在数学里，一个正交座标系定义为一组正交座标，其座标曲面都以直角相交。座标曲面定义为座标的等值曲面，或等值超曲面。例如，三维直角座标是一种正交座标，它的为常数，为常数，为常数的座标曲面，都是互相以直角相交的平面，都互相垂直。

正交座标时常用来解析一些出现于量子力学、流体动力学、电动力学、热力学等等的偏微分方程。举例而言，选择一个恰当的的正交座标来解析氢离子的波函数或消防水管的喷水，也许会比用直角座标方便的多。这主要是因为恰当的正交座标能够与一个问题的对称性相配合，从而促使应用分离变量法来成功的解析关于这问题的方程序。分离变量法是一种数学技巧，专门用来将一个复杂的维问题变为个一维问题。很多问题都可以简化为拉普拉斯方程或亥姆霍兹方程，这些方程序可以用很多种正交座标来分离。

In mathematics, orthogonal coordinates are defined as a set of d coordinates q = (q, q, ..., q) in which the coordinate surfaces all meet at right angles (note: superscripts are indices, not exponents). A coordinate surface for a particular coordinate q is the curve, surface, or hypersurface on which q is a constant. For example, the three-dimensional Cartesian coordinates (x, y, z) is an orthogonal coordinate system, since its coordinate surfaces x = constant, y = constant, and z = constant are planes that meet at right angles to one another, i.e., are perpendicular. Orthogonal coordinates are a special but extremely common case of curvilinear coordinates.