To calculate a percentage, divide the part by the whole and multiply by 100: 50 out of 200 is 50 ÷ 200 × 100 = 25%. To find a percentage of a number, multiply the number by the percentage and divide by 100: 25% of 200 is 50.
Our free percentage calculator answers the three questions people ask most: what is X% of Y, X is what percent of Y, and what is the percentage change from one number to another. Below are the formulas, worked examples and the mistakes that trip people up.
The three percentage formulas
Almost every percentage problem is one of these three:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 17.5% of 240 = 42 |
| X is what % of Y? | X ÷ Y × 100 | 18 is 25% of 72 |
| % change from X to Y | (Y − X) ÷ X × 100 | 80 to 100 = +25% |
How to find a percentage of a number
Convert the percentage to a decimal by dividing by 100, then multiply. To find 15% of $64:
- 15 ÷ 100 = 0.15.
- 0.15 × 64 = 9.60.
A useful shortcut: X% of Y always equals Y% of X. So 8% of 50 is the same as 50% of 8, which is 4.
How to work out what percent one number is of another
Divide the part by the whole, then multiply by 100. If you score 42 out of 48 on a test:
- 42 ÷ 48 = 0.875.
- 0.875 × 100 = 87.5%.
How to calculate percentage increase or decrease
Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive result is an increase and a negative result is a decrease. If a price rises from $80 to $100:
- Difference: 100 − 80 = 20.
- Divide by the starting value: 20 ÷ 80 = 0.25.
- Multiply by 100: +25%.
Percentage change is not symmetrical, because the starting value changes. Going back from $100 to $80 is a 20% decrease, not 25%.
| From | To | Change |
|---|---|---|
| 80 | 100 | +25% |
| 100 | 80 | −20% |
| 50 | 75 | +50% |
| 75 | 50 | −33.33% |
This is why a 50% loss needs a 100% gain to get back to where you started.
How to reverse a percentage
To find the original number before a percentage increase, divide by (1 + the percentage as a decimal). If a price is $117 after a 30% markup, the original was 117 ÷ 1.30 = $90. Taking 30% off $117 gives $81.90, which is wrong, because the 30% was calculated on $90, not $117.
The same logic removes tax from a tax-inclusive price, which the sales tax calculator does automatically with its "Price includes tax" switch.
Percent vs percentage points
When a rate itself changes, the difference is measured in percentage points. If an interest rate rises from 4% to 5%, it has gone up by 1 percentage point, which is a 25% increase relative to where it started. Mixing the two up can make a change sound much smaller or larger than it is.
How to use the percentage calculator
- Open the percentage calculator. It has three panels, one for each question.
- What is X% of Y? Enter the Percentage and the Number. The result shows with a summary such as "25% of 200 = 50.00".
- X is what % of Y? Enter the Part and the Whole. The whole cannot be zero.
- Percentage Change: Enter the From and To values. The result is labeled as an increase or a decrease. The starting value cannot be zero.
- Results update as you type and are rounded to two decimal places. Negative numbers work in every panel.
Common uses and mistakes
Percentages show up in everyday money decisions. You can use the dedicated discount calculator for sale prices, the tip calculator for restaurant bills, and the ROI calculator for investment returns. Our guide on how to calculate sale prices shows percentages at work on real purchases.
- Using the wrong base. Percentage change is always divided by the starting value, not the ending value.
- Adding successive changes. A 10% rise followed by a 10% fall leaves you at 99% of the original, not 100%, because the second change applies to a bigger number.
- Subtracting a percentage to reverse it. Divide by (1 + rate) instead, as shown above.
- Confusing percent with percentage points. A rate moving from 2% to 3% is a 1-point rise but a 50% increase.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage, then divide by 100. For example, 20% of 150 is 150 × 20 ÷ 100 = 30.
How do I calculate what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 out of 120 is 30 ÷ 120 × 100 = 25%.
What is the formula for percentage change?
Percentage change = (new value − old value) ÷ old value × 100. A rise from 80 to 100 is a 25% increase, and a fall from 100 to 80 is a 20% decrease.
Why doesn't a 10% increase followed by a 10% decrease cancel out?
The decrease is calculated on the larger, increased number. 100 rises to 110, and 10% of 110 is 11, so the final value is 99, a net loss of 1%.
What is the difference between percent and percentage points?
Percentage points measure the plain difference between two percentages, while percent measures relative change. A rate going from 4% to 5% rises by 1 percentage point, which is a 25% relative increase.
How do I find the original number before a percentage increase?
Divide the final number by 1 plus the percentage as a decimal. A price of $117 after a 30% increase was originally 117 ÷ 1.30 = $90.