A ratio calculator for proportions, simplifying and sharing
This free ratio calculator handles the four ratio problems that come up in maths class and in everyday life: finding the missing number in a proportion such as 3 : 4 = 9 : ?, reducing a ratio to its simplest form, dividing an amount in a given ratio, and converting between ratios, fractions and percentages.
Ratios appear in recipes, maps, screen sizes, concrete mixes, partnership profits and exam questions. The calculator works with whole numbers, decimals and fractions, keeps its arithmetic exact when simplifying, and shows each step so you can see the cross-multiplication or the greatest common divisor at work.
How to use the Ratio Calculator
- Pick a task: Solve A:B = C:D, Simplify, Divide an amount or Convert.
- To solve a proportion, fill three of the four boxes and leave the unknown one empty (it has a dashed border).
- To simplify, type the ratio with colons — for example 1.5 : 2.25 : 3 or 1/2 : 1/3.
- To share an amount, enter the total and the ratio, such as 1000 and 2:3:5.
- To convert, type a ratio (2:3), a percentage (40%) or a fraction (3/8).
- Read the answer, the extra forms in the tiles and the numbered working; “Copy result” puts the answer on your clipboard.
Ratio Calculator features
Any missing value
Solves for A, B, C or D in A : B = C : D, or checks whether two complete ratios are equivalent.
Decimals and fractions
Ratios like 0.75 : 1.5 or 2/3 : 1/4 are scaled to whole numbers exactly before simplifying.
Three or more terms
Simplify and share with ratios such as 2 : 3 : 5 or 1 : 2 : 4 — not just pairs.
Share table
Dividing an amount lists each share’s fraction, percentage and value, plus a check that they add up.
Ratio, fraction or percentage
Converts in every direction, including part-to-whole and part-to-rest ratios.
Solving a proportion with cross-multiplication
Two ratios are in proportion when they describe the same relationship. Writing A : B = C : D as A/B = C/D and cross-multiplying gives A × D = B × C, which can be rearranged for any one unknown.
Example: a recipe uses 3 cups of flour for every 4 eggs. How much flour for 9 eggs? Write 3 : 4 = ? : 9 — so the unknown is C — then C = A × D ÷ B = 3 × 9 ÷ 4 = 6.75 cups. In the calculator, enter 3, 4, leave C empty and type 9 for D.
Map scales work the same way. On a 1 : 50,000 map, 4.2 cm represents 4.2 × 50,000 = 210,000 cm, which is 2.1 km.
How to simplify a ratio
- Whole numbers: divide every term by their greatest common divisor. 12 : 18 : 30 has a GCD of 6, so it simplifies to 2 : 3 : 5.
- Decimals: multiply every term by 10, 100 or 1,000 until they are whole, then divide by the GCD. 1.5 : 2.25 becomes 150 : 225, then 2 : 3.
- Fractions: multiply by the least common multiple of the denominators. ½ : ⅓ × 6 = 3 : 2.
- Mixed units: convert to the same unit first. 50 cm : 2 m is 50 : 200 = 1 : 4, not 25 : 1.
- Unit ratios such as 1 : 1.5 are handy for comparing, which is how screen shapes are described; the Aspect Ratio Calculator is built for that.
Dividing an amount in a ratio
Add the ratio’s terms to find the total number of parts, divide the amount by that total to get the value of one part, then multiply each term by it. If three partners share a profit of ₹90,000 in the ratio 2 : 3 : 4, there are 9 parts of ₹10,000, so they receive ₹20,000, ₹30,000 and ₹40,000. The same steps split a $1,000 or £1,000 prize, a building budget or a concrete mix such as 1 : 2 : 4 (cement : sand : gravel).
| Ratio | Part-to-whole fractions | Percentages | First ÷ second |
|---|---|---|---|
| 1 : 1 | 1/2 and 1/2 | 50% : 50% | 1 |
| 1 : 3 | 1/4 and 3/4 | 25% : 75% | 0.333… |
| 2 : 3 | 2/5 and 3/5 | 40% : 60% | 0.666… |
| 3 : 5 | 3/8 and 5/8 | 37.5% : 62.5% | 0.6 |
| 16 : 9 | 16/25 and 9/25 | 64% : 36% | 1.777… |
Ratio Calculator FAQ
How do I find the missing number in a ratio?
Write the two ratios as fractions and cross-multiply. For 5 : 8 = 15 : x, 5x = 8 × 15 = 120, so x = 24. In the ratio calculator, enter the three known numbers and leave the unknown box empty.
How do I simplify a ratio with decimals?
Multiply all the terms by the same power of ten to make them whole numbers, then divide by their greatest common divisor. 0.6 : 1.5 → 6 : 15 → 2 : 5.
How do I divide a number in a given ratio?
Add the ratio’s terms, divide the amount by that sum and multiply by each term. £600 in the ratio 1 : 2 gives 3 parts of £200, so the shares are £200 and £400.
How do I convert a ratio to a percentage?
Divide each term by the total of all the terms and multiply by 100. For 3 : 7 the total is 10, so the parts are 30% and 70%. To compare the first term with the second instead, divide 3 by 7 to get 42.86%.
Is a ratio the same as a fraction?
They are closely related. The ratio 2 : 3 compares two quantities, and 2/3 says the first is two-thirds of the second. But as parts of a whole, 2 : 3 means 2/5 and 3/5 — so always check whether a question means part-to-part or part-to-whole. The Fraction Calculator helps with the fraction arithmetic.
Does the order of a ratio matter?
Yes. 2 : 3 and 3 : 2 are different: the first term always matches the first thing named. Saying “boys to girls is 2 : 3” means 2 boys for every 3 girls.