🧮 Maths & science

Ratio calculator

Use any of the three tools: simplify a ratio, solve a proportion by leaving one box empty, or share a total in a ratio.

Free · no signup Runs in your browser

Simplified ratio—

    Solve a proportion a : b = c : d (leave one box empty)

    Missing term—

      Share an amount in a ratio

      Shares—

        How do I simplify a ratio?

        Divide every number in the ratio by their greatest common factor. The ratio 12 : 18 has a greatest common factor of 6, so it simplifies to 2 : 3. For ratios with decimals, such as 1.5 : 4.5, multiply all the numbers by a power of 10 first (to 15 : 45), then divide by the greatest common factor (15), giving 1 : 3. The calculator does this for up to six numbers and also shows each part as a fraction and a percentage of the total.

        Ratios and proportions

        A ratio compares quantities of the same kind: 2 : 3 says that for every 2 of the first there are 3 of the second. It can be written with a colon, as a fraction (2/3) or in words ('2 to 3'). Two ratios that simplify to the same thing are equivalent, and an equation that says two ratios are equal, such as 3 : 4 = 9 : x, is a proportion. To solve it, cross-multiply: a : b = c : d means a × d = b × c, so x = 4 × 9 ÷ 3 = 12. Leave exactly one of the four boxes empty and the calculator finds it.

        Proportions are how recipes scale (a recipe for 4 that you need for 10), how maps work (a scale of 1 : 50,000 means 1 cm on the map is 50,000 cm, or 500 m, on the ground), how currency and units are converted, and how a mix such as 50 : 1 gas and oil is made. Always keep the same order on both sides: the first term of each ratio should refer to the same thing.

        It runs in your browser. Nothing you enter is sent anywhere, and there is no sign-up.

        Sharing an amount in a ratio

        To divide a total in a ratio, add the parts, find the value of one part, and multiply. Sharing $1,000 in the ratio 3 : 2 gives 5 parts, so one part is $200 and the shares are $600 and $400. The same method shares profits between partners, an inheritance, a cost between households or the ingredients in a mix. The calculator accepts any number of parts and shows each share as an amount and as a percentage. For converting a ratio into a percentage use the percentage calculator, and for combining fractions the fraction calculator.

        When to use it

        • Scaling recipes, mixes and maps
        • Sharing costs or profits in agreed proportions
        • Homework on ratios and proportions
        • Finding an unknown quantity from three known ones

        Mistakes it helps you avoid

        • Mixing the order of the terms in the two ratios.
        • Reading 3 : 2 as 3/2 of the whole instead of 3 of 5 parts.
        • Forgetting to add the parts before dividing the total.
        • Simplifying only one term.

        The formula

        How the answer is worked out.

        • simplify: divide every term by the greatest common factor (multiply by 10ⁿ first if there are decimals)
        • proportion a : b = c : d → a × d = b × c; d = b × c ÷ a, c = a × d ÷ b, b = a × d ÷ c, a = b × c ÷ d
        • share: one part = total ÷ (sum of the parts); share i = part i × one part

        Decimals up to six places are handled by scaling to whole numbers. In the proportion tool exactly one box must be empty, and the divisor in the formula cannot be zero.

        Example: scaling a recipe

        A recipe uses 3 cups of flour for 4 servings. How much flour for 10 servings?

        1. Proportion3 : 4 = x : 10
        2. Cross-multiplyx = 3 × 10 ÷ 4 = 7.5

        7.5 cups of flour

        Enter 3, 4, empty, 10 in the proportion tool.

        Terms on this page

        Ratio
        A comparison of two or more quantities of the same kind.
        Proportion
        An equation stating that two ratios are equal.

        Common questions

        How do I simplify a ratio?

        Divide all the terms by their greatest common factor.

        What is a proportion?

        An equation saying two ratios are equal, like 3 : 4 = 9 : 12.

        How do I turn a ratio into a percentage?

        Divide each part by the total of the parts and multiply by 100. The calculator shows it.

        How do I split money in a ratio?

        Add the parts, divide the total by that sum, then multiply by each part.

        Is my data uploaded?

        No.

        Is anything I enter sent to a server?

        No. The calculation happens in your browser and nothing you type leaves your device.

        What to work out next

        Where these numbers come from

        Last verified 2026-10-25 The method on this page is checked against the sources above at least once a year. Spotted something out of date? Tell us and we will fix it.

        Related tools

        Percentage calculator

        Answer the four common percentage questions: what is X% of Y, X is what percent of Y, percentage change, and increase or decrease by a percentage.

        Open calculator

        Fraction calculator

        Add, subtract, multiply and divide fractions and mixed numbers, with the answer simplified and shown as a mixed number and a decimal.

        Open tool

        GCF and LCM calculator

        Find the greatest common factor and least common multiple of two or more whole numbers, with prime factorizations and the Euclidean algorithm steps.

        Open tool

        50:1 fuel mix

        Two-stroke fuel mixing in litres and millilitres, with a US-gallon toggle.

        Open calculator

        Reverse percentage

        Find the original number before a percentage increase or decrease was applied.

        Open calculator

        Average percentage

        Average percentages correctly by weighting each one by its sample size.

        Open calculator

        🧮 Maths and science calculators

        Homework tools that explain the method rather than just handing over an answer.

        See all 30 tools in this section