Weighing the Universe with the Cosmic Microwave Background

Variations in $\ensuremath{\Omega}$, the total density of the Universe, leave an imprint on the power spectrum of temperature fluctuations in the cosmic microwave background (CMB). We evaluate the precision with which $\ensuremath{\Omega}$ can be determined by a CMB map as a function of sky coverage, pixel noise, and beam size. Assuming only that the primordial density perturbations were adiabatic and with no prior information on the values of any other cosmological parameters, a full-sky CMB map at 0.5\ifmmode^\circ\else\textdegree\fi{} angular resolution and a noise level of $15\ensuremath{\mu}\mathrm{K}$ per pixel can determine $\ensuremath{\Omega}$ with a standard error of 5%. If all other cosmological parameters are fixed, $\ensuremath{\Omega}$ can be measured to better than 1%.