Ratio Calculator

Solve proportion problems by finding the missing value in a ratio. Enter any three known values in the format A : B = C : D and the calculator will solve for the unknown value.

Your Results

Enter three values above and click "Calculate".

Understanding and Using Ratios

A ratio is a way of comparing two or more quantities, showing their relative sizes. For example, if a recipe calls for 1 cup of sugar for every 2 cups of flour, the ratio of sugar to flour is 1:2. Proportions are equations where two ratios are set equal to each other. Our calculator is designed to solve these proportions.

How to Use the Ratio Calculator

Using the calculator is simple. The relationship is expressed as A : B = C : D.

Identify the three values you know.
Enter these three values into their corresponding fields (A, B, C, or D).
Leave the field for the value you want to find empty.
Click the "Calculate" button.
The calculator will display the missing value and show the simplified version of both ratios.

The Ratio Formula (Cross-Multiplication)

The calculator solves for the unknown value using cross-multiplication. The proportion A : B = C : D is mathematically equivalent to the fraction equation A/B = C/D. To find the unknown value, we cross-multiply:

A × D = B × C

From this central equation, we can derive the formula for any of the four values:

To find A: A = (B × C) / D
To find B: B = (A × D) / C
To find C: C = (A × D) / B
To find D: D = (B × C) / A

Practical Applications of Ratios

Ratios are used everywhere in daily life and various professional fields:

Cooking and Recipes: Scaling a recipe up or down. If a recipe for 4 servings needs 2 eggs, how many eggs do you need for 6 servings? (2 : 4 = X : 6)
Maps and Models: A map scale of 1:100,000 means 1 unit of distance on the map represents 100,000 units in the real world.
Finance: Many key financial metrics are ratios, like the Price-to-Earnings (P/E) ratio or Debt-to-Equity ratio. Explore more tools on our Financial Calculators page.
Screen and Image Dimensions: The aspect ratio of a screen, like 16:9, defines its shape.

Related Calculators

If you found this tool useful, you might also be interested in our other math tools:

Math Calculators - A full collection of calculators for various mathematical problems.
Percentage Calculator (Coming Soon) - For solving problems involving percentages, discounts, and increases.
Loan & Mortgage Calculator - To understand payments and interest based on financial ratios.