Massive stars (with mass m* > 8 solar masses Mmiddle dot in circle) are fundamental to the evolution of galaxies, because they produce heavy elements, inject energy into the interstellar medium, and possibly regulate the star formation rate. The individual star formation time, t*f, determines the accretion rate of the star; the value of the former quantity is currently uncertain by many orders of magnitude, leading to other astrophysical questions. For example, the variation of t*f with stellar mass dictates whether massive stars can form simultaneously with low-mass stars in clusters. Here we show that t*f is determined by the conditions in the star's natal cloud, and is typically about 105yr. The corresponding mass accretion rate depends on the pressure within the cloud--which we relate to the gas surface density--and on both the instantaneous and final stellar masses. Characteristic accretion rates are sufficient to overcome radiation pressure from about 100M middle dot in circle protostars, while simultaneously driving intense bipolar gas outflows. The weak dependence of t*f on the final mass of the star allows high- and low-mass star formation to occur nearly simultaneously in clusters.