Proportion Calculator
This proportion calculator finds the missing value in a statement like "A is to B as C is to X." Enter the three numbers you know, choose whether the relationship is direct or inverse, and you get X instantly. It is the classic rule of three, useful for scaling recipes, unit prices, map distances, and work and travel times.
Updated
Results
Results are estimates. See the methodology below.
How to use the proportion calculator
- Value A: the known quantity of the first pair, for example 3 pounds.
- Value B: what goes with A, for example $7.50 for those 3 pounds.
- Value C: the new quantity you are interested in, for example 5 pounds.
- Type of proportion: choose direct if more of one means more of the other, or inverse if more of one means less of the other.
The result is X, the value that goes with C. Keep units consistent: if A is in pounds, C must also be in pounds, and X comes out in the same unit as B.
How the calculator solves the proportion
Direct proportion
Two quantities are directly proportional when their ratio stays constant. Double one and the other doubles too. The proportion is written A / B = C / X, and cross-multiplying gives:
X = B × C ÷ A
Inverse proportion
Two quantities are inversely proportional when their product stays constant. Double one and the other is cut in half, as when more workers finish a job in fewer days. Here A × B = C × X, so:
X = A × B ÷ C
Because of the division, A cannot be zero in a direct proportion and C cannot be zero in an inverse one. Negative numbers are accepted, but most real-world proportions use positive quantities.
The calculator assumes the relationship is exactly proportional. Many everyday situations are only approximately so: bulk discounts break a direct price proportion, and adding workers stops helping once they get in each other's way.
Worked examples
1. Unit price at the deli (direct)
Three pounds of chicken cost $7.50. How much do five pounds cost? Enter A = 3, B = 7.50, C = 5 and choose direct. The calculator returns X = 12.5, so five pounds cost $12.50.
2. Painting a house (inverse)
Six painters need 10 days to paint a building. How long would four painters take, working at the same pace? Enter A = 6, B = 10, C = 4 and choose inverse. The result is X = 15 days: fewer workers, more time.
3. Reading a map (direct)
On a road map, 1 inch represents 2.5 miles. Two towns are 3.2 inches apart. With A = 1, B = 2.5, C = 3.2 and direct mode, X = 8 miles as the crow flies.
| Case | A | B | C | Mode | X |
|---|---|---|---|---|---|
| Chicken | 3 | 7.5 | 5 | Direct | 12.5 |
| Painters | 6 | 10 | 4 | Inverse | 15 |
| Map | 1 | 2.5 | 3.2 | Direct | 8 |
Direct or inverse? A quick test
Ask yourself: if C were twice as large as A, would the answer be twice as large as B, or half as large? Twice as many pounds cost twice as much, so price per pound is direct. Twice the speed takes half the time over the same distance, so speed and travel time are inverse. If neither is true, for example a taxi fare with a fixed starting fee, the situation is not a simple proportion and the rule of three will give a misleading answer.
Frequently asked questions
What is the rule of three?
The rule of three is a method for finding the fourth value of a proportion when three are known. In the direct case you multiply the two values that sit diagonally across from each other and divide by the third, which is exactly what this calculator does.
How do I solve a proportion by cross-multiplying?
Write the proportion as two equal fractions, A/B = C/X. Multiply diagonally to get A × X = B × C, then divide both sides by A. The same steps work with X in any position.
Can I use this to scale a recipe?
Yes. If a recipe for 4 servings uses 2 cups of flour and you want 6 servings, enter A = 4, B = 2, C = 6 in direct mode: you need 3 cups. Repeat for each ingredient. Baking times and pan sizes do not always scale proportionally, so adjust those by experience.
What is an example of inverse proportion?
Speed and travel time over a fixed distance, workers and days for a fixed job, or the number of people sharing a bill and each person's share. In all of these, the product of the two quantities stays the same.
Why does the calculator say a value can't be zero?
The formula divides by A in direct mode and by C in inverse mode, and division by zero is undefined. Check that you entered the values in the right fields.
Sources
Results assume an exact proportional relationship between the values you enter. Real situations such as bulk pricing or team productivity may not follow a strict proportion.