Formula
percentage = (numerator ÷ denominator) × 100
- denominator — must not be zero
A percentage is just a fraction with a denominator of 100.
Worked examples
3/4
- Numerator
- 3
- Denominator
- 4
Percentage
75%
Decimal: 0.75
5/8
- Numerator
- 5
- Denominator
- 8
Percentage
62.5%
Decimal: 0.625
How it works
3/4 is 3 ÷ 4 = 0.75, and 0.75 × 100 = 75%. The numerator and denominator can be decimals too, so 2.5/8 works as well.
A fraction larger than 1 gives a percentage above 100% (5/4 = 125%), and a negative fraction gives a negative percentage. Fractions that don't divide evenly give repeating decimals — 1/3 is 33.333…% — and the result is shown to up to 6 decimal places with trailing zeros dropped.
If you start with a part and a whole in real units — marks out of a total, say — Percentage Calculator or Marks Percentage Calculator do the same sum with clearer labels. To see the exact repeating digits of the decimal use the Fraction to Decimal Calculator.
Assumptions and limits
- Results are shown to at most 6 decimal places.