The rule of three is one of those bits of math that school teaches for a week and then never calls by name again, even though everyone keeps using it. Doubling a recipe? Rule of three. Converting currency in your head at the airport? Rule of three. Estimating how long the drive home will take? Same thing.
Once you can spot the pattern, a surprising amount of daily life becomes a quick mental calculation instead of a phone reach.
The setup
You know three values and you want a fourth. Two of the knowns belong together, and the third is related to the unknown in the same way. The only real decision is which kind of proportion you're dealing with: direct or inverse.
Direct proportion (most things)
When one quantity grows, the other grows by the same factor. If 2 kg of flour costs $6, then 5 kg costs (6 × 5) ÷ 2 = $15. Formula: X = (B × C) ÷ A. Anything where there's a 'per-unit' price falls here — fuel per kilometer, paint per square meter, salary per hour.
Inverse proportion (the sneaky one)
When one quantity grows, the other shrinks proportionally. If 4 workers finish a job in 6 days, how long would 8 workers take? Twice the workers means half the time: (4 × 6) ÷ 8 = 3 days. Formula: X = (A × B) ÷ C. Speed vs travel time, density vs volume, pressure vs volume — all inverse.
The two-second test
Ask yourself one question: if A doubles, does C double or halve? Doubles → direct. Halves → inverse. That's it. I use this on autopilot now. If the answer of your calculation looks ridiculous (more workers = more days?), you almost certainly chose the wrong type.
The mistakes I see most often
First, applying the direct formula to an inverse problem. The result will obviously be wrong, but in a hurry it's easy to miss. Second, mixing units. 6 hours is not 6 of anything measured in minutes. Convert before you compute, or your answer will be off by a factor of 60 and you won't know why.
Where this shows up in real life
Cooking: scaling a recipe for 4 to feed 7. Travel: if you cover 480 km in 6 hours, how far in 9? Shopping: comparing two pack sizes by price-per-100g. DIY: a tin of paint covers 12 m² — how many tins for 30 m²? Currency: 100 EUR = 108 USD, so 250 EUR equals…?
Use the calculator
Our Rule of Three Calculator handles both direct and inverse cases. Drop in your three knowns, pick the proportion type, and it'll show the formula it used alongside the answer. Handy for double-checking yourself, or for showing your work when a kid asks you for homework help.
Bottom line
The rule of three is the closest math gets to a Swiss Army knife. Nail the direct-vs-inverse decision and you'll handle a surprising chunk of everyday numerical problems without ever reaching for a calculator.