Percentage Calculator
Seven ways to work with percentages. Pick what you want to find, enter two numbers and get the answer with extra detail and the formula.
What a percentage is
A percentage is a fraction out of 100. Saying 25% means 25 out of every 100, which is the same as 25/100, the decimal 0.25, or one quarter. Because the scale is always 100, percentages make it easy to compare amounts of different sizes, like a test score out of 50 and one out of 80.
Percentage formulas
| What you want | Formula | Example |
|---|---|---|
| X% of Y | X ÷ 100 × Y | 15% of 200 = 30 |
| X is what % of Y | X ÷ Y × 100 | 30 is 15% of 200 |
| Percent change | (new − old) ÷ |old| × 100 | 80 to 100 = 25% increase |
| Percentage difference | |a − b| ÷ ((a + b) ÷ 2) × 100 | 60 and 90 = 40% |
| Find the whole | Y ÷ (X ÷ 100) | 50 is 20% of 250 |
| Increase by X% | Y × (1 + X ÷ 100) | 250 + 10% = 275 |
| Decrease by X% | Y × (1 − X ÷ 100) | 250 − 20% = 200 |
Percent change vs. percentage difference
Percent change has a direction: it starts from an old value and moves to a new one, like a price going from $80 to $100. Percentage difference compares two values when neither is the starting point, like the heights of two buildings, so it divides by the average of the two. Use change for before-and-after situations and difference for side-by-side comparisons.
Everyday examples
- Discounts: a $60 jacket at 25% off costs 60 × (1 − 0.25) = $45, so you save $15.
- Sales tax: 8.25% on a $120 purchase adds 0.0825 × 120 = $9.90, for a total of $129.90.
- Tips: 18% of a $42 bill is 0.18 × 42 = $7.56.
- Test scores: 42 right out of 50 is 42 ÷ 50 × 100 = 84%.
- Raises: going from $20 to $21.50 an hour is a 7.5% increase.
- Finding the original price: if a sale price of $45 is 25% off, the original is 45 ÷ 0.75 = $60.
Common mistakes
- Increase then decrease by the same percent: 100 up 50% is 150, and 150 down 50% is 75, not 100. The second percentage applies to a larger number.
- Mixing up percent and percentage points: going from 10% to 12% is a 2 percentage point rise but a 20% increase.
- Adding percentages of different bases: 10% of one number plus 20% of another is not 30% of anything.
- Using the wrong starting value: percent change always divides by the old value, not the new one.
Mental math shortcuts
- 10% of a number is the number with the decimal moved one place left. 10% of 85 is 8.5.
- 5% is half of 10%, and 1% is the decimal moved two places left.
- 15% is 10% plus 5%. 20% is double 10%. 25% is a quarter. 50% is half.
- X% of Y equals Y% of X, so 4% of 50 is the same as 50% of 4, which is 2.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 15% of 200, that is 0.15 × 200 = 30.
How do I find percent change?
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 one is a decrease.
Why is a 50% increase followed by a 50% decrease not back to the start?
The second percentage applies to a larger number. 100 up 50% is 150, and 150 down 50% is 75, not 100. The results show the percentage needed to get back to the original.
Is percent change the same as percentage points?
No. Going from 10% to 12% is a 2 percentage point rise, but a 20% increase in relative terms.
How do I find the original number before a percentage?
Use the Find the whole tab. If a number is 20% of the whole, divide it by 0.20 to get the whole. For a price after a discount, divide by (1 − the discount).
Can a percentage be more than 100?
Yes. 150% means one and a half times the base amount. Growth of 200% means the value tripled.
How do I turn a fraction into a percentage?
Divide the top by the bottom and multiply by 100. For 3/8, that is 0.375 × 100 = 37.5%.