➰ Cross Product Calculator
Calculate the cross product of two 3D vectors, including the resulting vector and its magnitude.
What the cross product is
The cross product of two 3D vectors A and B produces a new vector that is perpendicular to both A and B. Its magnitude equals the area of the parallelogram formed by A and B.
The formula
For A = (aₓ, aₛ, a₠) and B = (bₓ, bₛ, b₠), the cross product A × B = (aₛb₠ − a₠bₛ, a₠bₓ − aₓb₠, aₓbₛ − aₛbₓ). The magnitude of this resulting vector is found the usual way, as the square root of the sum of the squares of its components.
The cross product is widely used in physics and engineering to find torque, angular momentum, and surface normal vectors. This tool is for general math and educational purposes.
Last reviewed August 2026