We derive a simple expression for the correlation part of the kinetic energy of an inhomogeneous electron gas from density-functional theory. We show that in the local density approximation, this expression reduces to the virial theorem result ${t}_{\mathrm{xc}}=3{v}_{\mathrm{xc}}\ensuremath{-}4{\ensuremath{\epsilon}}_{\mathrm{xc}}$. We also derive the correction for an inhomogeneous gas using Langreth and Mehl's expression for the exchange-correlation energy from a nonuniform density.