Recent studies have shown that reducing the precision of floating‐point calculations in an atmospheric model can improve the model's computational performance without affecting model fidelity, but code changes are needed to accommodate lower precision or to prevent undue round‐off error. For complex and computationally expensive systems like the Energy Exascale Earth System Model, a method is needed to objectively and efficiently assess the quality of the lower‐precision simulations and to quickly identify problematic code pieces. This paper demonstrates that the accuracy of the computed solution can be evaluated through a simple and quantitative error metric based on time step convergence. The proposed test method can unambiguously detect the accumulation of precision error and objectively assess its impact on solution accuracy. Furthermore, since fast physical processes are known to affect key features of the multiyear mean climate in atmospheric models, we show that the convergence test applied to short simulations can provide useful information about the impact of reduced precision on a model's long‐term behavior. In contrast, the traditional method of climate model evaluation requires multiple years of simulations and involves inspecting many physical quantities for statistical significance in the presence of natural variability. The simplicity, computational efficiency, and objectivity of the proposed method makes it very attractive for high‐resolution model development. The method is also expected to be applicable to other models that numerically solve time evolution equations.