How to use the rule of three
Updated on June 30, 2026 · by Rafael Rossi
The rule of three finds an unknown value from a proportion between two quantities. It's one of the handiest everyday tools — recipes, prices, construction, maps. The key is first deciding whether the quantities are directly or inversely proportional.
Direct rule of three
When one quantity grows, the other grows in proportion (more flour → more loaves). Set up the proportion and cross-multiply:
a/b = c/x → x = (b × c) / a
Example: 3 kg of flour make 12 loaves. From 5 kg? 3/12 = 5/x → x = (12 × 5) ÷ 3 = 20 loaves.
Inverse rule of three
When one grows and the other shrinks (more workers → less time), the products are equal:
a × b = c × x → x = (a × b) / c
Example: 4 workers take 6 days. With 8 workers? (4 × 6) ÷ 8 = 3 days.
How to tell which to use
Test it: "if I double the first quantity, does the second double or halve?" Double → direct; halve → inverse. That one step avoids the most common mistake.
FAQ
What is cross-multiplying? In the direct rule a/b = c/x, you multiply the diagonal terms (a×x = b×c) and isolate x.
What about three or more quantities? That's the compound rule of three: analyze each quantity against the unknown separately.