Tighten a lug nut and you are doing a cross product with your hands — the twist you feel is perpendicular to both the wrench and the force. The cross product A × B of two 3D vectors produces a third vector perpendicular to both, with components Cx = Ay·Bz − Az·By, Cy = Az·Bx − Ax·Bz, Cz = Ax·By − Ay·Bx. Its magnitude |A × B| = |A||B|sin(θ) equals the area of the parallelogram the vectors span — zero when they point the same way, maximum when perpendicular.

The direction follows the right-hand rule: point your fingers along A, curl toward B, and your thumb shows the result. Physics runs on it: torque is r × F (which is why a longer wrench loosens rusted bolts), and the magnetic force on a moving charge is q(v × B). Game engines use it for surface normals and lighting. Enter all six components and the calculator returns Cx, Cy, Cz plus the magnitude.

With the pre-filled defaults — Vector A - x component (Ax) 1, Vector A - y component (Ay) 2, Vector A - z component (Az) 3, Vector B - x component (Bx) 4, Vector B - y component (By) 5, Vector B - z component (Bz) 6 — the Cross Product Calculator returns Cross Product - Cx -3.0000, Cross Product - Cy 6.0000, Cross Product - Cz -3.0000, Magnitude |A × B| 7.3485. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.