Rule of Three Calculator
If A gives B, what does C give? Direct and inverse proportion.
Good to know. If 3 painters take 8 days, 6 painters take 4. Twelve painters mostly take up the hallway.
How it works
In plain words
For a direct proportion, multiply B by C and divide by A. For an inverse proportion, multiply A by B and divide by C.
The formula
direct: X = B × C ÷ A inverse: X = A × B ÷ C
Worked example
A recipe for 4 people needs 300 g of pasta. For 6 people: 300 × 6 ÷ 4 = 450 g.
Sources
No outside data or rates: this is plain arithmetic.
6 automated tests check its answers on every change.
About the rule of three calculator
The rule of three is the quickest way to solve "if this, then that" problems. If 4 people need 300 g of pasta, how much do 6 people need? If 3 metres of fabric cost 27, what do 5 metres cost? If 2 cm on a map is 5 km, how far is 7 cm?
These are direct proportions: when one amount goes up, the other goes up by the same factor. The recipe method is to find the value of one unit first, then multiply. 300 g for 4 people is 75 g per person, so 6 people need 450 g. The formula does the same in one step: B × C ÷ A.
Some relationships go the other way. These are inverse proportions: when one amount goes up, the other goes down. If 3 painters take 8 days to paint a house, 6 painters take 4 days, assuming they work at the same rate and don’t get in each other’s way. If a trip takes 2 hours at 60 km/h, it takes 1.5 hours at 80 km/h. For these, the formula is A × B ÷ C.
Be careful to check that the relationship really is proportional. Doubling a recipe’s baking time won’t work, and ordering twice as much doesn’t always cost exactly twice as much. When in doubt, ask whether "twice as much of this" really means "twice (or half) as much of that".
Questions people ask
What is the rule of three?
A method for finding the fourth value in a proportion: if A gives B, then C gives X = B × C ÷ A.
How do I scale a recipe?
Use a direct proportion. For a recipe for 4 that you want for 6, multiply each amount by 6 and divide by 4.
What is an inverse proportion?
One where increasing one amount decreases the other, like more workers finishing a job faster. X = A × B ÷ C.