In this paper, we obtain upper bounds for the critical time T * of the blowup for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. Such estimates is rarely obtained and discuss in the papers on the subject No moment condition or/and entropy condition are required on the initial data; only the usual assumptions of non-negativity and finiteness of the mass is assumed. The result is expressed not only in terms of the supercritical mass M > 8π, but also in terms of the shape of the initial data.