NASA’s Socioeconomic Data and Applications Center (SEDAC) at Columbia University has a neat web application that allows users to estimate population (based on data from 2015) and land area for any shape drawn on the map.
According to the application, there were about 1.824 million people living inside the beltway in Washington, D.C., in 2015. The land area inside the beltway is about 668 square kilometers (or about 258 square miles).
Meanwhile, the Capitol Hill neighborhood (as defined by Google Maps) has an estimated population of just under 14,000 in a land area of 3 square kilometers (1.2 square miles).
(Thanks to Kottke.org for pointing out this resource.)