Percentage calculator
Five everyday percentage questions, answered as you type, each with the formula it used.
Runs entirely in your browser
Percentage of a number
What is % of ?
What percent one number is of another
is what % of ?
Find the whole from a percentage
is % of what?
Percentage change
From to is a change of what percent?
Increase or decrease by a percentage
by %
Answers are shown to 10 significant figures. Very large or very small results switch to e-notation, for example 1.5e-9.
How to calculate a percentage
- Find the row that matches your question, such as What is 15% of 80?
- Type the two numbers into that row. The answer appears straight away.
- Check the formula under the answer if you want to see how it was worked out, or to do the same sum by hand.
The formulas behind each row
Every percentage question is a rearrangement of one relationship: part = percentage ÷ 100 × whole. Which of the three you are missing decides the sum.
- Percentage of a number: part = p ÷ 100 × whole. 15% of 80 = 0.15 × 80 = 12.
- What percent: p = part ÷ whole × 100. 12 is 12 ÷ 80 × 100 = 15% of 80.
- Find the whole: whole = part ÷ (p ÷ 100). If 12 is 15% of something, that something is 12 ÷ 0.15 = 80.
- Percentage change: (new − old) ÷ |old| × 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%.
- Increase or decrease: new = old × (1 ± p ÷ 100). 80 increased by 15% is 80 × 1.15 = 92.
A common slip is to add and subtract percentages as if they were fixed amounts. A 10% discount followed by another 10% discount is a 19% discount in total, not 20%, because the second one applies to the already reduced price.
Tips
- Scaling an image or a video frame? The aspect ratio calculator keeps the proportions for you.
- Converting between metric and imperial before working out a share? Use the unit converter.
- Counting how many days are left until a deadline? Try the date difference calculator.
Questions
How do I work out a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 15 ÷ 100 × 80 = 12. The first row of the calculator does this for you.
How is percentage change calculated?
Subtract the old value from the new one, divide by the old value and multiply by 100: (new − old) ÷ old × 100. Going from 80 to 100 is a 25% increase; going from 100 to 80 is a 20% decrease. The two differ because each is measured against a different starting value. When the old value is negative, the change is measured against its size, so the sign of the answer still shows whether the value went up or down.
Why can't it work out a change from 0?
A percentage change divides by the starting value, and dividing by zero has no answer: any change away from 0 would be an infinite percentage. Describe that change in plain numbers instead, for example "up from 0 to 40".
What is the difference between percent and percentage points?
Percentage points are the plain difference between two percentages; percent compares them relative to each other. A rate that rises from 4% to 5% has gone up by 1 percentage point, which is a 25% increase in the rate. News reports and contracts often mean one and say the other, so check which is meant.
If a price rises 20% and then falls 20%, is it back where it started?
No. 100 increased by 20% is 120, and 120 decreased by 20% is 96. The fall is measured against the higher price, so it removes more than the rise added. To undo a 20% increase you divide by 1.2, which is a decrease of about 16.67%.
Why are some answers rounded?
Computers store most decimals as close binary approximations, so a sum like 10% of 3 can come out as 0.30000000000000004. Answers here are rounded to 10 significant figures, which removes that noise without affecting any realistic calculation.