By This percentage calculator handles the five percent questions people ask most: what is X% of Y, X is what percent of Y, the percent change (increase or decrease) from one value to another, percent error between a measured and a true value, and percent difference between two values. Choose the question, enter X and Y, and it shows the formula and the answer.
It’s free and needs no sign-up.
How to use it
- Choose the calculation from the menu.
- Enter X and Y as the menu describes. For percent change, X is the old value and Y the new one.
- Press Calculate.
Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | \( \frac{X}{100}\times Y \) | 15% of 80 = 12 |
| X is what % of Y? | \( \frac{X}{Y}\times100\% \) | 45 of 60 = 75% |
| Percent change | \( \frac{\text{new} - \text{old}}{\lvert\text{old}\rvert}\times100\% \) | 50 → 65 = +30% |
| Percent error | \( \frac{\lvert\text{measured} - \text{true}\rvert}{\lvert\text{true}\rvert}\times100\% \) | 9.6 vs 9.81 ≈ 2.14% |
| Percent difference | \( \frac{\lvert X - Y\rvert}{(X + Y)/2}\times100\% \) | 40 and 60 = 40% |
“Percent” means “per hundred”: 15% is \( \frac{15}{100} = 0.15 \).
Worked examples
A discount. A \$80 jacket is 15% off: \( 0.15 \times 80 = 12 \), so it costs \$68.
A test score. 45 correct out of 60 is \( \frac{45}{60} \times 100\% = 75\% \).
A price rise. A price goes from \$50 to \$65: \( \frac{65 - 50}{50} = 0.30 \), a 30% increase.
A decrease. Sales fall from 80 to 60: \( \frac{60 - 80}{80} = -25\% \), a 25% decrease.
A lab result. You measure \( g = 9.6 \) m/s² against the true 9.81: \( \frac{0.21}{9.81} \approx 2.14\% \) error.
Percent change isn’t symmetric
A 25% fall from 80 gives 60, but a 25% rise from 60 gives only 75. To undo a 25% decrease you need a \( 33\frac13\% \) increase. The base of each percentage is different, which is why “up 50% then down 50%” leaves you at 75% of where you started.
Repeated percentage changes
Applying the same percent change repeatedly multiplies by the same factor each time: growing 5% a year for 10 years multiplies by \( 1.05^{10} \approx 1.63 \), not \( 1.5 \). That’s compound growth; use the compound interest calculator and see exponential functions.
Common mistakes
- Dividing by the wrong value. Percent change divides by the original value.
- Adding percentages of different bases. 10% of 50 plus 10% of 200 isn’t 20% of anything simple.
- Percent vs percentage points. An interest rate going from 4% to 5% is a rise of 1 percentage point, but 25%.
Related guides
- Percentage Formula: How to Calculate Percentages
- Fractions: How to Add, Multiply and Divide
- Compound Interest Formula
- Exponential Functions
Further reading
- Percentage (Wikipedia) — definitions, calculations and common pitfalls.
- Relative change and difference (Wikipedia) — percent change, percent difference and percent error.
FAQ
How do I calculate a percentage of a number?
Multiply the number by the percent and divide by 100: 20% of 150 is \( 150 \times 0.2 = 30 \).
How do I work out percentage increase?
\( \frac{\text{new} - \text{old}}{\text{old}} \times 100\% \).
How do I find what percent one number is of another?
Divide and multiply by 100: 18 out of 72 is \( \frac{18}{72} \times 100\% = 25\% \).
What is percent error?
How far a measured value is from the true value, as a percentage of the true value.