How to use it
- 1Pick the calculator that matches your question, for example “What is 15 % of 80?”.
- 2Type your numbers. Decimals work with a comma or a point, and thousands separators such as
1,250or1 250are fine. - 3The answer appears as you type, with the calculation written out underneath so you can check it.
- 4Click the copy icon next to a result to paste it elsewhere.
How to calculate percentages
“Per cent” means per hundred, so 15 % is 15/100, or 0.15. To find a percentage of a number, multiply and divide by 100: 15 % of 80 is 15 × 80 / 100 = 12.
To find what percentage one number is of another, divide and multiply by 100: 12 out of 80 is 12 / 80 × 100 = 15 %. To find the whole when you know a part and its percentage, reverse it: if 12 is 15 %, the whole is 12 × 100 / 15 = 80.
Percentage change, difference and points
Percentage change compares a new value with the original: (new − original) / original × 100. Going from 80 to 100 is an increase of 25 %, but going from 100 back to 80 is a decrease of only 20 %, because each change is measured against a different starting value.
Percentage difference compares two values when neither is the original – two prices or two measurements. It divides the gap by the average of both values, so the order doesn’t matter: 80 and 100 differ by 22.22 % either way.
When a rate itself changes, say an interest rate from 10 % to 12 %, it has risen by 2 percentage points – which is a 20 % increase of the rate. Mixing the two is one of the most common mistakes in news and reports.
Adding and removing VAT, discounts and tips
Adding 21 % VAT to a price of 100 gives 121. Taking 21 % off 121 gives 95.59, not 100 – to get back to the original price, use “is X % of what number?”: 121 is 121 % of 100.
The same asymmetry applies to discounts: a 20 % discount followed by a 20 % increase turns 100 into 80 and then 96, not back into 100.
Questions and answers
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 20 % of 150 is 20 × 150 / 100 = 30. A quick mental shortcut: 10 % is the number with the decimal point moved one place to the left, so 10 % of 150 is 15 and 20 % is twice that.
How do I calculate a percentage increase?
Subtract the original value from the new one, divide by the original and multiply by 100. A price that rises from 50 to 65 has increased by (65 − 50) / 50 × 100 = 30 %. A negative result means a decrease.
How do I remove VAT from a price?
Divide the price including VAT by 1 plus the rate: with 21 % VAT, 121 / 1.21 = 100. In this calculator, use “is X % of what number?” with 121 and 121 %. Subtracting 21 % from the gross price gives a wrong, lower figure.
What’s the difference between percentage change and percentage difference?
Percentage change has a direction – from an old value to a new one – and divides by the old value. Percentage difference compares two values on equal terms and divides by their average. Use change for prices over time, difference for comparing two measurements or offers.
What is a percentage point?
A percentage point is the plain difference between two percentages. If unemployment goes from 4 % to 5 %, it has risen by one percentage point, which is a 25 % increase relative to the original 4 %.