Math tool

Percentage Calculator

Work out a percentage of a value, what share one number is of another, and the change between two values. Results update as you type.

Calculate percentages

Find Percentage of a Value

What is % of ?
Result: 30.00

Find What Percentage Value Is

is what % of ?
Result: 20.00%

Percentage Increase / Decrease

From to is what % change?
Result: +50.00% (Increase)

Percentage Calculator guide

Use the three calculators to find a portion of a value, express one value as a percentage of another, or calculate the change between two values.

The basic formulas

  • Part = value × percentage ÷ 100.
  • Percentage = part ÷ value × 100.
  • Percentage change = (new value − old value) ÷ old value × 100.

For percentage change, the old value cannot be zero. Check the units and rounding before using a result in a financial, academic, or reporting task.

Three questions, three boxes

Each calculator on this page answers a different question, and mixing them up is the most common way people get a percentage wrong.

  • What is 15% of 200? Answers 30. Use it for tips, discounts, tax, commission, and scores that are marked out of a total.
  • 20 is what percentage of 100? Answers 20%. Use it when you have a part and a whole and want to express the part as a share.
  • What is the change from 100 to 150? Answers +50.00% and labels it an increase. Use it for growth, decline, and comparing two figures.

Why the third one is measured against the old value

A percentage change is always relative to where you started, never to where you ended. That is why 100 rising to 150 is +50%, but 150 falling back to 100 is -33.33% and not -50%. The two are not mirror images, and treating them as though they are is the classic error in reporting.

The same asymmetry shows up in ordinary life: a 50% rise followed by a 50% fall does not return you to the start. It leaves you 25% below it.

Worked examples

  • A £240 basket with 15% off: 15% of 240 is 36, so you pay £204.
  • You scored 46 of 60. As a percentage that is 76.67%, not 46% and not 0.77%.
  • Subscriptions rise from £9 to £11. The change is 2 ÷ 9, which is +22.22%.

Two mistakes worth naming

  • A percentage of a percentage. 20% of 20% is 4%, because the second 20% applies to the smaller figure. 20% of 20% is not 20%.
  • Dividing the wrong way round. If you want "what percentage of the total", divide the part by the whole. Dividing the whole by the part gives a different and much larger number.

Before you use a result

Figures are shown to two decimal places. Check the units, and check whether the thing you are measuring is the right one — a percentage of a percentage, or a change measured against a total rather than a subset, will look plausible and be wrong. In financial, academic and reporting work, confirm the figure against the source.

Three questions that look alike and are not

The arithmetic here is simple. What causes mistakes is answering the wrong question, because three different everyday questions all sound like the same word and have different answers.

What is 20% of 80 is a multiplication: you are finding a part of a whole. 15 is what percent of 60 is a division expressed as a ratio: you are comparing a part to the whole. The price rose from 50 to 65, by what percent is a comparison against the starting value, so you divide the change by the number you started from, not by the number you ended at.

That last point is where most errors happen. A rise from 50 to 65 is a 30% increase. A fall from 65 back to 50 is a 23% decrease, not 30%, because the starting value changed. Percentages are always relative to something, and losing track of what that something is produces a confident wrong answer.

Check the direction and the base before trusting a result. If you are calculating a discount, the base is the original price; if you are adding tax, the base is the pre-tax amount. Working out which number is the base is the whole problem, and the division afterwards is the easy part.

Further reading: Read the full guide: Percentage Calculator

Common questions

What can it work out?

Three things: what a given percentage of a value is, what percentage one value is of another, and the percentage increase or decrease between two values. Those cover most everyday uses — a discount, a tip, a rise in a fee, a mark out of a total.

Why does percentage change need the starting value?

Because an increase is measured against where you started, not against the larger number. Going from 80 to 100 is a 25% rise, not 20%, because 20 is 20% of the 100 you ended at rather than of the 80 you had. This is the single most common way these questions get answered wrongly.

Is it uploaded anywhere?

No. Everything is calculated in this tab and no number is sent to a server or stored.

What about a percentage decrease to zero?

A percentage increase from zero is undefined rather than infinite — there is no starting point to measure against. A decrease to zero is fine, because the starting value exists. The tool reports the impossible case as undefined instead of inventing a number.

Can I use it with money and units?

Yes, the fields take any number, so a currency amount or a measurement works the same way. Keep the units consistent — a percentage change from metres to feet is arithmetic, not conversion.