What is a proportion?
A proportion says that two ratios are equal. When we write A : B = C : D, the relationship between A and B is exactly the same as between C and D. If you know any three numbers, the fourth is fixed, and that is what this tool works out.
How to use it
- Type three numbers into the four boxes. Leave the one you want to find empty.
- Press Calculate, or press Try an example to see one worked out.
- Read the answer and the explanation underneath. The same working is repeated in math form so you can copy it into homework or notes.
The method: cross-multiplication
Write the proportion as two fractions and multiply diagonally. The two products must be equal, so you can solve for the unknown:
For example, if 3 : 2 = C : 14, then 3 × 14 = 2 × C, so C = 42 ÷ 2 = 21.
Examples you can try
| Proportion | Missing value | Working |
|---|---|---|
| 3 : 2 = ? : 14 | 21 | 3 × 14 ÷ 2 |
| 5 : 8 = 15 : ? | 24 | 8 × 15 ÷ 5 |
| ? : 9 = 4 : 6 | 6 | 9 × 4 ÷ 6 |
| 7 : ? = 21 : 12 | 4 | 7 × 12 ÷ 21 |
| 1.5 : 4 = ? : 10 | 3.75 | 1.5 × 10 ÷ 4 |
Where proportions come up
- Recipes: if 3 cups of flour make 2 loaves, how much flour do 14 loaves need? 3 : 2 = ? : 14 gives 21 cups.
- Maps and models: 1 inch on the map is 5 miles, so 3.5 inches is 17.5 miles.
- Shopping: compare prices for different sizes by finding the cost for one unit (try the unit rate calculator).
- Work and speed: if you drive 120 miles in 2 hours, how far in 5 hours at the same speed? 120 : 2 = ? : 5 gives 300 miles.
Tips
- Keep the same order on both sides. If A and C are both "miles", then B and D must both be "hours".
- Leave exactly one box empty. If more are empty the problem has many answers; if none are empty, use the compare ratios calculator to check whether the two sides match.
- A zero in the denominator position cannot be divided by, so B and D cannot be zero.
Read our short guide with worked examples you can follow on paper.
Frequently asked questions
How do you solve a proportion?
Cross-multiply and divide. For A : B = C : D, the missing value is found from A × D = B × C. Divide both sides by the number next to the unknown.
Can the unknown be in any position?
Yes. Leave any one of the four boxes empty and the calculator solves for it.
What is the difference between a ratio and a proportion?
A ratio compares two quantities. A proportion is a statement that two ratios are equal.
Does it work with decimals and fractions?
It works with decimals. For a fraction such as 1/2, type 0.5.
Why does the calculator say a value cannot be zero?
Because dividing by zero is undefined. In a proportion, the number you divide by cannot be zero.