Cross Product Calculator
Calculate the cross product of two vectors — a new vector perpendicular to both — along with its magnitude.
About the Cross Product Calculator
The cross product combines two 3D vectors into a new vector that is perpendicular to both of the originals, with a length equal to the area of the parallelogram they span. Unlike the dot product, the cross product only exists in three dimensions, and its result depends on the order of the vectors — reversing the order flips the sign.
Formula: A × B = (AyBz − AzBy, AzBx − AxBz, AxBy − AyBx)
The direction of the resulting vector follows the right-hand rule: point your fingers along the first vector, curl them toward the second, and your thumb points along the cross product. If the two input vectors are parallel — or one of them is the zero vector — the cross product is the zero vector, since there's no unique perpendicular direction.
Cross products are essential in physics and engineering for computing torque, angular momentum and surface normals, and in 3D graphics for determining which way a triangle faces. Leave the z-components at zero for a purely 2D calculation, which returns a cross product pointing entirely along the z-axis.