How does the Cross Product Calculator work?

A × B = (AyBz−AzBy, AzBx−AxBz, AxBy−AyBx) Then: |A × B| = |A||B|sin(θ) Then: Result is perpendicular to both A and B Then: Right-hand rule determines direction.

Can you give an example of how to use the Cross Product Calculator?

Example: Input A=(1,0,0), B=(0,1,0) gives a result of A×B = (0,0,1) — unit z vector.

Is the Cross Product Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Cross Product Calculator?

Our Cross Product Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Cross Product Calculator

Cross Product Calculator (A × B)

A₁ (x)

A₂ (y)

A₃ (z)

B₁ (x)

B₂ (y)

B₃ (z)

✓A × B

(-3.0000, 6.0000, -3.0000)

|A × B| (magnitude)

7.3485

The cross product of two 3D vectors produces a third vector perpendicular to both. Its magnitude equals the area of the parallelogram formed by the two vectors. It is used in physics, 3D graphics, and engineering.

Symbol	Name	Unit	Description
u, v	two 3D vectors	—	—
\|u\|, \|v\|	magnitudes of vectors	—	—
θ	angle between vectors	—	—
n̂	unit normal vector perpendicular to both	—	—

Property	Formula/Description
Magnitude	\|A\|\|B\|sin θ
Direction	Perpendicular to both (right-hand)
Anti-commutative	A×B = −(B×A)
Parallel vectors	A×B = 0 when θ=0
Area	\|A×B\| = area of parallelogram

References

›Cross product — Khan Academy

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Cross Product Calculator

Cross Product Calculator (A × B)

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Cross Product Calculator (A × B)

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