The continuous matrices of atomic displacements and lattice distortion from face-centered-cubic (fcc) to body-centered-cubic (bcc) phases compatible with the hard-sphere geometry of iron atoms are calculated for different possible final orientation relationships (ORs), such as Bain, Pitsch and Kurdjumov-Sachs (KS). The angular distortion introduced in the calculations appears as a natural order parameter of the fcc bcc transitions. The average atomic displacement is lower with Pitsch and KS ORs than for Bain; one of these two distortions probably constitutes the natural mechanism for stress-free isolated small crystals. For matrix-embedded transformations that occur in bulk steels, the distortion associated with KS OR seems very appropriate: it has special mathematical properties and can explain the (225) habit planes with a simple O-lattice criterion. From these calculations, the fcc bcc martensitic transformation appears to be "angular distortive", and not of "shear" type as usually assumed. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.