Cross Product Calculator

About this calculator

This calculator computes the cross product of two 3D vectors, a × b, which — unlike the dot product — returns a new vector perpendicular to both inputs, with a magnitude equal to |a||b|sin(θ) and a direction given by the right-hand rule.

It's used in 3D graphics and game development to compute surface normals (the direction a face is pointing, essential for lighting), in physics for torque (τ = r × F) and angular momentum calculations, and in engineering for finding a plane's orientation from two vectors lying in it. The calculator also reports the magnitude of the resulting vector, which conveniently equals the area of the parallelogram formed by the two input vectors.