Cross Product Calculator
Vector cross product in 3D.
Enter your values
ⓘ Live results
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.
Worked example
Using the values the calculator loads with:
Inputs
- Vector a (x, y, z)3, -2, 5
- Vector b (x, y, z)1, 4, -2
Results
- a × b(-16, 11, 14)
- Magnitude23.93742
- Angle between vectors57.927°
- Parallelogram area23.93742
- Triangle area11.96871
Frequently asked questions
Is cross product commutative?
No — a × b = −(b × a).
What if vectors are parallel?
The cross product is the zero vector.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.