Ratio Calculator
Solve a proportion A : B = C : D for the missing term in any position, with cross-multiplication shown. Also simplifies ratios (including decimals and 3-part ratios), converts to 1 : n form, compares two ratios, scales a ratio and splits a total in a given ratio.
How it works
a : b = c : d ⇔ a × d = b × c · d = b × c ÷ a · c = a × d ÷ b · b = a × d ÷ c · a = b × c ÷ d · simplest form: divide every term by their GCF · split total T in a : b → T × a ÷ (a + b) and T × b ÷ (a + b)
Two ratios are equal when their fractions are equal: a/b = c/d. Cross-multiplying gives a × d = b × c, so any one missing term can be found from the other three. For the last term, x = b × c ÷ a. Pick which position is missing and the steps show the cross-multiplication with your numbers. This is the math behind scaling recipes, map distances, model sizes, screen aspect ratios and unit prices. The calculator also simplifies a ratio by dividing every term by the greatest common factor. Ratios with decimals are first multiplied up to whole numbers, so 1.5 : 2 becomes 15 : 20 and then 3 : 4. You also get the 1 : n and n : 1 forms and each part’s share of the total. Other modes compare two ratios by cross-multiplying, scale a ratio up or down, or divide a total in a given ratio, such as splitting money or mixing concrete. Switch on the three-part option for ratios like 1 : 2 : 3.
Worked example
A recipe uses flour and sugar in a 2 : 3 ratio and you have 10 cups of flour. Solve 2 : 3 = 10 : x. Cross-multiply: 2x = 3 × 10 = 30, so x = 15 cups of sugar. The scale factor is 10 ÷ 2 = 5. A 16 : 9 screen that is 1,920 pixels wide is 1,080 pixels tall, because 16 : 9 = 1,920 : x gives x = 9 × 1,920 ÷ 16. Splitting 100 in the ratio 2 : 3 makes 5 shares of 20, so the parts are 40 and 60.
Frequently asked questions
What if the unknown is in a different position?
Choose which term is missing — a, b, c or d — and the calculator rearranges the cross-multiplication for you. For x : 2 = 8 : 4, for example, 4x = 2 × 8, so x = 4.
Are ratios the same as fractions?
A two-part ratio maps directly to a fraction (2 : 3 means the first is 2/3 of the second), so the same cross-multiplication rules apply to both. As parts of a whole, though, 2 : 3 means 2/5 and 3/5 of the total.
How do I simplify a ratio like 24 : 36?
Divide both sides by their greatest common factor. GCF(24, 36) = 12, so 24 : 36 = 2 : 3. Ratios with decimals can be multiplied up first: 1.5 : 2 = 15 : 20 = 3 : 4. Choose “Simplify a ratio” to see these steps with your numbers.
How do I divide an amount in a ratio?
Add the terms to get the number of shares, divide the total by that number, then multiply by each term. Splitting 120 in the ratio 1 : 2 : 3 gives 6 shares of 20, so the parts are 20, 40 and 60.
How do I check whether two ratios are equivalent?
Cross-multiply. 2 : 3 and 4 : 6 give 2 × 6 = 12 and 3 × 4 = 12, so they are equal. 2 : 3 and 4 : 5 give 10 and 12, so 2 : 3 is the smaller ratio.
What do 1 : n and n : 1 mean?
They rescale a ratio so one side is 1, which makes comparisons easy. 200 : 800 is 1 : 4 (four times as much of the second) or, the other way round, 0.25 : 1. Map scales such as 1 : 50,000 are written this way.
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This calculator is for educational purposes. Double-check important results before acting on them.