This work studies the limits of far and near-field electromagnetic response of sub-wavelength scatterers, like the unitary limit of lossless scatterers and the ideal absorption limit of lossy particles. These limit behaviors are described in terms of analytic formulas that approximate finite size effects while rigorously including radiative corrections. This analysis predicts the electric and/or magnetic limit responses of both metallic and dielectric nanoparticles while quantitatively describing near-field enhancements. doi:10.1103/PhysRevB.00.005400