 Conformal radius

For a simply connected domain $D\ne \mathbb{C}$ and $z\in D$, the conformal radius is $|{\varphi }^{\prime }(0)|$, where $\varphi$ maps the unit disc conformally onto $D$ with $\varphi (0)=z$. Disc automorphisms fixing zero are rotations, so the value is independent of the chosen map.

The conformal radius is a concept from complex analysis and geometric function theory, particularly in the study of conformal mappings. It provides a measure of the "size" of a domain in a way that is invariant under conformal (angle-preserving) transformations.