The primary aim of this paper is the derivation and a proof of a simple and tractable formula for the stray field energy in micromagnetic problems. The formula is based on an expansion in terms of a special family of recently discovered functions. It remains valid even if the magnetization is not of constant magnitude or if the sample is not geometrically bounded. The paper continues with a direct and important application which consists in a fast summation technique of the stray field energy. The convergence of this method is established, and its efficiency is proved by various numerical experiments.