Percentage to Fraction Calculator

How it works

Every percentage is already a fraction with a denominator of 100. To convert, write the percentage as a fraction over 100, then reduce it to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).

The formula

Why this works: The word "percent" means per hundred, so any percentage is already a fraction with 100 on the bottom. Simplifying removes the common factor from both numbers, giving the same value in its lowest terms. For example, 75/100 and 3/4 represent exactly the same proportion.

Worked examples

When to use this

Converting a percentage to a fraction is useful whenever you need the exact proportional form of a value rather than its approximate decimal equivalent.

• Reading nutritional labels. A product label states 35% of the reference intake for fat. As a fraction that is 7/20 of the daily allowance, which is easier to work with mentally when dividing a portion.
• Probability and statistics. A 30% probability of rain means a 3/10 chance, which is cleaner to write in formulae and probability trees used in GCSE and A-Level maths.
• Cooking and scaling recipes. A recipe scaled to 75% of the original quantities means using 3/4 of each ingredient, which is far simpler to measure than multiplying by 0.75 on the spot.
• Teaching and maths homework. Primary and secondary maths courses require pupils to move fluently between percentages, decimals, and fractions. Showing that 60% = 3/5 reinforces equivalence and helps with mental arithmetic.
• Financial ratios. A lender who requires a 20% deposit on a property is asking for 1/5 of the purchase price. Fractions often make proportional reasoning more intuitive than percentages.

Understanding the result

The result is always expressed in its simplest or lowest form, meaning no whole number other than 1 divides evenly into both the numerator and the denominator. 75/100 simplifies to 3/4 because both share a common factor of 25. If the GCD is already 1, the fraction cannot be simplified further: 37/100 stays as 37/100.

For decimal percentages such as 37.5%, the process requires an extra step of multiplying both the percentage and 100 by 10 before applying the GCD. The result 3/8 is exact, not an approximation. Repeating decimal percentages like 33.33% (representing one third exactly) will not simplify to a clean fraction because the original value is irrational; use 1/3 directly in that case.

Percentages above 100% produce improper fractions where the numerator exceeds the denominator. For example, 150% becomes 3/2. This is mathematically correct and is sometimes expressed as a mixed number (1 and 1/2) depending on the context.

Related concepts

• ➡ convert the equivalent fraction back to a percentage to verify your answer
• ➡ convert any percentage to its decimal equivalent in one step
• ➡ apply the fraction to any whole number to find the corresponding amount

How to do this in Excel

Excel does not have a built-in percentage-to-fraction simplifier, but you can find the GCD and calculate the simplified numerator and denominator separately. Put the percentage value in cell A1, then use these formulas:

For whole-number percentages this works directly. For decimal percentages such as 37.5, you would first multiply by 10 to clear the decimal (giving 375 over 1000) and then apply GCD(375, 1000) instead.

How to do this without a calculator

Write the percentage as a fraction over 100. Then find the GCD by listing the factors of both numbers and picking the largest they share. For 60/100: factors of 60 include 1, 2, 4, 5, 10, 20; factors of 100 include 1, 2, 4, 5, 10, 20, 25, 50. The largest shared factor is 20, so 60/100 = 3/5.

A quicker shortcut for many percentages is to divide both by 10 first if both end in zero, then repeat. 80/100 becomes 8/10 becomes 4/5. For percentages divisible by 25 (25, 50, 75), dividing both by 25 gives the answer directly: 75/100 = 3/4.

For decimal percentages, multiply both the percentage and 100 by 10 to clear the decimal before you start. 37.5% becomes 375/1000, and then find the GCD of 375 and 1000 (which is 125) to get 3/8.

Common mistakes

Related calculators