Parameterless stopping criteria for recursive polynomial expansions to construct the density matrix in electronic structure calculations are proposed. Based on convergence-order estimation the new stopping criteria automatically and accurately detect when the calculation is dominated by numerical errors and continued iteration does not improve the result. Difficulties in selecting a stopping tolerance and appropriately balancing it in relation to parameters controlling the numerical accuracy are avoided. Thus, our parameterless stopping criteria stand in contrast to the standard approach to stop as soon as some error measure goes below a user-defined parameter or tolerance. We demonstrate that the stopping criteria work well both in dense and sparse matrix calculations and in large-scale self-consistent field calculations with the quantum chemistry program Ergo ( www.ergoscf.org ) .