How can I calculate the angular distance between 2 points on the circumference of a circle with only the distance along the circumference between the 2 points and the radius of the circle? I spent some time looking for the answer on how to do this but haven't found anything yet.
2026-03-26 23:09:39.1774566579
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Angular distance from radius of sphere and distance along circumference
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If you measure the central angle of an arc of a circle in radians, and if the angle measures $\phi$ and the arc $s,$ then they are related by the equation $$s=r\phi,$$ where $r$ is the radius of the circle.
This just says that the arc is directly proportional to the angle. If you're measuring your angles in $\theta$ degrees, note that we have $\phi=\frac{π\theta}{180°}.$
Basic idea: You know how far you have to go if you have to go around the whole circle (that's the circumference). That corresponds to $360^\circ$. Now consider how much of the circumference you're using. That corresponds to whatever the angle is.