About the Proportion Calculator
A proportion says that two ratios are equal, written A divided by B equals C divided by D. If you know three of the four numbers, the fourth is fixed, and you can find it by cross-multiplying. This calculator gives you four boxes: fill in any three, leave the one you want to find empty, and it solves the proportion and shows the cross products as a check. It is the classic rule of three used for scaling recipes, converting units, reading maps and solving word problems such as how much 7 items cost if 3 cost 12.
Updated October 2026
How to use the Proportion Calculator
- 1Fill in three of the four boxes A, B, C and D.
- 2Leave the box you want to find completely empty.
- 3The calculator solves the proportion straight away.
- 4Check the line that shows both cross products are equal.
- 5Copy the finished proportion to use in your answer.
Setting up a word problem
Write down what you know as a pair of matching units. If 5 litres of paint cover 40 square metres and you need to cover 70 square metres, put litres on top and area on the bottom: 5/40 = x/70. Enter 5, 40 and 70, leave the last box empty, and the answer is 8.75 litres.
Proportions also underpin similar shapes in geometry. If a model is built at one tenth of real size, every length on the model is one tenth of the real length, so a proportion converts between them. The same idea explains why enlarging a photo keeps its shape when the width and height grow by the same ratio. Whenever two quantities rise and fall together at a steady rate, a proportion describes the link, and this calculator solves it in a second.
Where proportions appear
- Recipes: scaling ingredients up or down.
- Maps and models: converting a measured distance using a scale.
- Money: unit prices, tips and exchange rates.
- Science: concentrations, densities and dilution problems.
Checking your answer
The two cross products must match. If A times D does not equal B times C, one of the numbers was typed wrongly. You can also test by dividing: 3 ÷ 4 and 9 ÷ 12 should both come to 0.75. For simplifying a ratio use the Ratio Calculator, and the Fraction Calculator and Simplify Fraction Calculator tidy up the result.
Features
- Solves for any one of the four positions
- Cross-multiplication check
- Accepts decimals and negatives
- Clear message when two or more boxes are empty
- Protects against division by zero
- Private and offline-friendly
Frequently asked questions
What is a proportion?
A proportion is an equation stating that two ratios or fractions are equal, such as 3/4 = 9/12. The four numbers are linked, so knowing any three lets you work out the fourth.
How do I solve a proportion?
Cross-multiply and divide. For a/b = c/d, multiply a by d and b by c, then isolate the unknown. With 3/4 = 9/x you get 3 × x = 4 × 9, so x = 36 ÷ 3 = 12.
What is the rule of three?
It is an older name for solving a proportion with three known quantities. If 3 pens cost 12, then 7 pens cost 7 × 12 ÷ 3 = 28. Set up the proportion 3/12 = 7/x and the calculator gives the answer.
Does the order of the numbers matter?
Yes, you need to keep like quantities in the same positions. If the top row is pens and the bottom is price, both ratios must follow that pattern. Swapping one side flips the answer.
What happens if a box is zero?
Zero in the numerator is fine in some positions, but zero where you divide makes the proportion impossible to solve. The calculator tells you when that happens instead of showing a wrong value.
How is this different from a ratio calculator?
A ratio calculator simplifies or scales a ratio. A proportion calculator finds a missing value so that two ratios become equal. Use it when you already know how things relate and want the unknown amount.