欧几里得空间R中一个曲面S是可定向（orientable）的如果一个二维图形（比如）沿着曲面移动后回到起点不能使它看起来像它的镜像（）。否则曲面是不可定向（non-orientable）的。

更确切地，应用于非嵌入曲面，一个曲面可定向如果不存在从二维球B与单位区间的乘积到曲面的连续函数，使得f(b,t)=f(c,t)当且仅当b=c对任何t ∈ [0,1]，并存在一个反射映射使得f(b,0) = f(r(b),1)对每个b ∈ B。

一个抽象曲面（即一个二维流形）可定向如果在曲面上连续存在一个一致的逆时针方向旋转概念。这等价于问平面是否包含一个子集同胚于莫比乌斯带。从而对曲面来说，莫比乌斯带可认为是所有不可定向性之来源。

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point. A choice of surface normal allows one to use the right-hand rule to define a "clockwise" direction of loops in the surface, as needed by Stokes' theorem for instance. More generally, orientability of an abstract surface, or manifold, measures whether one can consistently choose a "clockwise" orientation for all loops in the manifold. Equivalently, a surface is orientable if a two-dimensional figure such as in the space cannot be moved (continuously) around the space and back to where it started so that it looks like its own mirror image .