This paper is dedicated to the classical Hadamard formula for asymptotics of eigenvalues of the Dirichlet-Laplacian under perturbations of the boundary. We prove that the Hadamard formula still holds for C-1-domains with C-1-perturbations. We also derive an optimal estimate for the remainder term in the C-1,C-alpha-case. Furthermore, if the boundary is merely Lipschitz, we show that the Hadamard formula is not valid. (C) 2020 Elsevier Masson SAS. All rights reserved.