the price you paid by (1 − discount ÷ 100). An item bought for 80 after 20% off was originally 80 ÷ 0.8 = 100. The Discount Calculator does this for you.

What is the difference between percent and percentage points?

Percentage points measure the gap between two percentages, percent measures relative change. An interest rate going from 5% to 7% has risen two percentage points, or 40%.

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