Rule of Three Calculator
Solve direct and inverse proportion problems: enter the known pair and the new value to get the result, a three-step solution and the formula used.
The more, the more: If A belongs to B, how much belongs to X?
Known assignment
If A ⇒ B, then X ⇒ ?
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Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
What is the rule of three?
The rule of three is a method for proportional calculations. Given three known values, you can find the fourth. Set up the proportion, cross-multiply, and divide to find the unknown value.
What is the difference between direct and inverse proportionality?
In direct proportionality, both values increase together (more workers = more output). In inverse proportionality, as one increases the other decreases (more workers = less time per task).
Does the calculator show the working steps?
Yes. In addition to the final result the calculator displays the intermediate steps so you can follow the solution — ideal for school, university or homework.
Guide
What is the Rule of Three Calculator?
The rule-of-three calculator solves proportional and inversely proportional problems in three steps and shows the full solution path.
How does the Rule of Three Calculator work?
Choose proportional or inversely proportional. Enter three known values. The calculator solves in three steps: starting situation, reduce to one unit, scale to the target value. Each step is explained.
Key Data and Facts
Proportional: x = (b * c) / a. Inversely proportional: x = (a * b) / c. Applications: prices, recipe quantities, working time, currencies.
Step-by-Step Guide
How to solve rule-of-three problems step by step: 1. Determine the type of relationship: proportional (the more, the more) or inversely proportional (the more, the less). 2. Write down the starting situation: Two values that belong together, e.g. 5 apples cost 3 EUR. 3. Reduce to the unit: For the proportional case: 1 apple = 3 / 5 = 0.60 EUR. For the inversely proportional case: form the product: 5 x 3 = 15. 4. Scale up to the target value: Proportional: 8 apples = 0.60 x 8 = 4.80 EUR. Inversely proportional: 8 workers need 15 / 8 = 1.875 hours. 5. Typical applications: converting recipes (proportional), comparing prices, converting currencies, working-time problems (inversely proportional). 6. Short formula for proportional: x = (b x c) / a. Short formula for inversely proportional: x = (a x b) / c. The calculator shows each step individually.
Calculation Example
Direct proportion: 5 apples cost 3 EUR. What do 8 apples cost? 1 apple = 3/5 = 0.60 EUR. 8 apples = 8 x 0.60 = 4.80 EUR. Inverse proportion: 6 workers need 10 days. How long do 4 workers need? 6 x 10 / 4 = 15 days.
Sources
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Reviewed by Konstantin Iakovlev · Last updated:
Mathematics
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