Take the tour ×  I know that the Earth isn't a sphere, not even
an ellipsoid, but for my measurements, its an acceptable
approximation. Assuming I have a coordinate(lat,lon) and a
distance( e.g.: 1000km ), what is the surface area on the earth
with that distance radius?  share|improve this question add
comment  2 Answers  up vote 1 down vote accepted  Just a small
amplification of the answer by Ross Millikan. Use the same
notation as the article he linked to. I take it that your $1000$
km is the surface of the Earth distance from the center $C$ of
your circle to the furthest points $P$ from the center. In the
picture linked to, $C$ is the top of the sphere, and $P$ is any
point on outer edge of the bottom of the cap.  Assume that this
surface of the Earth distance is $d$, and that is is $\le$ $1/4$
of the circumference of the Earth (that's not necessary, but it
makes visualization easier). Let the radius of the Earth be $r$.
Then the angle $\theta$ subtended by the arc $CP$ at the centre
of the Earth is give