Planetary impact craters have a high degree of radial symmetry. This hampers efforts to identify the azimuthal impact direction for most craters – the radially symmetric component of an impact crater swamps any asymmetries that may be present. We demonstrate how the asymmetric component can be isolated and the direction of the asymmetries quantified using a two-dimensional eigenfunction expansion over a circular domain. The complex coefficients of expansion describe the magnitude and phase (angular alignment) of each term. From the analysis of hypervelocity impact craters formed in the laboratory, with impact angles ranging from 0° to 50° from the surface normal, we show that asymmetries which reveal the impact direction are still present at just 10° from the surface normal, and that the phase of one complex coefficient of expansion, c11, indicates the impact direction. Analysis of the lunar crater Hadley shows bilateral symmetry in the radially asymmetric component, which may be due to oblique impact. The 31-km lunar ray crater Kepler has morphological features that indicate the azimuthal impact direction. Coefficient c11 gives an azimuthal impact direction similar to that expected from the morphology, although post-impact gravitational collapse and slumping obscure the result to some degree. Ray craters may provide a means of testing the method for smaller 'simple' craters when data are available.