Magnetism in nanographenes [also known as polycyclic aromatic hydrocarbons (PAHs)] is studied with first principles density functional calculations. We find that an antiferromagnetic (AFM) phase appears as the PAH reaches a certain size. This AFM phase in PAHs has the same origin as the one in infinitely long zigzag-edged graphene nanoribbons, namely, from the localized electronic state at the zigzag edge. The smallest PAH still having an AFM ground state is identified. With increased length of the zigzag edge, PAHs approach an infinitely long ribbon in terms of (1) the energetic ordering and difference among the AFM, ferromagnetic, and nonmagnetic phases and (2) the average local magnetic moment at the zigzag edges. These PAHs serve as ideal targets for chemical synthesis of nanographenes that possess magnetic properties. Moreover, our calculations support the interpretation that experimentally observed magnetism in activated carbon fibers originates from the zigzag edges of the nanographenes.