One-loop N = 8 supergravity coefficients from N = 4 super Yang-Mills

We use supersymmetric generalised unitarity to calculate supercoefficients of box functions in the expansion of scattering amplitudes in N = 8 supergravity at one loop. Recent advances have presented tree-level amplitudes in N = 8 supergravity in terms of sums of terms containing squares of colour-ordered Yang-Mills superamplitudes. We develop the consequences of these results for the structure of one-loop supercoefficients, recasting them as sums of squares of N = 4 Yang-Mills expressions with certain coefficients inherited from the tree-level superamplitudes. This provides new expressions for all one-loop box coefficients in N = 8 supergravity, which we check against known results in a number of cases.