We analyse the global primary energy use and total CO<sub>2</sub> 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 CO<sub>2</sub> emissions. Our best estimates for 2020 are 800 EJ yr<sup>−1</sup> for global energy use and 14 Gt yr<sup>−1</sup> for global CO<sub>2</sub> emissions, with both being above almost all other published forecasts. This suggests the energy and total CO<sub>2</sub> emissions landscape in 2020 may be significantly more challenging than currently envisaged.