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Although Earth is slightly flattened at the poles, it behaves largely as a sphere. On a spherical surface, the distance between two points can be expressed both as an angle and as a linear length. For a sphere of radius r, the arc length L generated by an angular change of A degrees is given by L = 2πrA / 360.
With Earth’s radius well established at 6,371 km (NASA), this formula lets you convert directly between degrees and meters.
Plugging NASA’s Earth radius into the arc‑length equation and converting to meters gives a single degree of longitude or latitude as roughly 111,139 m. Over a full 360° rotation the circumference comes to about 40,010,040 m, slightly below the equatorial circumference of 40,030,200 m due to Earth’s equatorial bulge.
Every point on Earth is identified by a pair of angles: latitude (north‑south position relative to the equator) and longitude (east‑west position relative to the Greenwich meridian). Knowing both angles for two locations allows you to estimate the surface distance between them, though the calculation is an approximation because Earth is curved.
First determine the angular separation in latitude and longitude:
Multiply each angular difference by 111,139 m to obtain the corresponding linear distance in each direction. Treating the latitude and longitude separations as the legs of a right‑angled triangle, apply the Pythagorean theorem to estimate the straight‑line surface distance:
d = √(x² + y²)
where x is the latitude separation in meters and y is the longitude separation in meters.
