Cross Multiply Calculator
Solve for the unknown in a proportion using cross multiplication.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
Cross multiplication multiplies the numerator of each fraction by the denominator of the other, turning a proportion into a simple equation. It is the fastest way to find a missing term.
Worked example
calculated with the default values below
Numerator of first fraction 5 · Denominator of first fraction 8 · Numerator of second fraction 20 Missing value 32.0000 · Cross-multiplication product 160.0000 · Ratio a ÷ b 0.625000
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
x = b × c ÷ a
- a
- Known numerator a
- b
- Known denominator b
- c
- Known numerator c
Requires nonzero a, b, and c for a unique missing denominator; x = b × c ÷ a. Ratio a ÷ b is defined when b ≠ 0; cross-multiplication product = b × c.
Frequently asked questions
What if a numerator or denominator is zero?
The missing denominator is uniquely defined only when a, b, and c are all nonzero. If any is zero, the calculator leaves x unavailable because the proportion is undefined or does not determine a unique denominator. The ratio a ÷ b is still shown when b is nonzero, and the cross product b × c is always shown.