Rule of Three Calculator
Rule of Three Calculator solves a direct proportion when three corresponding quantities are known. If A relates to B as C relates to X, the unknown is B×C÷A. This assumes a constant direct rate and compatible units; it is not appropriate for inverse relationships, tiered pricing, fixed fees, nonlinear scaling, or a zero first term.
Runs locally — files stay on your deviceIf 3 items cost 12, what do 5 items cost at the same rate?
Five items cost 20.
Formula: 12 × 5 ÷ 3 = 20
A direct proportion preserves one constant ratio
A:B = C:X means A/B = C/X. Cross-multiplication gives A×X = B×C, so X = B×C/A when A is nonzero.
How it works
Place corresponding quantities in the same positions, keep units consistent, and confirm that doubling one quantity should double the other before solving.
Key concepts
Correspondence matters
Items must align with items and cost with cost; swapping one pair produces the wrong unknown.
Direct proportion passes through zero
A fixed rate model implies zero of one quantity corresponds to zero of the other.
When to use it
- Scale a recipe or unit-price relationship.
- Convert between directly proportional quantities.
- Check cross-multiplication in a proportion.
When not to use it
- Do not use it for inverse proportion.
- Do not model discounts, fixed charges, or nonlinear formulas.
- Do not divide by a zero A value.
Worked examples
Unit cost
- Input
3 items → 12; 5 items → X- Expected output
20
The constant cost is four per item.
Recipe scale
- Input
4 servings → 300 g; 10 servings → X- Expected output
750 g
The recipe scales directly.
Fixed delivery fee
- Input
Cost includes a fixed 5 fee- Expected output
Direct rule may fail
Total cost no longer passes through zero.
Common mistakes
Misaligning corresponding units
Cross-products compare different relationships. Correction: Write labels beside all four positions.
Using inverse proportion
More workers and fewer hours can move in opposite directions. Correction: Use an inverse model where the product is constant.
Ignoring a fixed component
A constant-rate proportion cannot represent it. Correction: Separate fixed and variable parts.
Best practices
- Write units beside inputs.
- Verify direct proportionality first.
- Estimate the expected direction and magnitude before calculating.
Related operations and differences
Percentage Calculator
Choose Percentage Calculator when you need to calculate a percentage of any number.; use Rule of Three Calculator specifically for ratio.
Proportion Calculator
Choose Proportion Calculator when you need to solve A:B = C:X safely.; use Rule of Three Calculator specifically for ratio.
Percentage Increase Calculator
Choose Percentage Increase Calculator when you need to find the percentage change between two values.; use Rule of Three Calculator specifically for ratio.
Ratio Calculator
Choose Ratio Calculator when you need to calculate the ratio between two numbers.; use Rule of Three Calculator specifically for ratio.
Average Calculator
Choose Average Calculator when you need to find the arithmetic mean of a number list.; use Rule of Three Calculator specifically for ratio.
Fraction to Decimal
Choose Fraction to Decimal when you need to convert a numerator and denominator to decimal.; use Rule of Three Calculator specifically for ratio.
Limitations and privacy
- Only one direct proportion is modeled.
- A must be nonzero.
- Rounding and real-world fixed or nonlinear effects are not included.
Numbers and results remain in this browser.
Frequently asked questions
What is the rule-of-three formula?
X = B×C÷A for A:B = C:X.
Can it solve inverse proportion?
No. This page models direct proportion.
Why must A be nonzero?
The solution divides by A.
Do units need to match?
Corresponding positions must use compatible units.