We calculate the radiation of acoustic waves into the atmosphere by surface gravity waves on the ocean surface. We show that because of the phase speed mismatch between surface gravity waves and acoustic waves, a single surface wave radiates only evanescent acoustic waves. However, owing to nonlinear terms in the acoustic source, pairs of ocean surface waves can radiate propagating acoustic waves if the two surface waves propagate in almost equal and opposite directions. We derive an analytic expression for the acoustic radiation by a pair of ocean surface waves, and then extend the result to the case of an arbitrary spectrum of ocean surface waves. We present some examples for both the two-dimensional and three-dimensional regimes. Of particular note are the findings that the efficiency of acoustic radiation increases at higher wavenumbers, and the fact that the directionality of the acoustic radiation is often independent of the shape of the spectrum.