Expressions suitable for numerical evaluation, are given for the parameters characterizing the locations of the R-cutoff (upper X-mode cutoff), the L-cutoff (lower X-mode cutoff) and the O-mode cutoff for electromagnetic waves in relativistic plasmas. The ion motion is ignored, and it is assumed that the plasma is collisionless and in thermodynamic equilibrium. A new derivation of the relativistic cutoff expressions, starting from first principles, is given, together with a heuristic explanation for the relativistic shift of the O-mode cutoff.