数学上，共形变换（英语：Conformal map）或称保角变换，来自于流体力学和几何学的概念，是一个保持角度不变的映射。

更正式的说，一个映射

称为在 共形(或者保角)，如果它保持穿过 的曲线间的定向角度，以及它们的取向也就是说方向。共形变换保持了角度以及无穷小物体的形状，但是不一定保持它们的尺寸。

共形的性质可以用坐标变换的导数矩阵雅可比矩阵的术语来表述。如果变换的雅可比矩阵处处都是一个标量乘以一个旋转矩阵，则变换是共形的。

In mathematics, a conformal map is a function that preserves angles locally. In the most common case, the function has a domain and an image in the complex plane.

More formally, a map

is called conformal (or angle-preserving) at a point u₀ if it preserves oriented angles between curves through u₀ with respect to their orientation (i.e. not just the magnitude of the angle). Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature.