Resonant interaction of light with nanoparticles is essential for a broad range of nanophotonics and plasmonics applications, including optical antennas, photovoltaics, thermoplasmonics, and sensing. Given this broad interest, analytical formulas are highly desirable to provide design guidelines for reaching the conditions of ideal absorption. Here we derive analytical expressions to accurately describe the electric and magnetic modes leading to ideal absorption. Our model significantly improves on accuracy as compared to classical models using Green's functions or a Mie coefficient expansion. We demonstrate its applicability over a broad parameter space of frequencies and particle diameters up to several wavelengths. We reveal that ideal absorption is attainable in homogeneous spherical nanoparticles made of gold or silver at specific sizes and illumination frequencies. To reach ideal absorption at virtually any frequency in the visible and near infrared range, we provide explicit guidelines to design core-shell nanoparticles. This work should prove useful for providing experimental designs that optimize absorption and for a better understanding of the physics of ideal absorption.