The length of the shorter arc is the great-circle distance between the points.

The great-circle distance between airports may therefore give an approximation of flight length.

Flight lengths can therefore often be approximated to the great-circle distance between two airports.

Great-circle distance the shortest distance between any two points on the surface of a sphere.

Equipped with the great-circle distance, a great circle becomes the Riemannian circle.

The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes.

It is near the Malian border and with a great-circle distance of about 15 km from the Malian town of Manankoro.

In two dimensions, the chordal metric on the sphere is not intrinsic, and the induced intrinsic metric is given by the great-circle distance.

The length of the minor arc of a great circle is taken as the distance between two points on a surface of a sphere, namely the great-circle distance.

In metric space theory and Riemannian geometry, the Riemannian circle (named after Bernhard Riemann) is a great circle equipped with its great-circle distance.

Because d is then large (approaching πR, half the circumference) a small error is often not a major concern in this unusual case (although there are other great-circle distance formulas that avoid this problem).

Because the Earth is nearly spherical (see Earth radius) equations for great-circle distance can be used to roughly calculate the shortest distance between points on the surface of the Earth (as the crow flies), and so have applications in navigation.