Free Ratio Calculator – Solve Proportions & Simplify

How the Ratio Calculator Solves and Simplifies Proportions

A ratio compares two quantities, and a proportion says two ratios are equal. This calculator handles both jobs: fill in any three boxes of A : B = C : D, leave the fourth blank, and it returns the missing value along with the A : B ratio reduced to its lowest terms. Students working through proportion problems, cooks scaling a recipe for a different number of guests, designers holding an aspect ratio while resizing, and anyone mixing fuel, paint, or fertiliser to a stated ratio all use the same operation. It replaces the cross-multiplication step most people can do but frequently do the wrong way round. The mechanism is cross-multiplication. From A ÷ B = C ÷ D you get A × D = B × C, and rearranging that for whichever term is blank gives you the answer: D = B × C ÷ A, C = A × D ÷ B, B = A × D ÷ C, or A = B × C ÷ D. The tool detects which box is empty and picks the right rearrangement, so you never have to set it up yourself. Simplifying works separately: it finds the greatest common divisor of the two whole numbers and divides both by it. The GCD of 8 and 12 is 4, so 8 : 12 becomes 2 : 3. The one situation with no answer is when the rearrangement would divide by zero, in which case the calculator simply waits for usable input instead of showing something meaningless. Work through a real one. A cake recipe uses 250 g of flour for 4 servings, and you need 7 servings. Set it up as 250 : 4 = ? : 7. Cross-multiplying gives 250 × 7 ÷ 4 = 437.5, so you need 437.5 g of flour. The simplify side is separate: a 1920 × 1080 screen has a GCD of 120, which reduces to 16 : 9, the aspect ratio you would actually quote. Both operations use the same two-number input, just answering different questions. The uses are everyday. A two-stroke engine specifying a 50 : 1 petrol-to-oil mix needs 100 ml of oil for 5 litres of petrol, and getting that wrong seizes the engine. A designer resizing a 1200-pixel-wide banner to 800 pixels uses the proportion to find the matching height and avoid a stretched image. A map at 1 : 50,000 scale converts 3.5 cm on paper into 1.75 km on the ground. And a small business comparing two suppliers, one quoting 12 kg for ₹960 and another 20 kg for ₹1,560, puts both on a per-kilogram basis to see which is genuinely cheaper: ₹80 against ₹78 a kilogram, a gap the headline prices hide entirely. The classic beginner error is inverting the ratio: writing 4 : 250 = 7 : ? instead of 250 : 4 = ? : 7 gives 0.112 rather than 437.5, and the answer is so obviously wrong that it is easy to catch — until the numbers are closer together and it slips through. Keep the same quantity type on the same side of the colon in both ratios, and sanity-check the direction of the answer: scaling up should produce a bigger number. Also note that simplification only applies to whole numbers, since a GCD of decimals is not meaningful, and that ratios do not carry units, so 250 : 4 tells you nothing about whether you are working in grams or kilograms — you have to track that yourself. Everything runs in your browser, so the numbers you enter are never uploaded or stored.

Ratio Calculator Formula & Method

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