This paper introduces an ultrahigh-speed algorithm for calculating isotope distributions from molecular formulas, elemental isotopic masses, and elemental isotopic abundances. For a given set of input data (molecular formula, elemental isotopic masses, and elemental isotopic abundances), and assuming round-off error to be negilgible, the new algorithm rigorously produces isotope distributions whose mean and standard deviation are “correct” in the sense that an error-free algorithm would produce a distribution having the same mean and standard deviation. The peak heights are also “correct” in the sense that the height of each nominal isotope peak from the ultrahigh-speed calculation equals the integrated peak area of the corresponding nominal isotope peak from an exact calculation. As a consequence of these properties, the algorithm generally places isotope peaks within millidaltons of their true centroids. The method uses Fourier transform methods and relates closely to two other recently introduced algorithms. The suite of capabilities provided by these three algorithms is sufficient to solve an extremely wide range of problems requiring isotope distribution simulation.