The fission of solitary waves propagating over variable topography is investigated. In previous theories, to predict the number and the amplitudes of disintegrated solitons in the wave packet generated from a solitary wave, the parameters of the water environment and the incident solitary wave are required. However, it is difficult to measure these parameters in the ocean because of their temporal and spatial variations. In this paper, a fission law, in the form of the expressions of the number and the amplitudes of the disintegrated solitons, is derived from the partial information available on the wave packet. Theoretical analysis shows that the law is suitable for describing the fission of both surface and internal solitary waves and is also applicable to the cases of wave damping and wave breaking. Comparisons between the model output and the results from laboratory experiments, numerical simulations and field observations available in the literature demonstrate that the fission law can efficiently estimate the number and the amplitudes of solitons in the wave packet generated by a solitary wave.