Rule of Three Calculator
Solve proportional problems easily with our Rule of Three calculator. Perfect for math, cooking, finance, chemistry, and everyday calculations.
How to Use This Calculator:
- Select whether your problem involves direct or inverse proportion
- Enter three known values (A, B, and C)
- The calculator will compute the fourth value (D)
- Review the solution steps to understand the calculation
- Copy the result if needed
Understanding the Rule of Three
Direct Proportion
When two quantities are directly proportional, their ratio remains constant. If A is to B as C is to D, then A/B = C/D. To find D, use: D = (B × C) / A.
Example: If 5 apples cost $2, how much do 15 apples cost? (5/2 = 15/D → D = $6)
Inverse Proportion
When two quantities are inversely proportional, their product remains constant. If A × B = C × D, then to find D use: D = (A × B) / C.
Example: If 6 workers build a wall in 10 days, how long would 15 workers take? (6×10 = 15×D → D = 4 days)
Practical Applications
The Rule of Three is used in cooking (recipe scaling), finance (currency conversion), chemistry (stoichiometry), construction (material estimates), and many everyday calculations.
Historical Context
Known since ancient times, the Rule of Three was fundamental in medieval mathematics. Indian mathematicians called it "Trairāśika" and it was central to European commercial arithmetic.
Common Use Cases
Cooking & Baking
Adjust recipes when changing serving sizes. If a cake recipe for 8 people requires 2 cups of flour, how much flour is needed for 12 people? (8/2 = 12/D → D = 3 cups)
Currency Conversion
Convert between currencies when traveling. If $1 = €0.85, how many euros will you get for $150? (1/0.85 = 150/D → D = €127.50)
Speed and Time
Calculate travel time at different speeds. If you drive 300 km in 4 hours at constant speed, how long to drive 450 km? (300/4 = 450/D → D = 6 hours)
Shopping Discounts
Determine sale prices. If a $40 shirt is discounted to $30, what's the discounted price of a $60 shirt from the same store? (40/30 = 60/D → D = $45)
Rule of Three Calculator FAQ
How do I know if a problem is direct or inverse proportion?
In direct proportion, quantities increase or decrease together (more workers → more production). In inverse proportion, one quantity increases as the other decreases (more workers → less time needed). Test by considering how changing one variable affects another.
Can the Rule of Three handle units?
Yes, but you must ensure consistent units across the proportion. Convert all measurements to the same unit system before calculating. The calculator doesn't automatically convert units.
What if I have more than four variables?
The basic Rule of Three handles simple proportions. For complex relationships with multiple variables, you might need extended methods like the Compound Rule of Three or algebraic equations.
How accurate are the results?
The calculator provides precise mathematical results, but real-world applications may require rounding to practical values (e.g., whole items, standard measurements). The tool displays 4 decimal places by default.
Can I calculate any of the four values?
This calculator solves for D when A, B, and C are known. To solve for a different variable, rearrange your known values so the unknown is in the D position or use the proportion rules manually.
Why Use Our Rule of Three Calculator?
Master Proportional Reasoning
Our Rule of Three calculator simplifies proportional thinking for students, professionals, and anyone needing quick, reliable ratio calculations. Whether adjusting recipes, converting measurements, or solving math problems, this tool helps you find correct proportions effortlessly.