In a direct proportion, two quantities grow or shrink together. If A is to B as C is to X, then X = B × C / A. Example: 3 workers produce 6 items per day; 5 workers would produce 10.
Rule of Three Calculator
Solve direct, inverse and compound proportions with step-by-step equations.
Direct, inverse and compound rule of three with detailed solution.
The rule of three is a method for solving proportions when three values are known and a fourth is unknown. In a direct proportion (A/B = C/X), increasing one value increases the other proportionally. In an inverse proportion (A×B = C×X), increasing one value decreases the other. For compound cases, use multiple columns each with an individual proportion type.
Fill in three values and see X calculated automatically.
- Choose the proportion type: direct or inverse.
- Enter values A, B and C.
- The result X and the step-by-step solution are shown instantly.
Sources and references for this tool
These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
- Proporção (matemática) — WikipediaWikipedia — Definition of direct and inverse proportion and the rule of three.
- Cross-multiplication — Khan AcademyKhan Academy — How to solve proportions by cross-multiplication, the basis of the rule of three.
- Razão e Proporção — NCTMNCTM — Pedagogical principles on ratio and proportion in mathematics education.