Can I use degrees as a unit like inches or meters for the purpose of computing the total area of the sky? I want to figure out what percentage of the sky the full Moon takes up. Can someone verify my logic?: There's 360 degrees in a circle, so the circumference of the sky (both the half we see and the half that's set) is 360 degrees. Therefore, the radius of the sky is 360 / 2pi = 57.2957795130824 degrees. (This is the part that seems strange to me, using degrees as a unit for radius, which is a straight line). So the entire sky is 4 pi r^2 = 4 * pi * 57.2957795130824^2 = 41252.9612494193 square degrees. The Moon subtends 1/2 degree in the sky. So the radius of the Moon is 1/4 degree. So the Moon occupies pi r^2 = pi * 0.25^2 = 0.196349540849362 square degrees. Therefore the Moon takes up 0.196349540849362 / 41252.9612494193 = 4.75964718416732E-06, or (multiply by 100 for percentage) ~0.0005 %. Since the sky we see is only 1/2 the total sky, the Moon occupies ~0.001% of the visible sky. Seems a little small.