Rule of Three Calculator
Solve proportions with the rule of three: if A gives B, then C gives what? Uses cross-multiplication to find the unknown fourth value in any ratio.
The Rule of Three is a method for solving proportional relationships when three values are known and the fourth is unknown. It is one of the oldest and most universally useful mathematical tools.
Direct proportion formula:
A / B = C / X → X = (B × C) / A
Or equivalently: if A relates to B as C relates to X, then cross-multiply to solve.
Inverse proportion formula:
A × B = C × X → X = (A × B) / C
Use inverse proportion when increasing one quantity decreases the other (e.g., more workers = less time).
Worked example — Direct proportion: If 5 kilograms of apples cost $8.50, how much do 8 kilograms cost?
- X = (8 × 8.50) / 5 = 68 / 5 = $13.60
Worked example — Inverse proportion: If 4 workers can complete a job in 9 days, how long will 6 workers take?
- X = (4 × 9) / 6 = 36 / 6 = 6 days
Percentage as Rule of Three: What percentage is 45 of 180?
- 180 is to 100% as 45 is to X%
- X = (45 × 100) / 180 = 25%
Unit conversions as Rule of Three: Convert 75 miles to kilometers (1 mile = 1.60934 km):
- X = (75 × 1.60934) / 1 = 120.7 km
Where this rule appears:
- Cooking: scaling recipes up or down
- Finance: currency conversion, sales tax, discounts
- Science: stoichiometry and unit analysis
- Construction: scaling blueprints and material estimates
- Medicine: dosage calculations based on body weight
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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