Ratio Calculator
Solve a proportion a : b = c : x for the missing value, with the scale factor shown.
How it works
a : b = c : x → x = b × c ÷ a
Two ratios are equal when their fractions are equal: a/b = c/x. Cross-multiplying gives a×x = b×c, so the missing term is b×c ÷ a. This is the math behind scaling recipes, map distances, model sizes and unit prices.
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.
Frequently asked questions
What if the unknown is in a different position?
Rearrange so the unknown is last. Since a : b = c : x is the same statement as b : a = x : c, you can always swap both pairs the same way and read off the answer.
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.
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 = 3 : 4.
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This calculator is for educational purposes. Double-check important results before acting on them.