Percentage calculator

How to use it

1. Pick the question. Choose one of the five buttons: X% of Y, X is what % of Y, change from A to B, add or subtract a percentage, or find the whole from a percentage.
2. Type the two numbers. Decimals are fine with a dot or a comma. Negative numbers work too, for example to measure a change in a loss or a temperature.
3. Read and copy the answer. The result updates as you type, with a sentence that explains it and a bar chart to scale. Use Copy result to paste the sentence into a message or a spreadsheet.

The five percentage formulas

Per cent means "for every hundred": 15% is 15 out of 100, or the decimal 0.15. Every percentage problem is a version of one relationship, part = whole × percentage ÷ 100. Depending on which two numbers you know, you solve it for the third.

Two of these formulas divide, so they have a forbidden value. You cannot ask what percentage something is of zero, and a change from a starting value of zero has no percentage: going from 0 to 10 visitors is an increase of 10, not of some finite percent. The calculator says so instead of printing "infinity".

The percentage change divides by the absolute value of the start, |A|. That way a move from −50 to −25 (a loss that halves) shows as a 50% improvement, and a move from −50 to −100 as a 100% worsening, which is how analysts read such figures.

Percentage points or percent? Not the same thing

When the numbers you compare are already percentages, there are two ways to describe the change, and they are easy to mix up. If a mortgage rate goes from 4.25% to 5%, it has risen by 0.75 percentage points (the plain difference), but by 17.65% in relative terms (the change measured against 4.25).

News reports about interest rates, unemployment, tax rates and polls should use percentage points for the difference. "Unemployment fell 2%" is ambiguous: from 10% to 8% is 2 points, while a 2% fall from 10% leads to 9.8%. In the Change from A to B mode the calculator shows both numbers side by side: the difference B − A and the percentage change.

A rule of thumb: if you subtract two percentages, the answer is in points. If you divide the difference by the starting value, the answer is in percent.

Worked examples

Common mistakes with percentages

• Up and down are not symmetric. +50% and then −50% does not return to the start: 100 becomes 150 and then 75. Each percentage is taken from a different base.
• Percentages do not add up across different bases. Two successive rises of 10% make 21%, not 20%, because the second 10% is applied to the already increased figure.
• Taking the percentage from the wrong number. A change is always measured against the starting value. From 80 to 100 is +25%, from 100 to 80 is −20%.
• Reversing an increase by subtracting. If a price includes a 20% surcharge, the original price is the total divided by 1.2, not the total minus 20%. Use the reverse mode, or the VAT calculator for taxes.
• Rounding too early. Keep all decimals until the end and round only the final result; the calculator shows up to four decimals.

For money that grows month after month, such as the interest on a loan, a single percentage is not enough: the interest is calculated on a balance that changes each month. The loan calculator builds the full schedule.

Sources

• Definition of percentage and percentage change: OECD, Glossary of Statistical Terms, "Percentage change" (OECD, 2008).
• Difference between percentage points and percentages: UK Office for National Statistics, Style guide, "Percentages and percentage points".
• Arithmetic of percentages and proportions: any secondary school mathematics curriculum; the formulas above are the standard definitions.

The examples on this page are calculated with the same code as the calculator, so the numbers in the text always match the tool.

Frequently asked questions