Watch a flight tracker for New York to Tokyo and the plane seems to wander north over Alaska — the pilots are not lost; they are taking the shortcut. In plain words, the shortest path between two points on a sphere is a great-circle arc, and its length equals Earth's radius times the angle between the points in radians: distance = R × θ. New York to London spans about 0.087 radians of Earth's 3,959-mile radius, giving roughly 3,450 miles — noticeably less than any flat-map guess. Pilots filing flight plans, sailors plotting crossings, and GPS routing engines all compute great-circle distances, because flat maps stretch the poles and only the sphere's own geometry tells the truth.

This calculator evaluates the arc-length formula. Type the central angle in degrees into the Variable A box, say 50, and the sphere's radius into the Variable B box, say 3959 for Earth's miles. Read the geodesic distance from the Result box. Try 90 degrees to confirm a quarter of Earth's circumference — about 6,218 miles — and double-check your angle is in degrees, not radians, before trusting the answer.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Geodesic Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.