Proportion Calculator

If a/b = c/d, then the diagonal products are equal: a × d = b × c. From there, isolate whichever variable is unknown by dividing. Solving for d gives d = (b × c) / a. Solving for a gives a = (b × c) / d. The reason this works is that multiplying both sides of an equation by the same nonzero number does not change equality — multiplying a/b = c/d by b × d clears both denominators in one step.

Cross-multiplication only applies when both sides are a single ratio. It does not work for a/b + e = c/d or a/b × c = e/f. For more complex expressions, isolate the ratio first, then cross-multiply.

A cookie recipe calls for 2 cups of flour and makes 24 cookies. How much flour do you need for 30 cookies? Set up 2/24 = x/30. Cross-multiply: 2 × 30 = 24 × x, so x = 60/24 = 2.5 cups. Notice the units cancel cleanly because both ratios are in 'cups per cookie' — that consistency is the most common place beginners go wrong.

A road map shows 1 inch = 25 miles. The distance between two cities measures 3.4 inches. Set up 1/25 = 3.4/x. Cross-multiply: x = 25 × 3.4 = 85 miles. The same setup handles scale drawings (architectural plans, model kits) and aspect-ratio resizing (a 1920 × 1080 image needs a 1280 width to keep the 16:9 ratio: 1920/1080 = 1280/y, so y = 720).

Cross-products are the test. 2/3 and 8/12 are proportional because 2 × 12 = 3 × 8 = 24. 2/3 and 7/12 are not, because 2 × 12 = 24 but 3 × 7 = 21. A small cross-product gap usually means a rounding artifact (recipe scaling at restaurants tolerates a few percent); a large gap means the relationship is not actually linear and a proportion is the wrong model.

Inverse relationships need a different setup. If 4 workers paint a wall in 6 hours, how long does it take 6 workers? This is inverse, not direct, proportion: workers × hours = constant. 4 × 6 = 24, so 6 workers take 24/6 = 4 hours.

Percentages are proportions over 100. 'What is 15% of 240?' becomes 15/100 = x/240, giving x = 36. Our dedicated Percentage Calculator handles this pattern with single-purpose inputs if proportions feel like overkill.