In geometry, a hyperplane is a linear, affine, or projective subspace of codimension 1. In particular, in a three-dimensional space, a hyperplane is the usual plane. In a two-dimensional space, a hyperplane is a line. In a one-dimensional space, a hyperplane is a point.

An affine hyperplane can be described by a non-degenerate linear equation of the following form:

a₁x₁ + a₂x₂ + ... + a_nx_n = b.

A linear hyperplane is similar but with b = 0.

See also hypersurface.

The term realm has been advocated for a three-dimensional hyperplane, but this is not in common use.

A hyperplane is not to be confused with a hypersonic aircraft.