Cross Product Calculator
Calculate a × b for two three-dimensional vectors in a right-handed Cartesian basis. Components are unitless numbers.
Formula
a × b = (aᵧb_z − a_zbᵧ, a_zbₓ − aₓb_z, aₓbᵧ − aᵧbₓ).
Result x component ≈ (0)×(0)-(0)×(1) · Result y component ≈ (0)×(0)-(1)×(0) · Result z component ≈ (1)×(1)-(0)×(0)
How to use
- Enter x, y and z components of a.
- Enter x, y and z components of b in the same basis.
- Read the three components of a × b.
Examples
- (1, 2, 3) × (4, 5, 6) = (−3, 6, −3).
Frequently asked questions
Does order matter?
Yes. Swapping a and b negates the result.
What if the vectors are parallel?
Their cross product is the zero vector; a zero input vector also gives zero.
Does this convert physical units?
No. Inputs are mathematical components without units; physical data must first use consistent units.
Sources
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