# Free online ratio calculator

> A ratio compares two quantities by division. This calculator simplifies ratios to lowest terms, shows the decimal equivalent, and solves proportion problems.

Simplify ratios, find the decimal equivalent, and solve proportions. Supports two-term and three-term ratios.

**Interactive version:** https://onlinecalculator.me/math/ratio/
**Category:** Math

## How to use

1. Enter values for **A** and **B**.
2. Optionally enter **C** to solve proportions (A:B = x:C or A:B = C:x).
3. Click **Calculate**.
4. See the simplified ratio, decimal form, and proportion solutions.

## Formulas

**Simplified ratio:** Divide both terms by GCD(A, B).

**Decimal:** A ÷ B

**Proportion (x:C):** x = A × C ÷ B

**Proportion (C:x):** x = B × C ÷ A

## Worked example

**Ratio 6:8:**
- GCD(6, 8) = 2
- Simplified: 6÷2 : 8÷2 = **3:4**
- Decimal: 6÷8 = **0.75** (75%)

**Proportion: 3:4 = x:12**
- x = 3 × 12 ÷ 4 = **9**
- So 3:4 = 9:12 ✓

## Frequently asked questions

### How do you simplify a ratio?

Find the greatest common divisor (GCD) of both numbers and divide each by it. For 6:8, GCD is 2, so 6÷2 = 3 and 8÷2 = 4, giving simplified ratio 3:4.

### What is a proportion?

A proportion states that two ratios are equal. If A:B = x:C, then x = A×C÷B. For example, if 3:4 = x:12, then x = 3×12÷4 = 9.

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

The decimal form of A:B is A÷B. For 3:4, the decimal is 3÷4 = 0.75, which equals 75%.

### Can ratios have decimal or fractional parts?

Yes. A ratio like 1.5:2 is equivalent to 3:4. The calculator handles decimal inputs and simplifies them to integer form.

### What is a three-term ratio?

A three-term ratio like 2:3:5 compares three quantities simultaneously. It can describe mixtures, scales, or divisions. For example, to split $1,000 in a 2:3:5 ratio, multiply each part by 1000÷10.

## Sources

- [Ratio](https://en.wikipedia.org/wiki/Ratio) — Wikipedia
- [Ratio](https://mathworld.wolfram.com/Ratio.html) — Wolfram MathWorld

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