AbstractReduced‐precision floating‐point arithmetic is now deployed routinely in numerical weather forecasting over short timescales. However, the applicability of these reduced‐precision techniques to longer‐timescale climate simulations—especially those that seek to describe a dynamical, changing climate—remains unclear. We investigate this question by deploying a global atmospheric, coarse‐resolution model known as Simplified Parameterizations PrimitivE Equation DYnamics (SPEEDY) to simulate a changing climate system subject to increased concentrations, over a 100‐year timescale. Whilst double precision is typically the operational standard for climate modelling, we find that reduced‐precision solutions are sufficiently accurate. Rounding the floating‐point numbers stochastically, rather than using the more common “round‐to‐nearest” technique, improves the performance of the reduced‐precision solutions notably. Over 100 years, the mean bias error (MBE) in the global mean surface temperature (precipitation) relative to the double‐precision solution is +1.8 K ( mm(6 hr)) when integrating numerically at half precision (10 significant bits) with stochastic rounding. By examining the resultant climatic distributions that arise after 100 years, the difference in the expected value of the global surface temperature relative to the double‐precision solution is K and that for precipitation is mm(6 hr). Whilst further research is necessary to extended these results to more complex and higher‐resolution models, they indicate that reduced‐precision techniques and stochastic rounding could be suitable for the next generation of climate models and motivate the use of low‐precision hardware to this end.