For \(\kappa\) an infinite cardinal, a stationary subset \(S\subseteq \kappa\) is said to reflect if there is some limit ordinal \(\gamma <\kappa\) such that \(S\cap \gamma\) is stationary in \(\gamma\). A reflection cardinal is a cardinal \(\kappa\) carrying a proper \(\kappa\)-complete normal ideal \({\mathcal I}\) such that if \(X\in {\mathcal I}^+\) then \(\{\) \(\alpha\) : \(X\cap \alpha\) is stationary in \(\alpha\) \(\}\in {\mathcal I}^+\) (where as usual, \({\mathcal I}^+\) is the family of subsets of \(\kappa\) not in \({\mathcal I}).\) In this paper the authors show that the consistency strength of the existence of a regular cardinal such that every stationary set reflects is the same as the consistency strength of the existence of a regular reflection cardinal. (It is the same as the consistency strength of the existence of a regular cardinal \(\kappa\) such that every \(\kappa\)-free abelian group is \(\kappa^+\)-free, which is the motivation for the authors' interest in this question.) They also show that in L, the first reflection cardinal is greater than the first greatly Mahlo cardinal and less than the first weakly compact cardinal.