Ratio Calculator
Simplify a ratio, find the missing term in a proportion, or split a total by a ratio.
Simplified ratio
2 : 3
After scaling to whole numbers, every term was divided by their greatest common divisor, 6.
This tool is for information only. For homework, measurements or dosing, check the result yourself.
What are ratios and proportions?
A ratio compares two or more quantities. A ratio of 12:18 says that for every 12 units of the first there are 18 of the second. A proportion states that two ratios are equal: A:B = C:D. If you know three of the four values you can find the fourth.
A : B = C : D ⇒ A × D = B × CA = B × C ÷ DB = A × D ÷ CC = A × D ÷ BD = B × C ÷ AWorked example: if 3:4 = 9:D then D = 4 × 9 ÷ 3 = 12. The cross products match: 3 × 12 = 4 × 9 = 36.
Simplifying a ratio
To simplify a ratio, divide every term by their greatest common divisor. For 12:18 that divisor is 6, giving 2:3. If there are decimals the calculator first scales everything to whole numbers: 1.5:2.25 becomes 150:225 and reduces to 2:3. You can use more than two terms: 6:9:15 simplifies to 2:3:5.
Splitting a total by a ratio
To share an amount in a given ratio, add the ratio terms, divide the total by that sum, then multiply by each term. Splitting 120 in the ratio 2:3 gives a sum of 5. The shares are 120 ÷ 5 × 2 = 48 and 120 ÷ 5 × 3 = 72.
| Total | Ratio | Part 1 | Part 2 |
|---|---|---|---|
| 120 | 2:3 | 48 | 72 |
| 100 | 1:1 | 50 | 50 |
| 1,000 | 1:4 | 200 | 800 |
Direct and inverse proportion
This calculator solves direct proportion, where one value rises in step with the other. If 3 kg of apples cost 90, then for 5 kg you set 3:90 = 5:D and get D = 150. In inverse proportion one value falls as the other rises, such as workers and time to finish a job. For that case use the fact that the product stays constant: A × B = C × D.