What a percentage means
"Percent" means "per hundred." Writing 25% is another way of writing the fraction 25/100 or the decimal 0.25. Converting between a percentage and a decimal is just a matter of dividing or multiplying by 100, which is why every formula on this page contains a "× 100" or "÷ 100" step.
Formulas used
| Question | Formula |
|---|---|
| What is P% of X? | P ÷ 100 × X |
| X is what % of Y? | X ÷ Y × 100 |
| % change from A to B | (B − A) ÷ |A| × 100 |
The change formula divides by the absolute value of the starting number so that a move from −50 to −25 is reported as a 50% increase (the value went up), matching the direction of the change.
Worked examples
Sales tax: what is 8.25% of $64?
- Convert the percentage to a decimal: 8.25 ÷ 100 = 0.0825.
- Multiply: 0.0825 × 64 = 5.28.
- The tax is $5.28, so the total is $69.28.
Test score: 42 out of 48 is what percent?
- Divide the part by the whole: 42 ÷ 48 = 0.875.
- Multiply by 100: 87.5%.
Price change: from $80 to $60
- Find the difference: 60 − 80 = −20.
- Divide by the starting value: −20 ÷ 80 = −0.25.
- Multiply by 100: −25%, a 25% decrease.
Common mistakes
- Using the wrong base. A change is always measured against the starting value, not the ending value.
- Adding successive percentages. Two 10% increases make a 21% increase overall (1.1 × 1.1 = 1.21), not 20%.
- Confusing percent with percentage points when comparing rates such as interest or unemployment.
Precision and assumptions
Results are calculated in double-precision floating point and rounded to 12 significant digits to remove binary rounding artifacts (so 10% of 0.3 shows 0.03, not 0.030000000000000002). Displayed values show up to six decimal places. Thousands separators (commas) in your input are ignored.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 80 is 0.15 × 80 = 12.
What is the difference between percentage change and percentage points?
Percentage change compares the size of a change to the starting value. Percentage points are the simple difference between two percentages: a rate moving from 4% to 5% is a 1 percentage point increase but a 25% percentage change.
Why can't I calculate a percentage change from zero?
Percentage change divides by the starting value. Division by zero is undefined, so any change from zero cannot be expressed as a percentage.
Is a 50% increase followed by a 50% decrease back to the original?
No. 100 increased by 50% is 150, and 150 decreased by 50% is 75. Each percentage applies to a different base value.