Rule of three (cross multiplication)
Good old cross multiplication, made fast. Enter 3 known values, the tool computes the 4th instantly. Handles units, decimal commas and large numbers. No sign-up.
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The rule of three, daily-life math weapon
The rule of three (also called cross multiplication) is probably the most useful everyday math trick. It finds a fourth proportional value from three known ones, with no algebra. The operation boils down to one multiplication then one division: (B × C) ÷ A.
3 typical use cases
Cooking
Recipe for 4 people with 300 g of flour. For 6 people: (300 × 6) ÷ 4 = 450 g.
Driving
6 L per 100 km. For 450 km: (6 × 450) ÷ 100 = 27 L of fuel.
Shopping
2 kg of apples for €4.50. For 1.5 kg: (4.50 × 1.5) ÷ 2 = €3.37.
How does it work?
Writing the values as a proportion A / B = C / X, you find X by multiplying across:
- A — the reference amount (known)
- B — what it maps to (known)
- C — the new amount (known)
- X = (B × C) ÷ A — the unknown
Watch out for inverse proportions
The standard rule of three only works when both sides move the same way: more quantity → more price. But if 3 painters take 4 hours to paint a wall, 6 painters take 2 hours (not 8). In that case the formula flips to (A × B) ÷ C. This tool computes the direct (proportional) version.
Calculator features
- Live result: it refreshes at every keystroke, no click needed.
- Free-form units: kg, $, km, L… the unit is carried over to the result.
- 1-click copy: built-in button to copy the result to the clipboard.
- Decimal comma supported: type 2,5 or 2.5, both work.
FAQ
Rule of three or cross multiplication, is it the same?
Yes, exactly the same method. It's called "cross multiplication" because writing the values as fractions (A/C = B/X) makes the calculation form an imaginary cross (B times C, divided by A).
Does it work with percentages?
Absolutely. A percentage is just a proportion where the reference value (A) is 100. The rule of three is the mathematical foundation of every percentage calculation.
Beware of inversely proportional values
The classic rule of three only works if quantities move together (more quantity = more price). If 3 painters need 4 h to paint a wall, 6 painters need 2 h (not 8 h). In that inverse case the formula becomes (A × B) ÷ C. This tool handles the direct (proportional) version.
Can I use the French decimal comma?
Yes. You can enter both "2,5" and "2.5". Spaces are ignored too, so you can write readable large numbers like "1 500".
Why is the result limited to 4 decimals?
For readability. In daily life, beyond 4 decimals the result becomes unreadable and extra precision is not meaningful (except in very specific scientific cases).
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