We propose a quantitative model for triplet superconductivity in Sr_2RuO_4 based on first principles calculations for the electronic structure and magnetic susceptibility. The superconductivity is due to ferromagnetic spin fluctuations, that are strong at small wave vectors. The calculated effective mass renormalization, renormalized susceptibility, and superconducting critical temperature are all in good agreement with experiment. The most stable superconducting solution has order parameters of comparable magnitude on all three sheets of the Fermi surface. We also propose an explanation of the discrepancy between the Fermi surface topology observed in the photoemission and in de Haas-van Alphen experiments.