The exchange constantsJTTJTR, andJRRin the garnet seriesR3Fe5O12(R= Y3+, Gd3+, Tb3+, Dy3+, Ho3+, Er3+, Tm3+, or Yb3+) have been obtained using the molecular field approximation. The low‐temperature magnetization data for all the garnets except Y and Gd garnets have been fitted assuming a temperature‐dependent canting on the rare‐earth sublattice. These exchange constants are found to be comparable to those obtained for the rare‐earth intermetallicRFe4Al8.