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Percentage Calculator

Six percentage questions, each with its own tab. Every answer comes with the figures it is made of, named in plain English, and the working that produced it — so you can check it, or learn it.

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%

The share you want to take.

The number you are taking it out of.

Loaded with an example. Type over either field.

Answer

30

20% of 150 is 30

The number
150
20% of it
30
The rest
120

What each figure is

A percentage means nothing on its own. These are the numbers it is made of.

  • 20%30
  • The rest120
  • The numberYou entered thiswhat you are taking a share of150
  • 20% of itthe share you asked for — the answer30
  • The restthe other 80%, left behind120

How that was worked out

Each step, and why it is that step.

  1. Step 1 — Turn the percentage into a decimal

    20% = 20 ÷ 100 = 0.2

    Per cent means "out of a hundred", so every percentage sum starts by dividing by 100.

  2. Step 2 — Multiply by the number

    0.2 × 150 = 30

    "Of" means multiply. That is the whole trick, and it is the same in every one of these questions.

Check it backwards: 30 ÷ 150 × 100 = 20% — back to the percentage you asked for

Straight to one question

Check this before you rely on it. A free everyday calculator, provided as a guide — not tax, accounting, financial or legal advice. The working is shown above so you can verify it against your own figures. See our terms of use.

How it works

STEP 1

Pick the question

A percentage of a number, what one number is as a percentage of another, an increase, a decrease, the change between two figures, or the difference between them. They are six different sums, and picking the wrong one is the commonest error of the lot.

STEP 2

Type your two numbers

The labels change to match the question, and each field says what belongs in it, so you always know which number goes where. It recalculates as you type — there is no button to press.

STEP 3

Read the breakdown, then the working

Every figure the answer is made of is named twice — once the way a textbook would, once in plain English — with the one you typed marked. Under it, each step of the arithmetic with the reason for that step, and a check that runs the sum backwards.

The guideHow to calculate percentages — the five sums people actually needTo find P% of a number, multiply by P ÷ 100. To find what one number is as a percentage of another, divide the part by the whole and multiply by 100.Read it

Common questions

How do I work out a percentage of a number?

Divide the percentage by 100, then multiply by the number. 20% of 150 is 0.2 × 150 = 30. The "% of a number" tab does this and shows both steps.

If I increase by 10% and then decrease by 10%, why don’t I get back to where I started?

Because the second percentage is taken from a bigger number. £100 increased by 10% is £110, and 10% of £110 is £11 — so you come back to £99, not £100. This catches people out constantly, which is why the increase and decrease tabs are separate.

What is the difference between percentage change and percentage difference?

Change has a direction and is measured against the starting figure: from 150 to 180 is a 20% increase. Difference is symmetric — neither number came first — so it is measured against the midpoint of the two, making 150 and 180 an 18.18% difference. The test is simple: swap your two numbers. If the answer should stay the same, you want difference. Both have their own tab here.

How do I work out a discount?

Use "Decrease by %". 30% off £150 is £150 − (0.30 × £150) = £105, and the breakdown shows the £45 you saved as its own line. Careful in reverse, though: adding 30% back to £105 gives £136.50, not £150, because the same percentage is a smaller amount once the number has shrunk.

What is the percentage formula?

Every one of these questions is the same two moves: divide by 100 to turn a percentage into a decimal, then multiply. Going the other way — finding what percentage one number is of another — you divide first and multiply by 100 at the end. The working on this page shows those moves with your own numbers rather than as letters.

Is a percentage point the same as a percent?

No, and mixing them up is how statistics get misreported. If a rate goes from 4% to 5%, that is a rise of one percentage point but a 25% increase. Use the "Change between two" tab for the percentage, and simple subtraction for the points.

Can it handle negative numbers?

Yes. For percentage change the calculation divides by the magnitude of the starting number, so going from −50 to −25 correctly reads as a 50% improvement rather than −50%.

Why does change from zero not give an answer?

Because there is no meaningful answer. Any increase from zero is infinitely large as a percentage, so the calculator says so rather than showing a misleading number.

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