What the ratio calculator does
The ratio calculator handles the two most common ratio problems: solving a proportion A:B = C:D when one of the four values is unknown, and simplifying a ratio to its lowest terms. Both modes show the calculation step by step, so the tool works as a quick checker and a learning aid at the same time.
Solving a proportion
A proportion is a statement that two ratios are equal. If three of the four values are known, the fourth comes from cross-multiplying:
A × D = B × C
Rearranged for each unknown: A = (B × C) ÷ D, B = (A × D) ÷ C, C = (A × D) ÷ B, D = (B × C) ÷ A. Leave one field blank in the calculator and it picks the correct rearrangement automatically.
Simplifying a ratio
To simplify, divide both terms by their greatest common divisor (GCD). The Euclidean algorithm finds the GCD in seconds: 12:8 → GCD(12, 8) = 4 → 3:2. The simplified ratio carries the same proportional meaning but in the smallest whole numbers, which is easier to read and use in further calculations.
Where ratios show up
- Recipes. 2 cups flour : 1 cup sugar — scale up or down by keeping the ratio.
- Maps. A 1:50,000 scale means 1 cm on the map equals 50,000 cm (500 m) on the ground.
- Aspect ratios. 16:9 displays, 4:3 photos, 21:9 ultrawide.
- Mixing. 3:1 concrete (aggregate:cement), 1:20 oil:fuel for a two-stroke engine.
- Finance. Price-to-earnings, debt-to-equity, current ratio.
- Mechanics. Gear ratios, lever advantages.
Ratios vs fractions vs percentages
They are related forms of the same idea. The ratio 3:4 corresponds to the fraction 3/(3+4) = 3/7 (the share of one part out of the whole) or the ratio fraction 3/4 (the relative size of one to the other), and to 75% when comparing the smaller to the larger. Pick the form that matches the question you are answering.
Use with the other tools
For fractions specifically, the fraction calculator adds, subtracts, multiplies and divides with step-by-step working. For percentages, see the percentage calculator.