Math

Cross Product Calculator

Vector cross product in 3D.

Enter your values

Results update instantly as you type — no submit needed.

Results
a × b
(-16, 11, 14)
Magnitude
23.93742
Angle between vectors
57.927°
Parallelogram area
23.93742
Triangle area
11.96871

Quick answer

The cross product produces a vector perpendicular to both inputs, with magnitude equal to the parallelogram area they span.

a × b = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁)

How to use the Cross Product Calculator

  1. 1Enter the three components of vector a.
  2. 2Enter the three components of vector b.
  3. 3Read the resulting perpendicular vector.

Frequently asked questions

Is cross product commutative?

No — a × b = −(b × a).

What if vectors are parallel?

The cross product is the zero vector.