Use this Rule of 3 calculator to quickly solve proportions in direct and inverse relationships.
What is the Rule of 3?
The Rule of 3 (sometimes called the “rule of three” in arithmetic) is a fast way to solve proportion problems. If you know three values in a proportional relationship, you can calculate the fourth value immediately. It is widely used in budgeting, cooking, construction estimates, travel planning, and unit conversions.
When to use this calculator
1) Direct proportion
Use direct proportion when values move in the same direction: if one value increases, the other increases too. Example: if 2 notebooks cost $10, then 5 notebooks cost more.
- Formula: X = (B × C) ÷ A
- Interpretation: “A is to B as C is to X.”
2) Inverse proportion
Use inverse proportion when values move in opposite directions: if one goes up, the other goes down. Example: more workers usually means fewer days to complete the same job.
- Formula: X = (A × B) ÷ C
- Interpretation: “A with B corresponds inversely to C with X.”
Practical examples
Shopping math
3 kg of apples cost $12. How much do 7 kg cost? This is direct proportion, so: X = (12 × 7) ÷ 3 = $28.
Recipe scaling
A recipe for 4 servings uses 300g of flour. How much flour for 10 servings? X = (300 × 10) ÷ 4 = 750g.
Work and time
8 workers finish a task in 15 days. How many days for 12 workers (same workload)? Inverse proportion: X = (8 × 15) ÷ 12 = 10 days.
Common mistakes to avoid
- Mixing up direct and inverse relationships.
- Using inconsistent units (hours vs minutes, kg vs grams, etc.).
- Dividing by zero (A or C cannot be zero depending on the selected rule).
- Rounding too early in multi-step calculations.
Quick workflow for accurate answers
- Choose whether the relationship is direct or inverse.
- Enter A, B, and C values with consistent units.
- Click Calculate X.
- Check the displayed formula and substitution line for verification.
Why this calculator helps
Mental math is great, but small errors in proportions can become expensive in real-world decisions. This calculator gives a clear formula, a substitution step, and the final result instantly—so you can move from guesswork to confidence in seconds.