MATH · RATIO
Ratio Calculator
Simplify a ratio to its lowest terms, or solve a proportion a:b = c:? to find the missing fourth term.
2:3
About This Calculator
A ratio compares two quantities. Simplified ratios are easier to read and scale. The Proportion mode extends ratios to three-term problems — given a:b and c, find the fourth term d such that a:b = c:d.
How It Works
In Simplify mode, enter two numbers to get their reduced ratio using GCD. In Proportion mode, also enter a third value c and the calculator solves for the missing fourth term using cross-multiplication.
The Formula
Simplify: (a/gcd):(b/gcd) Proportion: d = (b × c) / a
- gcd
- greatest common divisor of a and b
- d
- unknown fourth term in the proportion
Frequently Asked Questions
- What is a ratio?
- A ratio expresses the relative sizes of two quantities. 8:12 means "for every 8 of one thing, there are 12 of another" — or equivalently 2:3 when simplified.
- How is proportion solving useful?
- If a recipe uses 2 cups of flour for 3 servings, proportion solving tells you how much flour is needed for 10 servings — 15 cups (2:3 = 10:15).
- What happens when the first term is zero?
- When a = 0 in proportion mode, the formula divides by zero. The calculator returns an error. Ratios like 0:5 can still be simplified (to 0:1) in Simplify mode.