Cross Product Calculator Online— Quick Guide & How to Use
The cross product is a core operation in vector algebra that produces a vector perpendicular to two input vectors. Whether you’re a student, engineer, or developer, a fast cross product calculator makes solving 2D and 3D problems quick and error-free.
Cross Product Calculator
Result will appear here.
What is the Cross Product?
For two vectors A = (Ax, Ay, Az) and B = (Bx, By, Bz), the cross product A × B is:
A × B = (Ay·Bz − Az·By,\n Az·Bx − Ax·Bz,\n Ax·By − Ay·Bx)
This operation returns a vector orthogonal to both A and B and its magnitude equals the area of the parallelogram spanned by A and B:
|A × B| = |A||B|sin(θ)
When to use a Cross Product Calculator
- Quickly computing orthogonal vectors for physics and 3D graphics.
- Solving torque, angular momentum, and normal vector problems.
- Verifying hand calculations or classroom exercises.
How to use the Cross Product Calculator (step-by-step)
- Enter components for Vector A and Vector B. For 2D vectors, set Az = 0 and Bz = 0.
- Click Calculate to get the result vector and its magnitude.
- Use the Copy button to paste results into notes or reports.
Example
If A = (1, 2, 3) and B = (4, 5, 6) then:
A × B = (2·6 − 3·5, 3·4 − 1·6, 1·5 − 2·4) = (12 − 15, 12 − 6, 5 − 8) = (−3, 6, −3)
Quick reference table
| Input type | Notes | Result |
|---|---|---|
| 2D vectors | Set z components to 0 | Produces vector perpendicular to plane (z-only for 2D) |
| Parallel vectors | θ = 0 → sin θ = 0 | Result = (0,0,0) |
| Perpendicular vectors | θ = 90° → sin θ = 1 | Magnitude = |
Related tools and keywords
- vector cross product calculator: for general vector inputs.
- cross product of two vectors calculator / cross product calculator 2 vectors: typical student queries.
- matrix cross product calculator: uses determinant form to compute components.
- how to calculate cross product using calculator: explains step-by-step entry and validation.
Best practices
- Double-check units and signs.
- For symbolic or matrix workflows, use determinant notation to cross-check numeric results.
- Use the calculator when speed and accuracy are needed — especially in labs and programming tasks.