Given the number of stars or habitable stars inside the imperial borders, the empire radius is: HStarDfactor = habitable star density factor, use 0.002 or see below.StarDfactor = star density factor, use 0.017 or see below.N hStars = number of stars with habitable planets.Given the empire radius in light-years, the number of stars and habitable stars inside the borders is: If the radius is over 500 light-years the equations will calculate give an incorrect result (too many stars). Warning, the galactic plane in the neighborhood of Sol is only about 1,000 light-years thick. It would be nice to be able to figure out how many stars are inside the empire, especially if you want to ensure that the Imperial Bureaucracy can actually handle it. The control radius between the Imperial (or Sector) Capital and the Rim give you the size of your empire. It is useful to be able to calculate a bit of geography for your interstellar empires. As previously mentioned, their empire will approximate an expanding sphere, with their homeworld at the center. Once our imperialists discover interstellar travel, they will spread to the surrounding stars in a manner similar to a watermelon hitting the sidewalk. Imagine a planet inhabited by imperialistic little opportunistic aliens, just like us, whose star is in a galaxy totally uninhabited by any other intelligent creatures (or at least uninhabited by creatures who can defend themselves). But this model more or less precludes the existence of an empire anyway, so it can be ignored by science fiction writers trying to build an empire. The much more messy and difficult to figure model of expansion is via Civilization Clusters. Starting at the origin planet the spherical colonization wave will grow at the rate of empire expansion. The simplest model of a growing galactic empire is a swelling balloon.