Abstract. Simple climate models can be valuable if they are able to replicate aspects of complex fully coupled earth system models. Larger ensembles can be produced, enabling a probabilistic view of future climate change. A simple emissions-based climate model, FAIR, is presented, which calculates atmospheric concentrations of greenhouse gases and effective radiative forcing (ERF) from greenhouse gases, aerosols, ozone and other agents. Model runs are constrained to observed temperature change from 1880 to 2016 and produce a range of future projections under the Representative Concentration Pathway (RCP) scenarios. The constrained estimates of equilibrium climate sensitivity (ECS), transient climate response (TCR) and transient climate response to cumulative CO2 emissions (TCRE) are 2.86 (2.01 to 4.22) K, 1.53 (1.05 to 2.41) K and 1.40 (0.96 to 2.23) K (1000 GtC)−1 (median and 5–95 % credible intervals). These are in good agreement with the likely Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5) range, noting that AR5 estimates were derived from a combination of climate models, observations and expert judgement. The ranges of future projections of temperature and ranges of estimates of ECS, TCR and TCRE are somewhat sensitive to the prior distributions of ECS∕TCR parameters but less sensitive to the ERF from a doubling of CO2 or the observational temperature dataset used to constrain the ensemble. Taking these sensitivities into account, there is no evidence to suggest that the median and credible range of observationally constrained TCR or ECS differ from climate model-derived estimates. The range of temperature projections under RCP8.5 for 2081–2100 in the constrained FAIR model ensemble is lower than the emissions-based estimate reported in AR5 by half a degree, owing to differences in forcing assumptions and ECS∕TCR distributions.