Calculators
Rule of Three Calculator
Solve direct and inverse proportion problems — the classic rule of three — with every step shown so you can verify the reasoning.
Every solution shows the cross-multiplication formula. Computed locally.
Direct or Inverse: The One Decision That Matters
Before plugging numbers in, decide whether the relationship is direct (more workers, more output) or inverse (more workers, fewer days): the inverse case divides instead of multiplying. Writing the four values in a 2×2 grid with the unknown in the empty corner makes the direction visible — and is the fastest way to catch the classic mistake of setting up an inverse problem as a direct one.
The Formula Behind the Result
- Enter three known values in the A→B, C→X layout.
- Choose direct proportion (more of A means more of B) or inverse (more of A means less of B).
- The result X is computed with cross-multiplication, and the intermediate steps are displayed.
- Common use cases: unit prices, recipe scaling, work-time estimates, and currency-free conversions.
Worked Example
Common Questions
How do I know if my problem is direct or inverse?
Ask: if the first quantity grows, does the second grow too (direct) or shrink (inverse)? Speed vs travel time is the classic inverse case.
Is the rule of three always valid?
Only when the relationship is truly proportional. Fuel consumption, for example, is not perfectly proportional at extreme speeds.
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