Percentage Calculator
Choose the percentage calculation you need. The tool shows the result, substituted formula and interpretation without combining different questions into separate pages.
Percentage formulas
- X% of Y: (X ÷ 100) × Y.
- X as a percentage of Y: (X ÷ Y) × 100.
- Percentage change: ((new − original) ÷ |original|) × 100.
- Increase by Y%: original × (1 + Y ÷ 100).
- Decrease by Y%: original × (1 − Y ÷ 100).
- Percentage difference: |X − Y| ÷ ((|X| + |Y|) ÷ 2) × 100.
Six checked examples
| Question | Calculation | Answer |
|---|---|---|
| What is 20% of 150? | (20 ÷ 100) × 150 | 30 |
| 30 is what percent of 120? | (30 ÷ 120) × 100 | 25% |
| Change from 80 to 100 | ((100 − 80) ÷ 80) × 100 | 25% increase |
| Increase 200 by 15% | 200 × 1.15 | 230 |
| Decrease 200 by 15% | 200 × 0.85 | 170 |
| Difference between 80 and 100 | 20 ÷ 90 × 100 | 22.222222% |
How to choose the correct calculation
Use “X% of Y” when a rate and base number are known. Use “X is what percent of Y” when comparing a part with a whole. Percentage change has a defined starting value and direction; percentage difference is symmetric and is appropriate when neither value is the baseline.
Limits and interpretation
A zero comparison value cannot be used as a denominator. Percentage change from zero is undefined in this calculator. A reduction above 100% can produce a negative result, which may be mathematically valid but unsuitable for quantities that cannot be negative. Results retain full numeric precision internally and are formatted to at most ten decimal places on screen.
Frequently asked questions
Are percentage change and percentage difference the same?
No. Change uses the original value as its denominator and has a direction. Difference uses the average magnitude of both values and is symmetric.
How do I add a percentage to a number?
Choose “Increase X by Y%.” The calculator multiplies the original number by 1 plus the percentage expressed as a decimal.
Can percentages be greater than 100?
Yes. For example, 150% of 40 is 60. Whether that result makes sense depends on the quantity being modeled.