Proportion Calculator
Solve for the missing value in a proportion (A is to B as C is to X).
About the Proportion Calculator
A proportion states that two ratios are equal — "A is to B as C is to X" — and solving for the missing fourth term is a skill used constantly in recipe scaling, map reading, unit conversion, and classroom math. This calculator solves for X directly.
How It Works
The calculator applies cross-multiplication: since A/B equals C/X in a valid proportion, cross-multiplying gives A×X = B×C, and solving for X gives X = (B×C)/A.
If A/B = C/X, then X = (B × C) / A.
Worked example
Scenario: Solving 4 : 9 = 12 : X — for example, scaling a recipe.
- Cross-multiply: 4 × X = 9 × 12 = 108.
- Divide by 4: X = 108 ÷ 4 = 27.
Result: X = 27.
How to recognize a proportion
A proportion compares two equal ratios. If 4 notebooks cost the same rate as 12 notebooks, the relationship can be written 4/price₁ = 12/price₂ after matching corresponding quantities. Keep like quantities in the same positions before cross-multiplying; reversing only one ratio changes the relationship.
Tips and common mistakes
- Keep units consistent on each side (cups with cups, miles with miles).
- Proportions assume a linear relationship; baking times and some chemistry don't scale linearly.
- A can't be zero, because the proportion would be undefined.
Assumptions & Limitations
- Assumes A is nonzero, since dividing by zero is undefined.
- Assumes the proportion is set up as A/B = C/X, matching the standard 'A is to B as C is to X' phrasing.
- If your problem is phrased differently (like A/B = X/C), rearrange the terms before entering them to match this calculator's A, B, C, X structure.