# Ratio Calculator

> To simplify a ratio, divide each term by their greatest common factor: 24 : 36 becomes 2 : 3 after dividing by 12. To solve 3 : 4 = 9 : x, cross-multiply to get x = 4 × 9 ÷ 3 = 12, and 1,200 split in the ratio 2 : 3 : 5 gives 240, 360 and 600.

- Interactive calculator: https://calculatorswithsteps.com/ratio-calculator
- Category: Math & Statistics Calculators
- Last updated: 2026-11-10
- Publisher: Calculators With Steps (calculatorswithsteps.com)

## How to use the ratio calculator

Pick what you want to do from the drop-down, enter your numbers and read the answer. The step-by-step working appears under the result.

| You want to | Choose | Example |
| --- | --- | --- |
| Reduce a ratio to lowest terms | Simplify a ratio | 24 : 36 = 2 : 3 |
| Simplify a ratio of 3 or 4 numbers | Simplify a ratio (fill C and D) | 12 : 18 : 30 = 2 : 3 : 5 |
| Find a missing value | Solve a proportion | 3 : 4 = 9 : x gives x = 12 |
| Check two ratios are equal | Solve a proportion (fill all four) | 3 : 4 and 9 : 12 are equal |
| Share money or a quantity | Divide an amount in a ratio | 1,200 in 2 : 3 : 5 = 240, 360, 600 |

In proportion mode, leave exactly one of the four boxes blank. The calculator solves for that box, so it handles A : B = C : x as well as x : B = C : D.

## Ratio formulas

A ratio A : B says that for every A of the first quantity there are B of the second. Ratios can be written as A : B, as the fraction A/B, or in words ("3 to 4"). The working behind each mode is short:

- **Simplest form:** A : B = (A ÷ GCF) : (B ÷ GCF), where GCF is the greatest common factor of the terms.
- **Proportion (cross-multiplication):** if A : B = C : D, then **A × D = B × C**, so D = B × C ÷ A.
- **Dividing an amount T in the ratio A : B : C:** one part = T ÷ (A + B + C), and each share = its part × one part.
- **Percentage share:** share of A = A ÷ (A + B) × 100.

To simplify a ratio that contains decimals, the calculator first multiplies every term by 10, 100 or 1,000 so that all terms are whole numbers. That does not change the ratio, because every term is scaled by the same amount.

## Worked examples

| Problem | Working | Answer |
| --- | --- | --- |
| Simplify 24 : 36 | GCF = 12, 24 ÷ 12 : 36 ÷ 12 | 2 : 3 |
| Simplify 1.5 : 2.5 | × 10 gives 15 : 25, GCF = 5 | 3 : 5 |
| Simplify 12 : 18 : 30 | GCF = 6 | 2 : 3 : 5 |
| Simplify a 1920 × 1080 screen | GCF = 120 | 16 : 9 |
| Solve 3 : 4 = 9 : x | x = 4 × 9 ÷ 3 | 12 |
| Split 1,200 in 2 : 3 : 5 | 10 parts, one part = 120 | 240, 360, 600 |

The split example is the one people get wrong most often. A ratio of 2 : 3 : 5 does not mean the first person gets 2/3 of anything. It means the amount is cut into 2 + 3 + 5 = 10 equal parts, and the first person takes 2 of them, which is 20% of the total.

## Ratios in cooking, mixing and screens

**Recipes.** Many rice recipes use 1 part rice to 2 parts water. For 3 cups of rice, solve 1 : 2 = 3 : x and you get 6 cups of water. Scaling a whole recipe works the same way: keep the ratio and change the amounts.

**Fuel and cleaning mixes.** A two-stroke engine that needs a 50 : 1 petrol-to-oil mix takes 100 mL of oil for 5 litres (5,000 mL) of petrol, because 50 : 1 = 5,000 : x gives x = 100. Make sure both sides use the same unit before you solve.

**Images and screens.** Aspect ratios are ratios of width to height. A 1920 × 1080 screen simplifies to 16 : 9, so a 1280-pixel-wide video at the same shape is 720 pixels tall. To work out what share each part is of a whole, the [percentage calculator](https://calculatorswithsteps.com/percentage-calculator) is handy, and the [fraction calculator](https://calculatorswithsteps.com/fraction-calculator) helps when a ratio is written as a fraction.

## Common ratio mistakes

- **Mixing units.** 30 cm to 2 m is not 30 : 2. Convert first: 30 cm : 200 cm = 3 : 20. The [unit converter](https://calculatorswithsteps.com/unit-converter) helps when the units differ.
- **Changing the order.** 2 : 3 and 3 : 2 are different ratios. Keep the terms in the order the question gives them.
- **Confusing part-to-part with part-to-whole.** In a class with a boy-to-girl ratio of 2 : 3, boys make up 2/5 of the class, not 2/3.
- **Adding to both terms.** Adding the same number to each term changes the ratio. Only multiplying or dividing every term by the same number keeps it equal.
- **Stopping too early.** 8 : 12 divided by 2 gives 4 : 6, but 4 and 6 still share a factor. Dividing by the GCF in one step (here 4) goes straight to 2 : 3. The [GCF and LCM calculator](https://calculatorswithsteps.com/gcf-lcm-calculator) shows the GCF for longer lists.

## Frequently asked questions

### How do you calculate the ratio of two numbers?

Write the numbers as A : B, then divide both by their greatest common factor (GCF). For 24 and 36 the GCF is 12, so 24 : 36 simplifies to 2 : 3. As a fraction that is 2/3, or about 0.666667.

### How do you simplify a ratio with three numbers?

Find the GCF of all three numbers and divide each one by it. For 12 : 18 : 30 the GCF is 6, so the ratio simplifies to 2 : 3 : 5.

### How do you simplify a ratio that has decimals?

Multiply every term by the same power of 10 to clear the decimals, then divide by the GCF. 1.5 : 2.5 becomes 15 : 25, and dividing both by 5 gives 3 : 5.

### How do I solve a proportion like 3 : 4 = 9 : x?

Cross-multiply and divide. 3 × x = 4 × 9 = 36, so x = 36 ÷ 3 = 12. The same method works whichever of the four terms is missing.

### How do you divide an amount in a ratio?

Add the parts of the ratio, divide the amount by that total to get the value of one part, then multiply each part by it. To split 1,200 in the ratio 2 : 3 : 5 there are 10 parts, one part is 120, and the shares are 240, 360 and 600.

### How do I turn a ratio into percentages?

Divide each part by the total of all the parts and multiply by 100. In 2 : 3 the total is 5 parts, so the first share is 40% and the second is 60%.

### What is the difference between a ratio and a proportion?

A ratio compares two or more quantities, such as 3 : 4. A proportion is a statement that two ratios are equal, such as 3 : 4 = 9 : 12. You can check a proportion by cross-multiplying: 3 × 12 and 4 × 9 are both 36.

### What height should a 1280-pixel-wide image be for a 16:9 aspect ratio?

Solve 16 : 9 = 1,280 : x. Cross-multiplying gives 16 × x = 11,520, so x = 720 and the image should be 1280 × 720 pixels.

## Sources

- [Wikipedia – Ratio](https://en.wikipedia.org/wiki/Ratio)
- [Wolfram MathWorld – Ratio](https://mathworld.wolfram.com/Ratio.html)
- [Khan Academy – Ratios, rates and percentages](https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic)