Ratio Calculator
Simplify a ratio or solve a proportion such as 3:4 = x:20.
Simplest form
2 : 3
24 : 36 divided by 12
A ratio compares two quantities: 12 boys to 18 girls, 16 units of width to 9 of height, 2 parts cement to 5 parts sand. This tool simplifies a ratio to its lowest terms and solves proportions where one of four numbers is missing.
It accepts decimals, so 1.5 : 2.5 simplifies to 3 : 5.
How ratio calculator works
To simplify, the calculator finds the greatest common divisor of the two numbers and divides both by it. Decimals are scaled up to whole numbers first.
To solve a proportion A : B = C : X, it uses cross-multiplication. A × X must equal B × C, so X = B × C ÷ A.
The formula
Simplified ratio = (A ÷ g) : (B ÷ g), where g = greatest common divisor
A : B = C : X → X = B × C ÷ AWorked example: simplifying, then scaling
12 : 18 has a greatest common divisor of 6, so it simplifies to 2 : 3.
Solve 3 : 4 = 20 : X. Cross-multiplying, 3 × X = 4 × 20, so X = 80 ÷ 3 = 26.67.
A screen with a 16 : 9 ratio and a width of 1,920 pixels has a height of 9 × 1,920 ÷ 16 = 1,080 pixels.
When to use this tool
- Scaling a recipe or a mix, such as paint, concrete or cordial.
- Resizing images and video while keeping the aspect ratio.
- Comparing rates, such as students to teachers.
- Solving proportion problems in maths homework.
Common mistakes to avoid
- Mixing units within a ratio. Convert both parts to the same unit first.
- Reading the order backwards. 2 : 3 and 3 : 2 are different ratios.
- Confusing part-to-part with part-to-whole. 2 : 3 girls to boys means girls are 2 out of 5 in total.
Frequently asked questions
- How do I simplify a ratio?
- Divide both numbers by their greatest common divisor. 12 : 18 divides by 6 to give 2 : 3.
- How do I solve a proportion?
- Cross-multiply and divide. For A : B = C : X, X equals B × C divided by A.
- Can a ratio use decimals?
- Yes. Multiply both numbers by a power of ten to make them whole, then simplify. 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5.
- How do I find the ratio of two quantities with different units?
- Convert them to the same unit first. 50 cm to 2 m is 50 cm to 200 cm, which is 1 : 4.
Learn more
- Guide · September 19, 2026How to Add, Subtract, Multiply and Divide Fractions
- Guide · September 19, 2026How to Simplify a Ratio and Solve Proportions
- Guide · September 19, 2026How to Calculate the Average (Mean, Median and Mode)
- Article · September 19, 2026Mean, Median or Mode: Which Average Should You Use?
Related tools
- Average CalculatorMean, median, mode, range and standard deviation for any list of numbers.
- Fraction CalculatorAdd, subtract, multiply and divide fractions, with simplified, mixed and decimal answers.
- Percentage CalculatorFind X% of a number, what percent one number is of another, or the total behind a percentage.
- Percentage Increase CalculatorFind the percentage increase between two numbers, or raise a number by a percentage.
- Percentage Decrease CalculatorFind the percentage decrease between two numbers, or reduce a number by a percentage.
- Percentage Difference CalculatorCompare two numbers as a percentage when neither one is the starting point.
Results are for information only and are not financial, legal or medical advice. The calculation logic is covered by automated tests, and examples on this page are worked out and re-checked before publishing. Spotted a mistake? Tell us.