Proportion Calculator (Rule of Three)
Solve direct proportions instantly: if A corresponds to B, find what C corresponds to. The classic rule of three, with the result as you type.
If A corresponds to B, then C corresponds to X.
Fill in the three known values (A must not be zero).
How it works
The rule of three solves problems where two quantities vary in direct proportion. You know three values and want the fourth: if A corresponds to B, then C corresponds to X. The calculator cross-multiplies for you:
X = (B × C) ÷ A
For example, if 2 kg of flour makes 10 loaves of bread, how many loaves do 5 kg make? Here A = 2, B = 10, C = 5, so X = (10 × 5) ÷ 2 = 25 loaves. Fill in the three known values and the result updates instantly — no button to press.
When to use
Any situation where quantities scale together: adjusting a recipe for more guests, converting a price per unit into a price for a batch, estimating how long a job takes with a different team size (when it scales linearly), scaling a map distance to real distance, or working out an equivalent dose per weight.
It's also the quickest sanity check for everyday claims — "if 3 tickets cost $75, is $120 for 5 tickets a fair price?" (No: 5 tickets should cost $125, so $120 is actually a small discount.)
Practical examples
Scaling a recipe
A recipe for 4 servings uses 300 g of pasta. For 10 servings: X = (300 × 10) ÷ 4 = 750 g. Enter A = 4, B = 300, C = 10.
Price per quantity
If 1.5 kg of grapes costs $9, how much do 4 kg cost? X = (9 × 4) ÷ 1.5 = $24.
Common mistakes
The most frequent error is applying the direct rule of three to quantities that are inversely proportional. If 4 workers finish a job in 12 days, 8 workers don't take 24 days — they take 6. When one quantity going up makes the other go down, the simple cross multiplication doesn't apply; you multiply A × B and divide by C instead.
Another slip is mixing units: if A is in kilograms, C must be in kilograms too, or the result is meaningless. Convert everything to the same unit before entering the values.
Frequently asked questions
Does this calculator handle inverse proportion?
It solves the direct rule of three (X = B × C ÷ A). For inverse proportion — where doubling one quantity halves the other — compute X = A × B ÷ C. You can still use the calculator: just swap A and C when the relationship is inverse.
Can I use decimals or fractions?
Decimals work normally (e.g. 1.5 or 0.75). For a fraction like 3/4, enter its decimal form, 0.75.
Why must A not be zero?
The formula divides by A. Division by zero is undefined — and in practical terms, "0 kg costs $10" gives no information to scale from.
What is cross multiplication?
Writing the proportion as A/B = C/X and multiplying diagonally: A·X = B·C, which rearranges to X = B × C ÷ A. It is exactly what this calculator does.