Ratio Calculator — Simplify & Solve Ratios
Simplify any ratio to its lowest terms, scale a ratio to a target total, or solve a proportion with a missing value. Every calculation shows step-by-step working including GCD and cross-multiplication.
What Are Ratios?
A ratio compares two or more quantities, showing how much of one thing there is relative to another. Written as A:B, it means "for every A of the first quantity, there are B of the second." Ratios are used everywhere — in cooking recipes (flour to sugar), map scales (1:50,000), financial analysis (debt-to-income), and mixing solutions (paint, concrete, cocktails).
Key Ratio Formulas
Simplify: A:B → (A/GCD) : (B/GCD)
Scale: A:B to total T → A×(T/(A+B)) : B×(T/(A+B))
Proportion: A:B = C:D → A×D = B×C (cross-multiply)
Real-World Ratio Examples
Recipes: A bread recipe calls for flour to water in a 5:3 ratio. If you use 500g of flour, you need 300g of water. Scaling up: for 2kg flour, you need 1.2kg water.
Maps: A 1:25,000 map scale means 1 cm on the map equals 25,000 cm (250 meters) in real life. A 4 cm distance on the map represents 1 km.
Finance: A debt-to-income ratio of 36:100 (or 0.36) means 36% of your income goes to debt payments. Lenders prefer this ratio below 43%.
Simplifying and Scaling Ratios
To simplify a ratio, find the Greatest Common Divisor (GCD) of all parts and divide each part by it. The GCD is found using the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until the remainder is zero. For example, GCD(12, 8): 12 = 1×8 + 4, then 8 = 2×4 + 0. GCD = 4. So 12:8 = 3:2.
Solving Proportions and Cross-Multiplication
A proportion states that two ratios are equal: A/B = C/D. To find a missing value, cross-multiply: A×D = B×C. Then solve for the unknown. This technique is used in scale drawings, unit conversions, recipe scaling, and similarity problems in geometry. Proportional reasoning is one of the most practical math skills, appearing in everything from calculating exchange rates to resizing images without distortion. Mastering cross-multiplication allows you to solve any proportion problem quickly and confidently.