How it works
The fraction is divided out to a decimal, then multiplied by 100 to express it as a percentage.
Worked through: for 5/2, the numerator divided by the denominator is 2.5, and 2.5 × 100 is 250, so the result is 250%. Some fractions have no exact decimal form — 1 ÷ 3 is 0.333... repeating — so the result is rounded to 12 significant digits and displayed to at most 10 decimal places, giving 33.3333333333% for 1/3.
The multiplication by 100 is the only step that separates this from the fraction to decimal calculator, which stops at 2.5 for 5/2. Turning a percentage back into a fraction runs the other way, on the percentage to fraction calculator; the guide to percentages sets both in context.
Formula: Percentage value = (numerator ÷ denominator) × 100
Examples
An eighth
1/8 = (1 ÷ 8) × 100 = 12.5%.
Three quarters
3/4 = (3 ÷ 4) × 100 = 75%.
A fraction larger than one
5/2 = (5 ÷ 2) × 100 = 2.5 × 100 = 250%. The fraction exceeds one whole, so the percentage exceeds 100%.
A fraction that does not divide exactly
1/3 = (1 ÷ 3) × 100 = 33.3333333333%, rounded to 10 decimal places, since one third has no exact decimal form.
Common uses
- Converting a score written as a fraction, such as 17/20, into a percentage for a report.
- Checking that a figure quoted as a fraction and the same figure quoted as a percentage agree.
- Reading a recipe fraction such as 2/3 as a percentage when scaling a mixture up or down.
Things to keep in mind
- The denominator cannot be zero.
- A fraction larger than one gives a percentage above 100, which is correct rather than an error: 5/2 returns 250%.
- Results are rounded to 12 significant digits and displayed to at most 10 decimal places, so a fraction whose decimal repeats, such as 1/3 or 1/7, is never exact.
- The division is plain arithmetic, so a fraction equal to one returns 100% and a fraction equal to zero returns 0%.