Percent to Fraction Calculator
Enter any percentage to convert it to a fully simplified fraction. Works with whole number percents, decimal percents, and percentages over 100%.
Percent to Fraction Reference Table
| Percent (%) | Fraction over 100 | Simplified Fraction | GCD Used |
|---|---|---|---|
| 1% | 1/100 | 1/100 | 1 |
| 2% | 2/100 | 1/50 | 2 |
| 4% | 4/100 | 1/25 | 4 |
| 5% | 5/100 | 1/20 | 5 |
| 10% | 10/100 | 1/10 | 10 |
| 12.5% | 125/1000 | 1/8 | 125 |
| 20% | 20/100 | 1/5 | 20 |
| 25% | 25/100 | 1/4 | 25 |
| 33.33% | 3333/10000 | ≈ 1/3 | 3333 |
| 40% | 40/100 | 2/5 | 20 |
| 50% | 50/100 | 1/2 | 50 |
| 60% | 60/100 | 3/5 | 20 |
| 66.67% | 6667/10000 | ≈ 2/3 | 3333 |
| 75% | 75/100 | 3/4 | 25 |
| 80% | 80/100 | 4/5 | 20 |
| 90% | 90/100 | 9/10 | 10 |
| 100% | 100/100 | 1 | 100 |
| 150% | 150/100 | 3/2 | 50 |
| 200% | 200/100 | 2/1 | 100 |
How to Convert Percent to Fraction
Percent to fraction conversion follows three steps: write the percent over 100, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that GCD.
Handling Decimal Percentages
When the percentage contains a decimal, multiply both the numerator and denominator by a power of 10 to eliminate the decimal before simplifying. For 12.5%, multiply top and bottom by 10 to get 125/1000, then find the GCD of 125 and 1000, which is 125, giving 1/8.
Percentages Over 100%
Percentages over 100% produce improper fractions where the numerator is larger than the denominator. For example, 150% becomes 150/100, which simplifies to 3/2. This is a valid fraction and does not need to be converted to a mixed number unless specifically required.
What Is the Greatest Common Divisor
The greatest common divisor is the largest number that divides evenly into both the numerator and the denominator. Finding the GCD is the key step in reducing a fraction to its simplest form.
The Euclidean algorithm finds the GCD efficiently. Divide the larger number by the smaller, take the remainder, and repeat until the remainder is zero. The last non-zero remainder is the GCD. For 75 and 100: 100 divided by 75 leaves remainder 25, then 75 divided by 25 leaves remainder 0, so GCD is 25. Dividing 75/100 by 25 gives 3/4.