Optimal stability polynomials are polynomials whose stability region is as large as possible in a certain region, here the negative real axis. We are interested in such polynomials which in addition, obey a certain order condition. An important application of these polynomials is the construction of stabilized explicit Runge–Kutta methods. In this paper we will give some properties of the roots of these polynomials, and prove that their error constant is always positive. Furthermore, for a given order, the error constant decreases as the degree increases.