We analyse the global primary energy use and total CO2 emissions time series since 1850 and show that their relative growth rates appear to exhibit periodicity with a fundamental timescale of ~60 years and with significant harmonic behaviour. Quantifying the inertia inherent in these dynamics allows forecasting of future "business as usual" energy needs and their associated CO2 emissions. Our best estimates for 2020 are 800 EJ yr−1 for global energy use and 14 Gt yr−1 for global CO2 emissions, with both being above almost all other published forecasts. This suggests the energy and total CO2 emissions landscape in 2020 may be significantly more challenging than currently envisaged.