Proportion Solver Calculator
A proportion sets two ratios equal: A/B = C/X. When you know three of the four terms, the fourth follows by cross multiplication. This is the everyday maths behind scaling a recipe, converting between units, reading a scale map, or working out a dose. This solver takes A, B and C and finds the unknown X in the proportion A/B = C/X. Enter the three known values to get the answer instantly.
Proportion solving formula
proportion: A / B = C / X
cross multiply: A * X = B * C
solve: X = (B * C) / A
Cross multiplication clears both fractions in one step, leaving a simple division for the unknown. The cross product check confirms A times X equals B times C.
Worked example
Solve 3/4 = 9/X. Cross multiplying: 3 times X = 4 times 9 = 36. So X = 36 / 3 = 12.00. Check: A times X = 3 times 12 = 36, and B times C = 4 times 9 = 36, confirming the answer.
Proportion solving: frequently asked questions
What is a proportion?
A proportion is a statement that two ratios are equal, written A/B = C/D. If three of the four terms are known, the fourth can be found by cross multiplication. Proportions are the foundation of scaling recipes, converting units, reading maps, mixing solutions and any situation where one quantity changes in fixed proportion to another.
How does cross multiplication solve a proportion?
In the proportion A/B = C/X, cross multiplication states that A times X equals B times C. Rearranging to solve for the unknown X gives X = (B times C) / A. This works because multiplying both sides of an equation by the same nonzero quantity preserves equality. Cross multiplication simply clears the fractions in one step.
What if my unknown is in a different position?
This solver places the unknown X in the denominator of the second ratio (A/B = C/X). If your unknown is elsewhere, relabel the terms so the unknown sits in that position, since any proportion can be rewritten that way. For example, X/B = C/D can be rearranged to A/X = D/C form by swapping. The underlying cross-multiplication rule is the same.
Why can no term be zero?
The terms B and X are denominators, and division by zero is undefined, so they must be nonzero. The term A is the divisor when solving for X (X = B times C divided by A), so it must also be nonzero. If A were zero, the proportion would imply C is zero as well, leaving X undetermined. The solver flags these cases rather than returning a misleading number.
Official sources
- National Institute of Standards and Technology: NIST Digital Library of Mathematical Functions.
- National Institute of Standards and Technology: NIST mathematics and statistics.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.