Rule of Three Calculator
Solve direct and inverse rule of three problems. The basis for percentages, scales, conversions, and proportions. With everyday examples step by step.
- Data verified · June 2026
- Edited by Martín Rodríguez
- Formula verified by automated tests
- Private — runs on your device
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How to use this calculator
Follow this tool’s steps, then review its formula, assumptions, and limits below.
X = (B x C) / A for direct and X = (A x B) / C for inverse.When to use this calculator
- Adjust a recipe from 4 servings to 6 people (direct).
- Calculate how much X kg of a product costs knowing the price of Y kg (direct).
- Figure out how long 6 people take on a task that 4 people complete in 6 hours (inverse).
- Convert currencies with a fixed exchange rate (direct).
- Calculate a percentage (every percentage is a rule of three).
Everyday Rule-of-Three Problems Solved (worked examples)
Common direct and inverse rule-of-three situations with the numbers worked out.
| Real-life problem | Type | Setup (A→B, C→X) | Formula | Answer |
|---|---|---|---|---|
| 3 kg chicken cost $12 — what do 5 kg cost? | Direct | 3→12, 5→X | X = (12×5)/3 | $20 |
| Recipe: 200 g rice for 4 — how much for 6? | Direct | 4→200, 6→X | X = (200×6)/4 | 300 g |
| 1 USD = 0.86 EUR — how many EUR is 250 USD? | Direct | 1→0.86, 250→X | X = (0.86×250)/1 | 215 EUR |
| Car does 120 km in 2 h — how far in 5 h? | Direct | 2→120, 5→X | X = (120×5)/2 | 300 km |
| What is 15% of 2000? | Direct | 100→2000, 15→X | X = (2000×15)/100 | 300 |
| 4 painters finish in 6 h — how long with 8? | Inverse | 4→6, 8→X | X = (4×6)/8 | 3 h |
| A tank lasts 12 days for 5 people — for 8? | Inverse | 5→12, 8→X | X = (5×12)/8 | 7.5 days |
| 6 taps fill a pool in 80 min — with 10 taps? | Inverse | 6→80, 10→X | X = (6×80)/10 | 48 min |
Direct proportion uses X = (B×C)/A (quantities grow together); inverse uses X = (A×B)/C (one grows as the other shrinks). Quick test: if making C bigger should make X bigger, it's direct; if it should make X smaller, it's inverse. Inverse problems keep the product A×B constant.
How it works
Direct Rule of Three
When two quantities are directly proportional: if one grows, the other grows in the same proportion.
A → B
C → X
X = (B x C) / AIntuition: the ratio B/A is constant. If A is multiplied by k, B must also be multiplied by k.
Examples of Directly Proportional Quantities
Step-by-Step Example
If 3 kg of chicken costs $12, how much do 5 kg cost?
3 kg → $12
5 kg → X
X = (12 x 5) / 3
X = 60 / 3
X = $20Inverse Rule of Three
When two quantities are inversely proportional: if one grows, the other decreases.
A → B
C → X
X = (A x B) / CIntuition: the product A x B is constant. If A is multiplied by k, B is divided by k.
Examples of Inversely Proportional Quantities
Step-by-Step Example
If 4 people paint a house in 6 hours, how long do 8 people take?
4 people → 6 hours
8 people → X
X = (4 x 6) / 8
X = 24 / 8
X = 3 hoursWith double the people, it takes half the time.
How Do I Know If It's Direct or Inverse?
Think of the extreme case:
1. Ask: if A increases a lot, what happens to B?
2. If B also increases → direct.
3. If B decreases → inverse.
Quick Reference Table
| Situation | Type |
|---|---|
| Kg of apples and price | Direct |
| Study hours and learning | Direct (normally) |
| Workers and task time | Inverse |
| Car speed and travel time | Inverse |
| Number of builders and meters built | Direct |
| Builders and days for the same project | Inverse |
Application in Percentages
Every percentage calculation is a rule of three with base 100:
100 → total value
X% → partial valueExample: What is 15% of 2000?
100 → 2000
15 → X
X = (2000 x 15) / 100 = 300Scaling Recipes
Recipe for 4 people: 200 g of rice. For 6 people:
4 people → 200 g
6 people → X
X = (200 x 6) / 4 = 300 gCommon Mistakes
1. Using direct when it's inverse: 'if 6 workers take 4 days, 12 workers take 8 days' — wrong! The inverse says 2 days.
2. Cross-multiplying incorrectly: in A → B, C → X, the direct formula is X = B x C / A, not A x C / B.
3. Mixing units: if A is in minutes and C is in hours, convert first.
4. Using rule of three where it doesn't apply: not all relationships are linear. For example, fuel consumption vs speed is NOT linear.
5. Confusing proportion with percentage: '20% of the class are women' is solved with a rule of three (base 100).
Example: scaling a cookie recipe from 12 to 18 cookies
12 cookies → 500 g flour. 18 cookies → X g flour.X = (B x C) / A = (500 x 18) / 12.(500 x 18) / 12 = 9000 / 12 = 750 g.Frequently asked questions
How do I know if I should use direct or inverse rule of three?
Is the rule of three the same as a proportion?
a/b = c/d. The rule of three is the procedure for solving a proportion when one of the 4 values is unknown. Every rule of three is based on a proportion, and every proportion is solved with a rule of three.Can the rule of three be used for percentages?
100 → 2000, 15 → X, so X = (15 x 2000) / 100 = 300. All discounts, increases, variations, and commissions are rules of three disguised as percentages.What is the compound rule of three for?
When should I NOT use the rule of three?
How do I convert between currencies with the rule of three?
1 USD = 0.92 EUR, then X EUR = (0.92 x 500) / 1 = 460 EUR to convert 500 USD. To go from EUR to USD: reverse the operation. Always make sure to use the correct exchange rate for your transaction type.Does the rule of three work with decimals and negatives?
3.5 kg → $7.50, X kg → $20.00 → X = (3.5 x 20.00) / 7.50 = 9.33 kg. With negatives: mathematically yes, but in real contexts it rarely makes sense (negative kilos or time don't exist). If negatives appear, you're probably modeling differences or variations, not absolute quantities.How do I adjust a recipe from 4 to 5 people?
X = (200 x 5) / 4 = 250 g. For each ingredient do the same calculation. You can also compute the scale factor 5/4 = 1.25 and multiply each ingredient by that number.Sources & references
Methodology & trust
Daily Life calculator with its formula verified automatically against Khan Academy - Ratios and Proportions, per our editorial policy and methodology.
Updated: June 2026. Parameters are verified periodically against the cited sources.
Calculations run 100% in your browser. We do not store or transmit your data.
Indicative results. For critical decisions, consult a professional.
Rodríguez, M. (2026). Rule of Three Calculator. Hacé Cuentas. https://hacecuentas.com/en/rule-of-three-calculator
Content licensed under CC-BY 4.0 — reuse it citing the source with a link to Hacé Cuentas.