Bioenergy is booming as nations seek to cut their greenhouse gas emissions. The European Union declared biofuels to be carbon-neutral, triggering a surge in wood use. But do biofuels actually reduce emissions? A molecule of CO2 emitted today has the same impact on radiative forcing whether it comes from coal or biomass. Biofuels can only reduce atmospheric CO2 over time through post-harvest increases in net primary production (NPP). The climate impact of biofuels therefore depends on CO2 emissions from combustion of biofuels versus fossil fuels, the fate of the harvested land and dynamics of NPP. Here we develop a model for dynamic bioenergy lifecycle analysis. The model tracks carbon stocks and fluxes among the atmosphere, biomass, and soils, is extensible to multiple land types and regions, and runs in ≈1s, enabling rapid, interactive policy design and sensitivity testing. We simulate substitution of wood for coal in power generation, estimating the parameters governing NPP and other fluxes using data for forests in the eastern US and using published estimates for supply chain emissions. Because combustion and processing efficiencies for wood are less than coal, the immediate impact of substituting wood for coal is an increase in atmospheric CO2 relative to coal. The payback time for this carbon debt ranges from 44–104 years after clearcut, depending on forest type—assuming the land remains forest. Surprisingly, replanting hardwood forests with fast-growing pine plantations raises the CO2 impact of wood because the equilibrium carbon density of plantations is lower than natural forests. Further, projected growth in wood harvest for bioenergy would increase atmospheric CO2 for at least a century because new carbon debt continuously exceeds NPP. Assuming biofuels are carbon neutral may worsen irreversible impacts of climate change before benefits accrue. Instead, explicit dynamic models should be used to assess the climate impacts of biofuels.