For example, assuming the Earth is a sphere of radius 6371 km, the surface area of the arctic (north of the Arctic Circle, at latitude 66.56° as of August 2016) is 2·63712|sin 90° − sin 66.56°| = 21.04 million km2, or 0.5·|sin 90° − sin 66.56°| = 4.125% of the total surface area of the Earth.
