In light of the recent experimental observation of Bose-Einstein condensation in dilute ${}^{87}\mathrm{Rb}$ gas cooled to nanokelvin-scale temperatures, we give a quantitative account of the ground-state properties of magnetically trapped Bose gases. Using simple scaling arguments, we show that at large particle number the kinetic energy is a small perturbation, and find a spatial structure of the cloud of atoms and its momentum distribution dependent in an essential way on particle interactions. We also estimate the superfluid coherence length and the critical angular velocity at which vortex lines become energetically favorable.