Cross Multiplication Calculator

Cross multiplication is a technique for solving proportions — equations where two fractions are set equal to each other (A/B = C/D). You multiply the numerator of each fraction by the denominator of the other, producing the equation A × D = B × C, which can then be solved for any unknown value.

Set up the proportion A/B = C/D with X in the unknown position. Cross multiply to get A × D = B × C, then isolate X by dividing both sides by the coefficient next to X. For example, if 4/10 = X/15, then 4 × 15 = 10 × X, so X = 60/10 = 6.

Yes. X can appear as the numerator or denominator of either fraction — A, B, C, or D. Simply enter 'X' in the appropriate field and numeric values in the other three. The calculator automatically detects the unknown position and solves accordingly.

Cross multiplication works because multiplying both sides of A/B = C/D by the common denominator (B × D) eliminates both fractions simultaneously. This leaves A × D = B × C — a simple linear equation. It's a shortcut derived from basic algebraic properties of equality.

To compare fractions A/B and C/D, compute A × D and B × C. If A × D > B × C, then A/B is the larger fraction. If A × D < B × C, then C/D is larger. If both cross products are equal, the fractions are equivalent.

If you provide all four numeric values, the calculator verifies whether the proportion A/B = C/D is valid. It checks that the cross products A × D and B × C are equal and confirms whether the equation is balanced or not.

Yes. The calculator handles negative numbers, decimals, and fractions as inputs. For example, inputs like -1, 3.4, or 0.5 are all valid. Just make sure only one field contains 'X' so the unknown can be determined.

Cross multiplication is used in cooking (scaling recipes), map reading (converting scale distances), finance (calculating proportional values), unit conversions, and solving similar-triangle problems in geometry. Any time two ratios must be kept equal, cross multiplication solves the unknown.