Ratio Calculator

Simplifying ratios and solving proportions

A ratio compares quantities in a fixed order. To simplify a ratio of whole numbers, divide both parts by their greatest common divisor. The order matters: a ratio of 2:3 is not the same relationship as 3:2.

Worked examples

The ratio 6:9 simplifies to 2:3 because both values divide evenly by 3. For an equivalent ratio, multiply or divide both parts by the same nonzero factor. If 2:3 = 4:x, then 2/3 = 4/x; cross-multiplying gives 2x = 12, so x = 6.

Ratios compare like units or quantities in a meaningful relationship. Convert measurements to compatible units before comparing, and check that the values refer to the same type of quantity. The missing-value mode assumes a direct proportion; situations where one variable does not scale in the same way require a different model.

Tips for accurate results

To scale a ratio, multiply or divide both sides by the same number. To solve a proportion a/b = c/d for an unknown d, use d = b × c ÷ a. For a recipe that uses 2 cups of rice to 3 cups of water, 5 cups of rice needs 7.5 cups of water.

Common mistakes and limits

Keep the order of the quantities consistent, since 2:3 and 3:2 are different. Make sure both sides use the same units, and be careful when a ratio describes parts of a whole rather than two separate amounts.