Calculating spin-orbit matrix elements with RACAH. RACAH is a computer program developed to simplify calculations involving generalized coupling coefficients. As a demonstration of its usefulness in doing this, we apply it to calculating the spin-orbit matrix elements of CrBr 3 . From those matrix elements we can derive the spin-orbit coupling coefficients, vital to discussing Kerr rotation. We base our calculations on a cluster consisting of a Cr 3+ ion, surrounded by six Br - ions in an octahedral configuration. The Racah-Wigner calculus, useful for doing such calculations, is built into RACAH in such a way as to provide a natural approach to choosing between possible group chains.