We have calculated the enthalpy of formation and bulk modulus for 19 typical binary sigma compounds with different atomic order (i.e. atomic constituent distribution or site occupancy preference on inequivalent sites of a crystal structure) based on the experimental site occupancy as well as completely ordered and hypothetically disordered states by using the EMTO-CPA (Exact Muffin-Tin Orbitals Coherent Potential Approximation) method. The calculation results show that at 0 K the sigma phase in ordered state bears a lower enthalpy of formation and a larger bulk modulus than the ones in less ordered state. (C) 2017 Elsevier B.V. All rights reserved.