In geometry, an affine plane is a two-dimensional affine space. Typical examples of affine planes are

• Euclidean planes, which are affine planes over the reals, equipped with a metric, the Euclidean distance. In other words, an affine plane over the reals is a Euclidean plane in which one has "forgotten" the metric (that it one cannot talk of lengths nor of angle measures).
• Vector spaces of dimension two, in which the zero vector is not considered as different from the other elements
• For every field or division ring F, the set F² of the pairs of elements of F
• The result of removing any single line (and all the points on this line) from any projective plane

All the affine planes defined over a field are isomorphic. More precisely, the choice of an affine coordinate system (or, in the real case, a Cartesian coordinate system) for an affine plane P over a field F induces an isomorphism of affine planes between P and F².