Vector Math
Cross Product Calculator
Generate the vector orthogonal to two 3D inputs and inspect its magnitude.
cross productvector productorthogonal vector
Cross Product (3D)
Compute the vector orthogonal to both inputs in ℝ³.
Note: Enter x, y, z components separately
A × B
(8.00, -13.00, 6.00)
‖A × B‖
16.401219
Cross product (ℝ³)
A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁)
The resulting vector is perpendicular to both inputs, making it useful for torque and area calculations.
How to use
- Enter two 3-component vectors.
- Confirm the components correspond to x, y, and z values.
- Review the cross product vector and its magnitude.
Example
Input: A = (1, 2, 3), B = (−3, 0, 4)
Output: A × B = (8, −13, 6), ‖A × B‖ ≈ 16.5529
FAQ & notes
Can I use this for 2D vectors?
The cross product in this calculator is defined for 3D vectors. Extend 2D vectors by adding a zero z-component if needed.
What if my vectors are parallel?
Parallel vectors produce a zero vector because they have no perpendicular component.