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ABSTRACT Galactic winds are a crucial player in galaxy formation and evolution, but observations of them have proven extraordinarily difficult to interpret, leaving large uncertainties even in basic quantities such as mass outflow rates. Here we present an analysis of the wind of the nearby dwarf starburst galaxy M82 using a semi-analytic model that is able to take advantage of the full three-dimensional information present in position–position–velocity data cubes measured in the H i 21-cm line, the CO J = 2 → 1 line, and the Hα line. Our best-fitting model produces position-dependent spectra in good agreement with the observations, and shows that the total wind mass flux in the atomic and molecular phases is ≈10 M⊙ yr−1 (corresponding to a mass loading factor of ≈2–3), with less than a factor of 2 uncertainty; the mass flux in the warm ionized phase is more poorly constrained, and may be comparable to or smaller than this. At least over the few kpc off the plane for which we trace the outflow, it appears to be a wind escaping the galaxy, rather than a fountain that falls back. Our fits require that clouds of cool gas entrained into the wind expand only modestly, suggesting they are confined by magnetic fields, radiative cooling, or a combination of both. Finally, we demonstrate that attempts to model the wind using simplifying assumptions such as instantaneous acceleration and a constant terminal wind speed can yield significantly erroneous results.