How to use the percentage calculator
- Choose a Calculation from the list.
- Fill in the boxes that appear. Their labels change with the calculation, for example Percentage P and Value X, or Total including the increase.
- For Successive percentage changes, type the changes into Changes in % (comma separated), using a minus sign for a fall.
- Read the answer and the Working line, which shows the formula with your numbers.
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What it does and when to use it
Most percentage questions are easy to ask and easy to get slightly wrong. This calculator gathers nine of them in one place:
| Calculation | Typical question |
|---|---|
| P% of X | What is a 15% tip on 240? |
| X is what percent of Y | I scored 30 out of 120. What percent is that? |
| Percentage change from X to Y | Sales went from 80 to 100. By how much did they grow? |
| Increase X by P% | What is 100 after a 20% rise? |
| Decrease X by P% | What is 100 after a 20% cut? |
| Original before a P% increase | What was the price before 20% VAT? |
| Original before a P% discount | What did it cost before 30% off? |
| Percentage points vs percent change | How big is a move from a 4% rate to 5%? |
| Successive percentage changes | What do three 10% rises add up to? |
If you only need the change between two numbers, the Percentage Change Calculator is a quicker, single-purpose version. For working with fractions instead of percentages, use the Fraction Calculator. For shopping offers specifically, the Discount Calculator handles sale prices and stacked discounts.
How it works
- P% of X = P ÷ 100 × X
- X as a percent of Y = X ÷ Y × 100
- Change = (Y − X) ÷ |X| × 100
- Increase or decrease = X × (1 ± P ÷ 100)
- Reverse an increase = total ÷ (1 + P ÷ 100), and reverse a discount = price ÷ (1 − P ÷ 100)
- Points = second rate − first rate, and relative change = points ÷ first rate × 100
- Successive changes: multiply the factors (1 + each change ÷ 100), then subtract 1 and turn the result back into a percentage.
The tool works with exact fractions, not floating-point numbers, so 10% of 0.3 comes out as exactly 0.03. Repeating decimals are shown with an ellipsis. It all runs in your browser.
Worked examples
- A percent of a number. 15% of 240 gives 15% of 240: 36.
- Removing 20% VAT. A total of 120 gives Original value: 100, with 20 of tax. The tool also points out that subtracting 20% of 120 would give the wrong answer, 96.
- Three 10% rises. “10, 10, 10” gives Overall change: 33.1%, with an overall multiplier of 1.331. The simple sum, 30%, is shown too, marked as not the answer.
- Up 50%, then down 50%. “50, -50” gives Overall change: -25%. 100 becomes 150, then 75.
- Rates from 4% to 5%. The result is a Difference in percentage points: 1 pp and a relative change of 25%.
Limits and tips
- Percentage change from zero has no answer, because there is nothing to compare with. The tool tells you so instead of showing a number.
- A discount of 100% or more cannot be reversed.
- Keep the direction straight. Going from 80 to 100 is a 25% rise, but going from 100 back to 80 is a 20% fall.
Frequently asked questions
How do I find a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 240 is 15 ÷ 100 × 240 = 36. Choose "P% of X" in the calculator.
How do I remove VAT or sales tax from a total?
Divide the total by 1 plus the rate. A total of 120 that includes 20% VAT was 120 ÷ 1.2 = 100 before tax. Subtracting 20% of 120 gives 96, which is wrong, because the tax was worked out on the smaller figure.
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages. Percent measures the relative change. A rate moving from 4% to 5% has risen by 1 percentage point, which is a 25% relative rise. Both are true, so check which one a headline is using.
Why don't successive percentage changes add up?
Each change applies to the result of the one before. Three 10% rises give 1.1 × 1.1 × 1.1 = 1.331, an overall rise of 33.1%, not 30%. A 50% rise followed by a 50% fall leaves you 25% down.
Can I use negative numbers or decimals?
Yes. Every mode accepts decimals, and the successive mode takes negative values for falls, such as "20, -15, 5". The tool uses exact fractions internally, so answers are not affected by rounding errors.
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