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About the rule of three
The rule of three solves a simple question: if A goes with B, what goes with C? You know three numbers and you want the fourth.
- If 3 kg of apples cost $12, how much do 5 kg cost?
- If 4 people need 300 g of pasta, how much do 6 people need?
- If 4 workers finish a job in 6 days, how long do 3 workers need?
Type the three numbers, choose direct or inverse, and the calculator gives the answer — with the steps, the way it is taught in school. It is called *regra de três* in Portuguese, *regla de tres* in Spanish, *Dreisatz* in German and *règle de trois* in French.
Features
- Direct and inverse — one tap switches between the two kinds
- The steps shown — "x = B × C ÷ A = 12 × 5 ÷ 3 = 20", with your own numbers
- A check — the two ratios (or the two products) come out equal
- Six examples — prices, fuel, recipes, percentages, workers and speed
- Decimals welcome — 2.5 or 2,5 both work
- Copy the result — answer and steps in one tap
- Saved on your device — your numbers are still there next time
Direct or inverse?
Ask yourself: when A goes up, does B go up too?
| Direct proportion | Inverse proportion | |
|---|---|---|
| When A goes up… | B goes up | B goes down |
| Examples | price and weight, distance and fuel, people and food | workers and days, speed and time, people and slices each |
| Formula | x = B × C ÷ A | x = A × B ÷ C |
| What stays the same | the ratio A : B | the product A × B |
Direct: 3 kg cost $12. 5 kg is more, so it costs more: 12 × 5 ÷ 3 = $20.
Inverse: 4 workers need 6 days. 3 workers is fewer people, so it takes longer: 4 × 6 ÷ 3 = 8 days.
How to work it out by hand
- Write the two pairs in two lines: A → B and C → x.
- Decide: direct or inverse?
- Direct: multiply across the diagonal (B × C) and divide by the number left (A).
- Inverse: multiply along the first line (A × B) and divide by C.
- Check: does the answer make sense? More kilos should cost more; more workers should take fewer days.
Percentages with the rule of three
Percent questions are direct proportions with 100 % as one number:
- 80 is 100 %, what % is 20? → 100 × 20 ÷ 80 = 25 %
- What is 15 % of 240? → 240 is 100 %, so x = 240 × 15 ÷ 100 = 36
For more percent questions, try the Percentage Calculator.
How to use it
- Choose Direct or Inverse at the top
- Type A and the value that goes with B
- Type C — the new value
- Read x in the result, with the steps under it
- Or tap an example to see how it works
Frequently asked questions
What is the rule of three?
A quick way to find a missing number when two pairs of values are in proportion. You know A, B and C, and you want the value x that goes with C.
What is the formula?
Direct proportion: x = B × C ÷ A. Inverse proportion: x = A × B ÷ C.
How do I know if it is inverse?
If one value goes up while the other goes down, it is inverse. Workers and days, speed and travel time, and the number of people sharing a pizza are all inverse.
Can I use decimals?
Yes. Type 2.5 or 2,5. The answer is shown with up to four decimal places.
Is it the same as cross multiplication?
Yes. Direct rule of three is cross multiplication: A ÷ B = C ÷ x, so x = B × C ÷ A.
Related tools
- Ratio Calculator — simplify a ratio or share an amount in a ratio
- Percentage Calculator — X % of Y, percent change and more
- Fraction Calculator — add, subtract, multiply and divide fractions
- Recipe Scaler — change a recipe for more or fewer people
- Unit Price Calculator — find the best deal per kilo or per item
