Cross Multiplication

Cross Multiplication is a common technique for finding an unknown value in a set of fractions, given that A/B = C/D. It may be used in aspect ratio calculation or to convert values between measurement systems.


This calculator determines the unknown value of a set using cross multiplication.



Cross multiplication arranges four values in a pair of fractions. In each fraction, the numerator and denominator represent identical values in two different measurement systems. The numerator of both fractions represents one system, and the denominator represents another.

The result is obtained by diagonally multiplying the two known values in the pair of fractions (the numerator of one with the denominator of the other), and dividing the result by the remaining known value (numerator or denominator).


To convert 123.456 inches to centimeters using cross multiplication, and knowing that one inch equals 2.54 centimeters, the formula can be written as follows.

1 in       123.456 in
-          -
2.54 cm    d cm
Since d is the unknown, the process would be:
a   c
- * -  ... then ... d = result / a
b   d
In the above example, this yields (123.456 in * 2.54 cm) / 1 in = 313.57824 cm. Note that in many cases one operation can be skipped, increasing calculation speed by 50%. In this example, there's no need for the division step, since dividing a number by 1 doesn't modify it. Also note that cross multiplication can't be performed if the third known value is zero.

Additional Reading

Cross Multiplication at
Comparing Fractions at The Math Page
Solving Proportions at AAA Math
The Cross Multiplication Method at Maths Teacher

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