A simple rule for the optimal global price of carbon is presented, which captures the geophysical, economic, and ethical drivers of climate policy as well as the effect of uncertainty about future growth of consumption. There is also a discussion of the optimal carbon budget and the amount of unburnable carbon and stranded fossil fuel reserves and a back-on-the-envelope expression are given for calculating these. It is also shown how one can derive the end of the carbon era and peak warming. This simple arithmetic for determining climate policy is meant to complement the simulations of large-scale integrated assessment model, and to give analytical understanding of the key determinants of climate policy. The simple rules perform very well in a full integrated assessment model. It is also shown how to take account of a 2 °C upper limit on global warming. Steady increases in energy efficiency do not affect the optimal price of carbon, but postpone the carbon-free era somewhat and if technical progress in renewables and economic growth are strong leads to substantially lower cumulative emissions and lower peak global warming.