Vector Math
Cross Product Calculator
Generate the vector orthogonal to two 3D inputs and inspect its magnitude.
Compute the vector orthogonal to both inputs in ℝ³.
Note: Enter x, y, z components separately
Cross product (ℝ³)
A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁)
The resulting vector is perpendicular to both inputs, making it useful for torque and area calculations.
How to use
- Enter two 3-component vectors.
- Confirm the components correspond to x, y, and z values.
- Review the cross product vector and its magnitude.
Example
Input: A = (1, 2, 3), B = (−3, 0, 4)
Output: A × B = (8, −13, 6), ‖A × B‖ ≈ 16.5529
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Cross Product Calculator: vector calculator, vector addition calculator, dot product calculator, cross product calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Cross Product Calculator: Computes the vector cross product in three dimensions. It's built around cross product, vector product, orthogonal vector, so you can go from a raw question to a checked answer without switching tools.
The math behind it: The resulting vector is perpendicular to both inputs, making it useful for torque and area calculations. The core relationship is A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁), shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter two 3-component vectors. (2) Confirm the components correspond to x, y, and z values. (3) Review the cross product vector and its magnitude. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering A = (1, 2, 3), B = (−3, 0, 4) returns A × B = (8, −13, 6), ‖A × B‖ ≈ 16.5529. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Can I use this for 2D vectors?
The cross product in this calculator is defined for 3D vectors. Extend 2D vectors by adding a zero z-component if needed.
What if my vectors are parallel?
Parallel vectors produce a zero vector because they have no perpendicular component.
What formula does the Cross Product Calculator use?
The resulting vector is perpendicular to both inputs, making it useful for torque and area calculations.
How do I use the Cross Product Calculator?
Enter two 3-component vectors. Confirm the components correspond to x, y, and z values. Review the cross product vector and its magnitude.