Percentage calculator
Pick the type of problem, enter two numbers, and the percentage calculator gives the answer instantly. To find X% of Y, multiply Y by X and divide by 100. For percent change between two values, compute (new − old) ÷ old × 100. The formulas are shown under every result.
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Percentage formulas
A percentage is a fraction out of 100. Every formula below comes from that one idea.
| Question | Formula |
|---|---|
| X% of Y | \( \dfrac{Y \times X}{100} \) |
| X is what % of Y | \( \dfrac{X}{Y} \times 100 \) |
| Increase by X% | value × (1 + X ÷ 100) |
| Decrease by X% | value × (1 − X ÷ 100) |
| Percent change from a to b | (b − a) ÷ a × 100 |
| Value before an X% change | final value ÷ (1 + X ÷ 100) |
The multiplier is the handiest shortcut: +20% means multiply by 1.20, and −35% means multiply by 0.65.
Common percentage mistakes
An increase followed by an equal decrease does not cancel out. A value of 100 that rises 20% becomes 120. A 20% drop then brings it to 96, not 100. To get back to 100 you need a 16.67% drop.
\[ \text{drop needed} = \dfrac{X}{100 + X} \times 100 \]
The other classic mix-up is percentage points. A rate that goes from 4% to 5% gains 1 percentage point, but it rose 25% in relative terms \( \left( \dfrac{1}{4} \right) \).
Doing percentages in your head
For 10%, move the decimal one place left. For 5%, take half of 10%. For 15%, add 10% and 5%. For 25%, divide by 4. For 50%, divide by 2.
| Percent | Of 240 |
|---|---|
| 10% | 24 |
| 5% | 12 |
| 15% | 36 |
| 25% | 60 |
3 real-life examples
15% of $240
Math: \( \dfrac{240 \times 15}{100} = \) $36. Handy for a deposit or a quick tip.
Rent going from $1,450 to $1,537
Percent change: \( \dfrac{1{,}537 - 1{,}450}{1{,}450} \times 100 = \) +6%. That is an $87 increase, or 6% of the old rent.
Finding a price before a hike
A subscription costs $12.60 after a 5% increase. Before: \( \dfrac{12.60}{1.05} = \) $12. Do not subtract 5% from $12.60: you would get $11.97, which is wrong.