Simplify ratios, solve proportions, and find missing values instantly.
A ratio compares two quantities by division. A proportion states that two ratios are equal. Ratios and proportions are fundamental in mathematics, science, cooking, finance, and engineering. They help describe relationships between quantities in a clear, standardized form.
The Ratio & Proportion Calculator on Calculator Expert lets you simplify any ratio to its lowest terms, solve for a missing value in a proportion (a:b = c:?), and check whether two ratios form a valid proportion. All computations are instant with step-by-step workings.
| Ratio | Description | Decimal Value |
|---|---|---|
| 1:1 | Equal | 1.000 |
| 1:2 | Half | 0.500 |
| 3:4 | Three-quarters | 0.750 |
| 2:3 | Two-thirds | 0.667 |
| 1:10 | One-tenth | 0.100 |
Enter your values in the empty input fields above and click "Calculate." All fields start empty so you can input any values you need. The result is displayed instantly with the working formula. Calculator Expert provides accurate, ad-free calculations for students, teachers, and professionals.
Method 1: Direct Division Method: Find the GCD of the two numbers using the Euclidean algorithm, then divide both by the GCD to get the simplified form.
Method 2: Cross Multiplication Method: For proportions a:b = c:d, cross multiply to get a×d = b×c, then solve for the unknown variable.
This calculator handles positive integers and decimals. Zero denominators and negative ratios that result in undefined comparisons will return an error. Ratios with irrational number results are rounded to 4 decimal places. Complex ratios involving three or more terms require individual pairwise comparisons.
In body measurement, the waist-to-hip ratio (WHR) is a classic example of a health ratio. A WHR above 0.90 for men or 0.85 for women indicates abdominal obesity. This is calculated directly as waist circumference divided by hip circumference — a simple ratio.
Ratios are used in map scale reading, recipe scaling in cooking, currency exchange calculations, investment portfolio allocation, speed and distance problems, and diluting chemical solutions in chemistry labs.