Rule of Three
Solve proportions visually — find the missing fourth value
25
About this calculator
Solve proportions visually using the rule of three. If A is to B as C is to X, this calculator finds X. Widely used in cooking, unit pricing, scaling recipes, and everyday proportional reasoning.
How to solve a proportion with the rule of three
- Choose direct or inverse proportion based on your problem.
- Enter the three known values A, B, and C.
- Read the missing fourth value D in the result.
- Check the proportion bars to see why the answer is what it is.
Common examples
- If 2 is to 5, then 6 is to 15
- If 3 is to 12, then 7 is to 28
- If 100 is to 25, then 60 is to 15
- If 1 is to 3.5, then 4 is to 14
- If 8 is to 2, then 20 is to 5
Frequently asked questions
What is the rule of three?
The rule of three solves a proportion: given three known values A, B, and C, it finds the fourth value D such that A is to B as C is to D. It is one of the most common everyday math tools, used to scale recipes, compare prices, and adjust measurements.
What is the difference between direct and inverse proportion?
In a direct proportion, both quantities grow or shrink together, so D = (B × C) ÷ A. In an inverse proportion, one quantity grows while the other shrinks proportionally, so D = (A × B) ÷ C. Pick the type that matches your situation.
When would I use an inverse proportion?
Use inverse proportion when more of one thing means less of the other — for example, more workers finishing a job in less time, or higher speed covering a fixed distance in less time.
Why does the calculator say the proportion is undefined?
If the divisor in the formula is zero (A in direct mode, or C in inverse mode), the proportion has no finite answer. The calculator shows an invalid state instead of a misleading number.