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We present the analytical framework for converting projected lightdistributions with a S\'ersic profile into three-dimensional lightdistributions for stellar systems of arbitrary triaxial shape. The mainpractical result is the definition of a simple yet robust measure of intrinsicgalaxy size: the median radius $r_\mathrm{med}$, defined as the radius of asphere that contains 50% of the total luminosity or mass, that is, the mediandistance of a star to the galaxy center. We examine how $r_\mathrm{med}$depends on projected size measurements as a function of S\'ersic index andintrinsic axis ratios, and demonstrate its relative independence of theseparameters. As an application we show that the projected semi-major axis lengthof the ellipse enclosing 50% of the light is an unbiased proxy for$r_\mathrm{med}$, with small galaxy-to-galaxy scatter of $\sim$10% (1$\sigma$),under the condition that the variation in triaxiality within the population issmall. For galaxy populations with unknown or a large range in triaxiality anunbiased proxy for $r_\mathrm{med}$ is $1.3\times R_{e}$, where $R_{e}$ is thecircularized half-light radius, with galaxy-to-galaxy scatter of 20-30%(1$\sigma$). We also describe how inclinations can be estimated for individualgalaxies based on the measured projected shape and prior knowledge of theintrinsic shape distribution of the corresponding galaxy population. We makethe numerical implementation of our calculations available.

Deprojecting Sersic Profiles for Arbitrary Triaxial Shapes: Robust Measures of Intrinsic and Projected Galaxy Sizes