Curvature radius of a constant-curvature space ($R_c=|K{|}^{-1/2}$)

A space with nonzero constant sectional curvature $K$ has curvature radius of a constant-curvature space $R_c=1/\sqrt{|K|}$. Scaling a metric tensor by $a^2$ divides its sectional curvature by $a^2$. In an FLRW metric whose spatial normalization is $k=\pm 1$, the spatial curvature of an FLRW universe is $K=k/a^2$, so its scale factor equals $R_c$. For $k=0$ there is no finite intrinsic curvature length.