Vector Cross Product Calculator
Calculate the cross product of two 3D vectors, and the resulting vector's magnitude.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter two 3D vectors to find their cross product and its magnitude.
Exactly 3 components, separated by commas.
Your result
-3, 6, -3
Cross product
Magnitude7.348
AI explanation
Formula
a × b = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁)Worked example
(1,2,3) x (4,5,6)
| Field | Value |
|---|---|
| Vector A (3D) | 1,2,3 |
| Vector B (3D) | 4,5,6 |
| Cross product | -3, 6, -3 |
| Magnitude | 7.3485 |
Assumptions
- The cross product is defined only for two 3-dimensional vectors — both inputs must have exactly 3 components.
Frequently asked questions
What does the cross product represent?
A new vector perpendicular to both input vectors, whose magnitude equals the area of the parallelogram they span — widely used in physics (torque, angular momentum) and 3D graphics (surface normals).
Why does this only work for 3D vectors?
The cross product, as commonly defined, only exists in 3 dimensions (and, in a generalized form, 7 dimensions) — for other dimensions, use the Dot Product Calculator instead.
Is a x b the same as b x a?
No — the cross product is anti-commutative: b × a = −(a × b), the reverse of a × b.