Percent means "per hundred". These are the percentage calculations people most often get wrong, each with a number you can check in the Percentage Calculator.
The formulas
| Name | Formula | Example |
|---|---|---|
| Percent of a number | part = percent / 100 × whole |
15% of 80 = 12 |
| What percent is a of b | percent = a / b × 100 |
18 is 25% of 72 |
| Percent change | (new − old) / old × 100 |
80 to 100 is +25%; 100 back to 80 is −20% |
| Percent difference (no "before") | |a − b| / ((a + b) / 2) × 100 |
80 and 100 differ by 22.22% |
| Percent error | |measured − true| / |true| × 100 |
9.8 measured against 9.81: 0.10% |
| Undo a percent change | original = final / (1 + change) |
60 after a 20% rise: original 50 |
| Tip | tip = bill × rate |
18% of $45.00 = $8.10 |
Percent versus percentage points
If an interest rate moves from 4% to 6%, it rose by 2 percentage points, which is a 50% increase ((6 − 4) / 4). Quote points for differences between two percentages and percent for relative change.
Why up then down does not cancel
A rise of 25% followed by a fall of 25% leaves you at 1.25 × 0.75 = 0.9375 of the start, 6.25% lower. A fall of 20% undoes a rise of 25% (1.25 × 0.8 = 1), because the second percentage applies to a different base.
Related tools
The Percent Error Calculator handles measurement error and the Ratio Calculator simplifies and scales ratios. Tip Calculator splits a bill, Fraction Calculator and Decimal to Fraction Calculator convert between forms, and Rounding Calculator and Significant Figures Calculator decide how many digits to keep. For anything else, use the Basic Calculator, Scientific Calculator, Long Division Calculator or Big Number Calculator.