# Ratio Calculator — Simplify Ratios & Solve Proportions

> Simplify a ratio like 8:12 to lowest terms, solve a proportion a:b = c:x for the missing number, and read the decimal value. Handles decimals and 3-part ratios.

- **Category:** Math
- **Interactive calculator:** https://youcalc.com/en/math/ratio-calculator/
- **Price:** Free, no sign-up required

## Overview

A ratio compares two (or three) quantities of the same kind — 8 cups of flour to 12 cups of water is the ratio 8 : 12. This calculator does the two jobs people reach for most. In simplify mode it reduces a ratio to its lowest whole-number terms (8 : 12 becomes 2 : 3) and reports the decimal value A ÷ B. In proportion mode it solves a true proportion A : B = C : x for the one term you are missing, which is exactly how you scale a recipe up, convert a map distance, or split a sum in a given ratio. Decimals such as 2.5 : 5 are handled by scaling every term up to whole numbers before reducing.

## How to read your result

In simplify mode the large figure is the ratio in its simplest form, with the greatest common divisor (GCD) and the decimal value A ÷ B shown beneath it; a ratio is already in lowest terms when its GCD is 1. Add a third value to reduce a three-part ratio such as 2 : 4 : 6 to 1 : 2 : 3. In proportion mode the headline is the missing term x, and the proportion row restates the full statement A : B = C : x with the gap filled in, so you can sanity-check that both halves really are equal.

## Method

To simplify, each term is first scaled to a whole number by a common power of ten (so 2.5 : 5 becomes 25 : 50), the greatest common divisor of the scaled terms is found with the Euclidean algorithm, and every term is divided by that GCD. The decimal value is simply A ÷ B. To solve a proportion A : B = C : x, the calculator cross-multiplies — A × x = B × C — and rearranges to x = (B × C) ÷ A. The same rearrangement finds any single missing term once the other three are known.

## Example

- **Setup:** Simplify 8 : 12, then solve the proportion 2 : 3 = 10 : x.
- **Result:** The greatest common divisor of 8 and 12 is 4, so 8 : 12 reduces to 2 : 3, with a decimal value of 8 ÷ 12 ≈ 0.6667. For the proportion, cross-multiplying gives x = (3 × 10) ÷ 2 = 15, so 2 : 3 = 10 : 15.

## Frequently asked questions

### How do I simplify a ratio to its lowest terms?

Find the greatest common divisor (GCD) of the terms and divide each term by it. For 8 : 12 the GCD is 4, so 8 ÷ 4 : 12 ÷ 4 gives 2 : 3. A ratio is already in lowest terms when the only number that divides every term is 1.

### Can I simplify a ratio that contains decimals?

Yes. The calculator scales every term up by a common power of ten until they are whole numbers, then reduces. So 2.5 : 5 becomes 25 : 50, which reduces to 1 : 2. The result is always expressed in whole numbers.

### How do I solve a proportion for the missing number?

Write it as A : B = C : x and cross-multiply, so A × x = B × C, which rearranges to x = (B × C) ÷ A. For 2 : 3 = 10 : x that is x = (3 × 10) ÷ 2 = 15. Switch to "Solve a proportion" mode and enter A, B and C.

### What is the decimal value of a ratio?

It is the first term divided by the second, A ÷ B. For 7 : 2 the decimal value is 3.5, meaning the first quantity is 3.5 times the second. It is shown only for two-part ratios, since a three-part ratio has no single decimal value.

## Related calculators

- [Rule of Three Calculator](https://youcalc.com/en/math/rule-of-three-calculator/)
- [Percentage Calculator](https://youcalc.com/en/math/percentage/)
- [Fraction Calculator](https://youcalc.com/en/math/fraction-operations/)
- [Golden Ratio Calculator](https://youcalc.com/en/math/golden-ratio-calculator/)
- [Aspect Ratio Calculator](https://youcalc.com/en/conversions-units/aspect-ratio-calculator/)

## Sources

- https://mathworld.wolfram.com/Ratio.html
- https://en.wikipedia.org/wiki/Ratio

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Interactive version: https://youcalc.com/en/math/ratio-calculator/ · From YouCalc — https://youcalc.com