Rule of Three Calculator
Free rule of three calculator. Solve direct and inverse proportions step by step. Enter three known values to find the fourth using cross-multiplication with a clear explanation of the process.
If A is to B, then C is to X. (More A → More B)
What is the Rule of Three?
The rule of three is a mathematical method that allows you to calculate an unknown value from three known values by establishing a proportional relationship between them. It is one of the most useful tools in applied mathematics, used in everyday calculations like cooking, shopping, and engineering.
Direct vs. Inverse Rule of Three
Direct proportion: when one quantity increases, the other also increases. Example: more hours worked = more money earned. Inverse proportion: when one quantity increases, the other decreases. Example: more workers = less time to finish the job.
Frequently Asked Questions
What is the formula for the direct rule of three?
If A is to B as C is to X, then X = (B x C) / A. You cross-multiply the known values and divide by the remaining value. This is also known as cross-multiplication.
When should I use the inverse rule of three?
Use the inverse rule of three when the two quantities are inversely proportional - that is, when increasing one causes the other to decrease proportionally. The formula becomes X = (A x B) / C.
Can the rule of three be used with percentages?
Yes. The rule of three is an excellent way to solve percentage problems. For example, to find what 25% of 80 is, set up: 100 is to 80 as 25 is to X, giving X = (80 x 25) / 100 = 20.