How the percentage calculator works
A percentage is a fraction with 100 as the denominator. "Percent" means "per hundred", so 15% is 15 out of every 100, or 0.15 as a decimal. Every percentage problem reduces to one of three questions, and this calculator handles all of them plus percent change and reverse percentages.
The three basic formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y x X / 100 | 15% of 200 = 30 |
| X is what percent of Y? | X / Y x 100 | 30 is 15% of 200 |
| Percent change from X to Y | (Y - X) / X x 100 | 50 to 75 = +50% |
Common percentage shortcuts
10% of a number is the number with the decimal moved one place left. 5% is half of that. 1% moves the decimal two places. Combine them: 15% of 80 is 8 (10%) plus 4 (5%) = 12. 20% is 10% doubled. 25% is a quarter, and 50% is half.
Percent increase and decrease
To increase a value by a percentage, multiply by (1 + rate). To decrease, multiply by (1 - rate). A 20% discount on $60 is 60 x 0.8 = $48. To undo a percentage change, divide by the same factor instead of subtracting the percent: $48 / 0.8 = $60, whereas adding 20% back to $48 gives $57.60, which is wrong.