  Recently, S\'a, Ribeiro and Prosen introduced complex spacing ratios to
analyze eigenvalue correlations in non-Hermitian systems. At present there are
no analytical results for the probability distribution of these ratios in the
limit of large system size. We derive an approximation formula for the Ginibre
universality class of random matrix theory which converges exponentially fast
to the limit of infinite matrix size. We also give results for moments of the
distribution in this limit.
