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Vector Cross Product Calculator
Compute the cross product of two 3D vectors and the magnitude of the result.
a.x
a.y
a.z
b.x
b.y
b.z
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How it works
a × b = (aybz − azby, azbx − axbz, axby − aybx)
The cross product returns a vector perpendicular to both inputs. Its magnitude equals the area of the parallelogram they span, and it is zero when the vectors are parallel.
Worked example
(1,2,3) × (4,5,6) = (−3, 6, −3).
Frequently asked questions
Why is the result a vector, not a number?
Unlike the dot product, the cross product yields a new vector — perpendicular to the plane of the two inputs.
What does zero magnitude mean?
The two vectors are parallel (or one is zero), so they span no area.
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This calculator is for educational purposes. Double-check important results before acting on them.