Cross Product Calculator

How the cross product calculator works

The three-dimensional cross product returns a vector perpendicular to both inputs, with direction set by the right-hand rule. Its magnitude equals the area of the parallelogram spanned by the vectors. This calculator evaluates the three signed two-by-two minors explicitly, reports the resulting vector, and computes its Euclidean magnitude for geometric interpretation.

The default first vector points along positive x and the second along positive y. Their verified cross product is 0, 0, 1, which points along positive z and has magnitude one. Reversing the input order would give 0, 0, minus 1, demonstrating why cross multiplication is anti-commutative rather than interchangeable.

Reading cross product calculator results privately

This operation is defined here only for ordinary three-dimensional real vectors. Parallel inputs produce the zero vector because their spanned parallelogram has zero area, and that zero result has no unique direction. Input order matters. Decimal components use floating-point arithmetic, so near-parallel vectors may leave tiny residual components rather than exact zeros. This cross product calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.