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.
This converter provides instant, accurate results for your measurement conversions. The UK uses a mix of metric and imperial measurements in daily life, which can make conversions a frequent necessity. Road signs use miles, food is sold in grams and kilograms, and height is often quoted in feet and inches despite the metric system being the official standard.
Understanding the conversion formula helps verify results and perform quick mental calculations when a tool is not available.
Common UK conversion factors: 1 inch = 2.54 cm, 1 foot = 30.48 cm, 1 mile = 1.609 km, 1 pound (lb) = 0.4536 kg, 1 stone = 6.35 kg, 1 pint (UK) = 568 ml, 1 gallon (UK) = 4.546 litres, 1 acre = 0.4047 hectares. Temperature conversions use the formula: Celsius = (Fahrenheit - 32) x 5/9.
To convert 5 feet 10 inches to centimetres: first convert to total inches (5 x 12 + 10 = 70 inches), then multiply by 2.54 to get 177.8 cm. For weight, a person weighing 12 stone 7 lbs is 12.5 stone, which equals 79.4 kg (12.5 x 6.35).
Source: Based on international measurement standards. Last updated March 2026.
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.
Data verified against official UK government sources. Last checked April 2026.