Vector Cross Product Calculator

Calculate the cross product of two 3D vectors. Free online vector cross product calculator.

The Vector Cross Product Calculator computes the cross product of two 3D vectors, producing a new vector perpendicular to both inputs. The magnitude equals the area of the parallelogram formed by the vectors. Enter vector components to find the cross product with step-by-step calculation.

Common use cases

  • Torque calculation in physics
  • Normal vector computation
  • Area of triangles and parallelograms
  • Computer graphics surface normals
  • Angular momentum calculations

How to use

  1. Enter components of Vector A (x, y, z)
  2. Enter components of Vector B (x, y, z)
  3. Click calculate for cross product
  4. View the resulting vector
  5. See the parallelogram area

FAQ

What is the cross product?

a×b produces a vector perpendicular to both a and b, with magnitude |a||b|sin(θ).

Is cross product commutative?

No, a×b = -(b×a). Order matters; reversing order reverses direction.

What's the right-hand rule?

Point fingers along a, curl toward b; thumb points in direction of a×b.

Does cross product exist in 2D?

Not as a vector. In 2D, a×b gives a scalar (the z-component if extended to 3D).