Quick answer
X% of Y = X × Y ÷ 100; X as a percent of Y = X ÷ Y × 100; percent change from A to B = (B − A) ÷ A × 100. Enter two numbers in the matching card above to get the result with the formula filled in.
How to calculate a percentage
This page combines the four most common percentage calculations: a percentage of a number, the ratio between two numbers, percent change, and increasing or decreasing a number by a percentage. It accepts thousands separators and rounds results to remove floating-point noise such as 0.1 + 0.2.
How to calculate a percentage
- 1
Pick the card for your question: “What is X% of Y?”, “X is what percent of Y?”, “Percentage change from A to B” or “Increase or decrease a number by a percentage”.
- 2
Enter both numbers. Separators such as 1,000,000 or 12.5 are fine; the “Read as” line under the box shows how the number was understood.
- 3
In the last card, choose “Increase” or “Decrease” before entering the starting number and the percentage.
- 4
Read the result and its working; click “Copy result” to paste it elsewhere, or “Clear all” to start over.
The four percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X × Y ÷ 100 | 15% of 200 = 15 × 200 ÷ 100 = 30 |
| X is what percent of Y? | X ÷ Y × 100 | 45 ÷ 60 × 100 = 75% |
| Percent change from A to B? | (B − A) ÷ A × 100 | (92 − 80) ÷ 80 × 100 = 15% (increase) |
| Y increased / decreased by X%? | Y × (1 ± X ÷ 100) | 1,000,000 minus 10% = 900,000 |
Easy-to-get-wrong calculations
| Situation | Common mistake | Correct result |
|---|---|---|
| Up 20%, then down 20% | Back to the start | 100 → 120 → 96: 4% below the start |
| Interest rate from 5% to 6% | Up 1% | Up 1 percentage point, i.e. a 20% increase (1 ÷ 5 × 100) |
| Down 50%, then up 50% | Back to the start | 100 → 50 → 75: still 25% lower |
| Price including 10% tax is 1,650 | Subtract 10% from 1,650 | Pre-tax price = 1,650 ÷ 1.1 = 1,500 |
There is no dedicated card for the pre-tax price yet; divide by hand as shown in the last row.
Examples
Sale price
A $45 shirt with 30% off: use “Increase or decrease”, choose Decrease, enter 45 and 30. You save $13.50 and pay $31.50.
Pay rise
Salary going from 52,000 to 55,900: “Percentage change” shows a 7.5% increase ((55,900 − 52,000) ÷ 52,000 × 100).
Test score
42 correct out of 48: “X is what percent of Y” with X = 42 and Y = 48 gives 87.5%.
Sales tax
8% tax on a $250 purchase: “What is X% of Y” with X = 8 and Y = 250 gives $20, for a total of $270.
Common mistakes
- Typing 1,500 to mean one and a half.
- On the English page a comma followed by exactly three digits groups thousands, so “1,500” is fifteen hundred (while “1,5” is read as 1.5). Use a dot for decimals and check the “Read as” line.
- Error when the starting value A is 0.
- Percent change divides by A, so it is undefined when A = 0. Compare the absolute difference instead.
- Mixing up the direction of change.
- The change card always goes from A (old) to B (new). Swapping them changes the answer: 80 to 100 is +25%, 100 to 80 is −20%.
- Too many decimal places.
- Up to 10 decimal places are shown so no precision is lost. Round money values to your own rules.
- Typing currency symbols ($, €).
- Enter digits, separators, a minus sign and optionally a trailing %; anything else is flagged as not a valid number.
Glossary
- Percent (%)
- A ratio out of 100: 25% means 25 parts in every 100.
- Percentage point
- The plain difference between two percentages: 5% to 6% is a rise of 1 percentage point.
- Base value
- The number you divide by when measuring change; a different base gives a different percentage.
- Significant digits
- The digits that carry information; results are rounded to 12 significant digits to remove floating-point error.
Frequently asked questions
What is the percent change formula?
Percent change = (new value − original value) ÷ original value × 100. A positive result is an increase, a negative one a decrease. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%.
How do I work out progress towards a target?
Use “X is what percent of Y” with X as what you achieved and Y as the target. 1,150 against a target of 1,000 is 115%.
Does it work with negative numbers?
Yes. For percent change from a negative starting value, the tool divides by its absolute value so the direction stays correct: from −50 to −25 is a 50% increase.
Are very large numbers shown correctly?
Numbers below 10²¹ are shown in full with separators; larger ones are written as “3 × 10²¹” instead of the hard-to-read “3E21”.
Why does 0.1 + 0.2 come out as exactly 0.3?
Computers store decimals in binary with tiny errors. Results are rounded to 12 significant digits to remove that noise.
Are my numbers stored?
No. Every calculation runs in your browser and nothing is sent or saved.
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