Converting between fractions and percentages is one of the most common tasks in everyday math. This calculator handles both directions: enter the numerator and denominator to get the percentage, or enter a percentage to get the fraction. Results are simplified automatically.
How to Convert a Fraction to a Percentage
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1
Enter the numerator (the top number of the fraction).
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2
Enter the denominator (the bottom number of the fraction). It cannot be zero.
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3
Read the percentage result in the "Fraction to percentage" panel.
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To convert a percentage to a fraction, enter it in the Percentage field and read the "Percentage to fraction" result.
Fraction to Percentage Method
Converting a fraction to a percentage is a two-step process. Divide the numerator by the denominator to get a decimal, then multiply that decimal by 100 to get the percentage.
For example, to convert 3/4: divide 3 by 4 to get 0.75, then multiply by 100 to get 75%. The fraction 3/4 is the same as 75%.
The fraction does not need to be simplified before converting. Both 4/8 and 1/2 give the same result of 50%.
Fraction to Percentage Formula
Where n is the numerator, d is the denominator, and p is the result as a percentage.
p = (n ÷ d) × 100
Common Fraction to Percentage Conversions
| Fraction | Division | Percentage |
|---|---|---|
| 1/2 | 1 ÷ 2 = 0.5 | 50% |
| 1/3 | 1 ÷ 3 ≈ 0.3333 | ≈ 33.33% |
| 2/3 | 2 ÷ 3 ≈ 0.6667 | ≈ 66.67% |
| 1/4 | 1 ÷ 4 = 0.25 | 25% |
| 3/4 | 3 ÷ 4 = 0.75 | 75% |
| 1/5 | 1 ÷ 5 = 0.2 | 20% |
| 1/8 | 1 ÷ 8 = 0.125 | 12.5% |
| 1/10 | 1 ÷ 10 = 0.1 | 10% |
Percentage to Fraction Method
To convert a percentage to a fraction, write the percentage value as the numerator and 100 as the denominator. Then simplify by dividing both numbers by their greatest common divisor.
For example, 40% becomes 40/100. The greatest common divisor of 40 and 100 is 20. Dividing both by 20 gives 2/5.
For percentages with decimal places, multiply numerator and denominator by a power of 10 to clear the decimal before simplifying. For example, 12.5% is 12.5/100 = 125/1000, and GCD(125, 1000) = 125, giving 1/8.
Common Percentage to Fraction Conversions
| Percentage | As a fraction | Simplified |
|---|---|---|
| 10% | 10/100 | 1/10 |
| 20% | 20/100 | 1/5 |
| 25% | 25/100 | 1/4 |
| 33.33% | 3333/10000 | ≈ 1/3 |
| 40% | 40/100 | 2/5 |
| 50% | 50/100 | 1/2 |
| 75% | 75/100 | 3/4 |
| 80% | 80/100 | 4/5 |
Connection to Percent Error
The fraction to percentage formula has a special use in measurement. When the numerator is the difference between an observed value and a true value, and the denominator is the true value, the formula becomes the percent error formula:
Percent error = |observed − true| ÷ true × 100
This measures how far off a measurement is as a percentage of the correct value.
This fraction to percent calculator converts any fraction to a percentage and any percentage back to a simplified fraction. Enter the numerator and denominator to get the percentage, or enter a percentage to get the equivalent fraction.