Five questions, one calculator
Pick the question from the list, enter two numbers, and the answer appears as you type. Open “Show the math” to see each step.
| Question | Example | Answer |
|---|---|---|
| What is X% of Y? | What is 20% of 150? | 30 |
| X is what percent of Y? | 30 is what percent of 150? | 20% |
| Percent change from X to Y | From 50 to 65 | 30% increase |
| Add or take off a percent | Take 15% off 80 | 68 |
| X is P% of what number? | 30 is 20% of what? | 150 |
How each one works
A percent is a number out of 100, so 20% means 20 ÷ 100 = 0.2. Every question above is that one idea used a different way.
- Percent of a number: percent ÷ 100 × number. 20% of 150 = 0.2 × 150 = 30.
- What percent: part ÷ whole × 100. 30 ÷ 150 = 0.2, so 20%.
- Percent change: (new − old) ÷ old × 100. From 50 to 65 the change is 15, and 15 ÷ 50 = 0.3, a 30% increase. A drop gives a negative number: from 80 to 60 is a 25% decrease.
- Add or take off a percent: number × (1 + percent ÷ 100) to add, or × (1 − percent ÷ 100) to take off. 80 minus 15% = 80 × 0.85 = 68.
- The whole from a part: part ÷ (percent ÷ 100). If 30 is 20% of something, it’s 30 ÷ 0.2 = 150.
Mistakes worth knowing about
Percent changes don’t cancel out. A price that rises 20% and then falls 20% ends lower than it started, because the fall is taken from the bigger number.
Percent change depends on where you start. Going from 50 to 100 is a 100% increase, but going back from 100 to 50 is only a 50% decrease.
Percentage points aren’t percents. A rate moving from 4% to 5% rose by 1 percentage point, which is a 25% increase in the rate.
Limits
Answers show up to 4 decimal places. A percent change from 0 has no answer, because any change from nothing is infinitely large. Everything runs in your browser.