Among the closed-shell hydrocarbons, the carbenes c- and l-C3H2 are the lightest ones to display a permanent electric dipole moment and be detectable by rotational spectroscopy. The cyclic form, cyclopropenylidene, is ubiquitous in the InterStellar Matter (ISM) of the Milky Way and external galaxies. As such, it serves as a marker to help in characterizing the physical conditions of the ISM. The linear form, propadienylidene, is less abundant. In order to get access to their absolute and relative abundances, it is essential to understand their collisional excitation/quenching schemes. We compute here a precise ab initio potential energy surface for the interaction of c- and l-C3H2 with helium, by means of a CCSD(T)-F12a formalism and a fit onto relevant spherical harmonics functions. We conduct quantum dynamical scattering in order to get precise cross sections using a coupled-channel approach for solving the nuclear motion. We average sections to have rates for rotational quenching from 5 to 150 K. We show that these new rates are vastly different, up to more than an order of magnitude, from the older rates presented in the literature, computed with angular momentum algebra only. We expect large differences in the astrophysical analyses of C3H2, including the chemical history of those ubiquitous carbenes.