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