Ratio Calculator
A ratio expresses the relationship between two quantities. The proportion A:B = C:D means that A×D = B×C (the cross-multiplication property). This calculator solves for any one missing term when the other three are known.
You can also simplify a ratio to its lowest terms by dividing both sides by their greatest common divisor (GCD). Ratios appear everywhere — in recipes, maps, finance, architecture, and mathematics.
How it works
A : B = C : D ⟹ A × D = B × C. To solve for a missing term, rearrange: e.g., D = (B × C) / A. To simplify A : B, divide both by GCD(A, B).
Use cases
- Scaling recipes up or down
- Solving proportion problems in math class
- Determining map or blueprint scales
- Mixing paint, cement, or chemical solutions in given ratios
Frequently asked questions
How do you solve a ratio with a missing value?
Use cross-multiplication: in A:B = C:D, the products A×D and B×C are equal, so you can rearrange to find any missing term. For example, to find D you compute D = (B × C) / A. Enter the three known values and the calculator solves the fourth automatically.
How do I simplify a ratio to its lowest terms?
Divide both numbers by their greatest common divisor (GCD). For example, 18:24 has a GCD of 6, so it simplifies to 3:4. The calculator finds the GCD and reduces the ratio for you in one step.
What does a ratio like 3:4 actually mean?
A ratio of 3:4 means that for every 3 parts of the first quantity there are 4 parts of the second, for a total of 7 parts. It describes relative proportion, not absolute amounts, so 3:4 is the same relationship as 6:8 or 30:40. This is why ratios can always be scaled up or simplified down.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, such as 3:4, while a proportion is a statement that two ratios are equal, such as 3:4 = 6:8. Solving a proportion means finding the value that makes both ratios equivalent, which is exactly what cross-multiplication does. This calculator handles both simplifying single ratios and solving proportions.
How do I scale a recipe using ratios?
Set up a proportion between the original quantity and the new one, then solve for the missing ingredient amount. For example, if a recipe uses a 2:3 flour-to-sugar ratio and you have 500 g of flour, solve 2:3 = 500:x to get x = 750 g of sugar. The calculator does this cross-multiplication instantly.