Abstract Using the Dirac–Fock relativistic wave functions in the position space the shape complexity, C LMC s , form of the statistical complexity measure due to Lopez-Ruiz, Mancini, and Calbet and the simple two parameter complexity measure, Γα,β, proposed by Shiner, Davison and Landsberg for atoms H–Lr are calculated. A comparison with the non-relativistic Hartee–Fock results is carried out to ascertain the influence of the relativistic effects on complexity. Unlike the non-relativistic Hartree–Fock results, which lead to the non-increasing C LMC s , the Dirac–Fock calculations lead to both C LMC s and Γα,β clearly displaying an increasing trend in complexity as the atomic number increases.