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
- 1Enter the three components of vector a.
- 2Enter the three components of vector b.
- 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.