Equilibrium free energy differences can be calculated accurately from repeated fast-growth thermodynamic integration (TI) based on Jarzynski's identity [Phys. Rev. Lett. 78, 2690 (1997)]. We derive expressions for the free energy differences. Error estimates allow us to quantify the relative efficiency of performing many fast-growth vs few slow-growth TIs for a given total computational cost. Fast-growth TI is illustrated through the calculation of the potential of mean force between two methane molecules and compared to umbrella sampling analyzed by using the weighted histogram analysis method. Fast-growth TI is well suited for parallel computer architectures, requiring only the simplest parallelism with repeated runs for different starting conditions.