Rule of Three Calculator
Find the unknown in direct and inverse proportions
If A → B, then C → X. When one grows, the other grows (cross-multiplication).
Free Rule of Three Calculator
Solve direct and inverse proportions for X
The rule of three finds a fourth value from three known ones. In a direct proportion the quantities rise together: if 3 pens cost 12, 5 pens cost X = 12 × 5 ÷ 3 = 20. In an inverse proportion one rises as the other falls: if 4 workers finish a job in 6 days, 8 workers need X = 4 × 6 ÷ 8 = 3 days. Pick the mode, enter A, B and C, and the answer appears with its formula. Ideal for scaling recipes, map scales, speed and time, price and quantity, and mixture problems.
Features
Direct and inverse
Both kinds of proportion in one tool
With the formula
Cross-multiplication shown step by step
Instant
Updates as you type
School friendly
Homework and exam practice
Formulas and Examples
Direct proportion
- A / B = C / X → X = B × C ÷ A
- 3 pens cost 12 → 5 pens cost 20
- Map: 2 cm = 50 km → 7 cm = 175 km
- Recipe for 4 uses 300 g flour → for 6 use 450 g
Inverse proportion
- A × B = C × X → X = A × B ÷ C
- 4 workers, 6 days → 8 workers, 3 days
- 60 km/h for 2 hours → 120 km/h for 1 hour
- More taps, less time to fill the tank
Frequently Asked Questions
How does the rule of three work?
For a direct proportion cross-multiply: if A/B = C/X then X = B × C ÷ A. For an inverse proportion the products are equal: A × B = C × X, so X = A × B ÷ C.
What is the difference between direct and inverse proportion?
In a direct proportion both quantities change the same way (more items, more money). In an inverse proportion they change in opposite directions (more workers, fewer days).
Can I solve percentage problems with it?
Yes: 15% of 200 is 100 → 15, so 200 → X = 30. For everyday use the percentage calculator is quicker.
What is a compound proportion?
A problem where more than two quantities change together (workers, days, hours). This tool solves two-quantity proportions; split a compound problem into two steps.
Can I enter decimals?
Yes, all fields accept decimals and negative numbers; results are shown with up to 6 decimal places.