Proportion calculator
Solve proportion problems, also known as the rule of three: enter three values, leave blank the one you are looking for, and get the result with the working explained.
Fill in three values and leave blank the one you want to calculate.
Step-by-step solution
- Formula
—- With your values
—
How to use it
- Choose the type of relationship: direct (if one goes up, so does the other), inverse (if one goes up, the other goes down), or compound (more than two quantities).
- For a simple proportion, fill in three of the four values and leave blank the one you want to calculate. You can name them, like pounds or dollars, so the sentence with the result reads clearly.
- For a compound proportion, enter the known result and add a row for each quantity that changes, saying whether the relationship is direct or inverse.
- Read the result and the step-by-step working, and copy the link if you want to share the problem.
Frequently asked questions
How do I know if the relationship is direct or inverse?
It is direct if, when one quantity goes up, the other goes up in the same proportion, like pounds of fruit and their price. It is inverse if, when one goes up, the other goes down, like the number of workers and the days they need to finish a job.
How do you solve a direct proportion?
Multiply the two values that sit diagonally from each other and do not include the unknown, then divide by the third. If 3 pounds cost $45 and you want to know the cost of 5, X = 45 × 5 ÷ 3 = $75. This is also called cross multiplication.
What about an inverse proportion?
In an inverse proportion the product stays constant: A × B = C × X. If 3 workers take 12 days, 4 workers take X = 3 × 12 ÷ 4 = 9 days.
What is a compound rule of three?
It links three or more quantities. You start from the known result and multiply by the ratio of each quantity: direct (new ÷ old) or inverse (old ÷ new).
Can I use decimals or fractions?
Yes. Type 2.5 or 1/2. You can also use a comma as the thousands separator, for example 1,250.
Is my data saved?
No. Everything is calculated in your browser and nothing is sent to a server.
What the rule of three is
It is a method for finding an unknown value when you know three others that are proportional to each other. In English it is usually taught as solving a proportion or cross multiplication. It is used in recipes, prices, speeds, maps, and work.
Direct proportion
If 3 pounds of apples cost $45, 5 pounds cost 45 × 5 ÷ 3 = $75. The ratio between price and pounds stays the same: $15 per pound.
Inverse proportion
If 4 workers finish a job in 6 days, 8 workers finish it in 4 × 6 ÷ 8 = 3 days. With more workers, fewer days: the product of workers times days is constant.
Compound proportion
If 4 workers working 6 days produce 120 pieces, 5 workers working 8 days produce 120 × (5 ÷ 4) × (8 ÷ 6) = 200 pieces. Workers and days are both directly related to the pieces.
Tips
- Before calculating, ask yourself whether doubling one quantity doubles the other (direct) or cuts it in half (inverse).
- Keep the same units in each column: pounds with pounds, hours with hours.
- Check the result with a quick estimate: if you double the data, the result should make sense.
Updated on September 29, 2026