Vector calculator

Cross Product Calculator

Compute A × B in three dimensions, with an optional two-dimensional scalar z-component mode.

Enter values

Vector A
Vector B

Enter values and select Calculate.

Formula and methodology

For 3D vectors, A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁). The 2D mode returns aₓbᵧ − aᵧbₓ, the scalar z-component after embedding both vectors in the xy-plane.

Worked example

For A = (1, 2, 3) and B = (4, 5, 6), A × B = (−3, 6, −3) and its magnitude is √54 ≈ 7.348469.

Assumptions and boundaries

  • Cross-product order matters: B × A is the negative of A × B.
  • Parallel vectors have the zero vector as their cross product.
  • The 2D result is a scalar z-component, not a two-component cross-product vector.
  • This page does not calculate a standalone dot product.

Inputs and results stay in this browser and are not sent to analytics.