Percentage Calculator

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.