Let \(P\in {\mathbb{R}}[X]\) be a polynomial with coefficients in the field \({\mathbb{R}}\). The additive complexity k of P is the minimal number of additions and subtractions required to compute P over \({\mathbb{R}}\). It is proved that there exists a constant C such that the number of distinct real zeros of P is \(\leq C^{k^ 2}\). The result is generalized to the additive complexity of polynomials in several variables.