We measured both angulation and translation on anteroposterior and
lateral roentgenograms of 100 fixed post-traumatic deformities (either
malunions or stiff [hypertrophic] non-unions) of long bones. We used
trigonometric formulae to calculate the true planes and actual magnitude of
both the angulation and the transverse translation of each deformity. We
found that the planes of angulation and translation for each osseous
deformity were rotated 43 +/- 25 degrees (mean and standard deviation) with
respect to each other; in fact, we found almost as many instances in which
the planes of angulation and translation of the fragments were within 10
degrees of perpendicular to each other as we did instances in which the
angulation and translation were within 10 degrees of being in the same
plane. Only seven angular deformities and six translational deformities
occurred along either the sagittal or the coronal plane; the remaining
deformities were in planes that were oblique to the standard reference
planes.