Quick guide
How to use this calculator
- Enter three components for a and b.
- Keep the vector order intentional.
- Read a × b; reversing the order reverses its sign.
Calculation method
Use the oriented 3D component formula
The cross product is perpendicular to both input vectors. This calculator preserves the right-hand-rule orientation of a × b.
Worked example
Cross the first two basis vectors
Use a = ⟨1,0,0⟩ and b = ⟨0,1,0⟩.
a × b = ⟨0,0,1⟩
Supported inputs
Precision and limits
Vector size
General vectors may contain 2–8 components; three-dimensional products require exactly three.
Entry precision
Each signed decimal may contain up to 30 digits and 15 decimal places.
Square roots
Squared magnitudes remain exact. Irrational roots and normalized components are explicitly labelled approximations.