An explicit solution to the Kirchhoff integral formulation for predicting acoustic radiation from a vibrating object is derived. The radiated acoustic pressure is shown to be expressible in terms of integrations of the normal and tangential components of the particle velocity over a surface that encloses the object. If this surface coincides with that of the vibrating object, then the normal component of the particle velocity is equal to that of the surface velocity, which is normally assumed given. The tangential component of the particle velocity, however, is different from that of the surface velocity, but is determinable experimentally by using an intensity probe. For a class of special cases in which the object dilates uniformly, the tangential component of the particle velocity is identically zero. Under this condition, the radiated acoustic pressure can be obtained by directly integrating the normal component of the surface velocity over the vibrating surface, rather than solving the surface acoustic pressure first, and then the radiated acoustic pressure, as it is traditionally done in the numerical solutions to the Kirchhoff integral formulation.