How to Use the Vector Cross Product Calculator
The cross product combines two vectors in 3D space into a new vector that's perpendicular to both. For vectors A(ax, ay, az) and B(bx, by, bz), the cross product A×B is (ay·bz - az·by, az·bx - ax·bz, ax·by - ay·bx). The resulting vector's direction follows the right-hand rule: curl your fingers from A toward B, and your thumb points the way.
The magnitude of the cross product, |A×B|, is exactly equal to the area of the parallelogram formed by A and B. That property makes the cross product essential for finding a surface's normal vector, computing surface orientation in 3D graphics, and calculating torque in physics. If the result comes out as the zero vector (0,0,0), it means the two vectors are parallel or one of them is itself a zero vector.
Unlike the dot product, which returns a single scalar, the cross product always returns a vector — and swapping the order flips its direction, since A×B = -B×A (it isn't commutative). Enter the six component values and this calculator shows you the resulting vector, its magnitude, and what the result means, all at once.
Frequently Asked Questions
The cross product combines two 3D vectors into a new vector perpendicular to both. Its direction follows the right-hand rule.
A zero cross product (0,0,0) means the two vectors are parallel, or one of them is the zero vector.
The magnitude equals the area of the parallelogram formed by the two vectors.