Enter the numerator (top) and denominator (bottom) of your fraction:
Converting a fraction to a percentage is a fundamental maths skill used in everyday life — from calculating discounts and test scores to understanding statistics and probability. The process is straightforward and requires just two steps.
Percentage = (Numerator ÷ Denominator) × 100
Step 1: Divide the numerator (top number) by the denominator (bottom number) to get the decimal form.
Step 2: Multiply the decimal by 100 to convert to a percentage.
Example: Convert 3/4 to a percentage.
These are the most frequently used fractions and their percentage equivalents, useful for mental arithmetic and quick reference:
| Fraction | Decimal | Percentage | Visual |
|---|
A mixed number contains a whole number and a fraction (e.g., 2¾). To convert to a percentage, first convert to an improper fraction:
Mixed numbers greater than 1 will always give percentages greater than 100%.
Some fractions produce recurring (repeating) decimals when converted. This happens when the denominator has prime factors other than 2 and 5:
When rounding recurring percentages, the standard practice is to round to 2 decimal places: 33.33%, 66.67%, 16.67%. In some contexts (like tax calculations), more decimal places may be required.
Fractions with different denominators are difficult to compare directly. Is 5/8 larger or smaller than 7/11? Converting to percentages immediately answers the question: 5/8 = 62.5%, 7/11 = 63.64% — so 7/11 is slightly larger. Percentages provide a common scale from 0 to 100 (and beyond for values greater than one whole), making comparison intuitive.
Converting raw test scores to percentages is one of the most common uses of the fraction-to-percentage formula. For a student scoring 18 out of 24 marks:
GCSE grade boundaries in England are expressed as raw marks, but teachers and students often want to understand them as percentages. For instance, if the grade 5 boundary on a paper worth 80 marks is 52, that represents 52/80 = 65%.
Tax rates in the UK are expressed as percentages, but understanding them as fractions can be helpful for mental arithmetic. The basic rate of income tax is 20%, which is 1/5. The higher rate is 40%, which is 2/5. VAT at 20% is also 1/5 of the pre-VAT price. National Insurance contributions can similarly be expressed as fractions for quick calculations.
Probability is naturally expressed as a fraction (outcomes that succeed / total outcomes) and is often converted to a percentage for clearer communication. Rolling a 6 on a fair die: probability = 1/6 = 16.67%. Drawing a heart from a deck: 13/52 = 25%. Flipping heads on a coin: 1/2 = 50%. In statistics and risk assessment, percentages derived from fractions are the standard form of communication.
A fraction can also be expressed as a ratio. 3/4 = 3:4, meaning for every 3 parts of one thing, there are 4 parts total — or alternatively a 3:1 ratio of part to remainder. Converting between fractions, percentages, decimals, and ratios is a core skill for GCSE and A-Level maths.
Divide the numerator by the denominator, then multiply by 100. Formula: percentage = (numerator ÷ denominator) × 100. Example: 3/4 → 3 ÷ 4 = 0.75 → 0.75 × 100 = 75%. For mixed numbers, convert to an improper fraction first: 2½ = 5/2 → 5 ÷ 2 = 2.5 → 2.5 × 100 = 250%.
1/3 as a percentage is 33.33...% (a recurring decimal). The exact value is 33⅓%. In practice, it is rounded to 33.3% or 33.33%. This is a recurring decimal because 3 is a prime factor that is neither 2 nor 5. Similarly, 2/3 = 66.66...% = 66⅔%.
3/4 as a percentage is exactly 75%. Calculation: 3 ÷ 4 = 0.75. 0.75 × 100 = 75%. This is a terminating decimal because 4 = 2², and fractions with denominators that are powers of 2 or 5 always produce terminating decimals. Common equivalents: 3/4 = 0.75 = 75% = 75 out of 100.
Step 1: Convert the mixed number to an improper fraction using the formula: (whole number × denominator + numerator) / denominator. Example: 3¼ = (3×4+1)/4 = 13/4. Step 2: Apply the formula: 13 ÷ 4 = 3.25 × 100 = 325%. Mixed numbers always give percentages above 100%.
18 out of 24 is 75%. Calculation: 18 ÷ 24 = 0.75 × 100 = 75%. You can also simplify the fraction first: 18/24 = 3/4 (dividing both by 6), and 3/4 = 75%. This is useful for test score calculations: 18 marks out of 24 = 75% on the paper.
A recurring decimal repeats infinitely. It occurs when the fraction's denominator has prime factors other than 2 and 5. Examples: 1/3 = 0.3333..., 1/6 = 0.16666..., 1/7 = 0.142857142857..., 1/9 = 0.1111.... In percentage form these are rounded: 1/3 ≈ 33.33%, 1/6 ≈ 16.67%, 1/7 ≈ 14.29%.
Write the percentage as a fraction over 100, then simplify. Example: 75% = 75/100 = 3/4 (dividing by 25). 33.33% ≈ 1/3. 12.5% = 12.5/100 = 125/1000 = 1/8. For a terminating decimal percentage, multiply numerator and denominator to remove the decimal: 12.5/100 = 125/1000, then simplify by finding the greatest common divisor.