`theta = "arccosine"(sin phi_1 * sin phi_2 + cos phi_1 *cos phi_2 *cos (| lambda_1 - lambda_2 |) ) `

The **Great Circle Central Angle** calculator computes the central angle made between two point on a sphere connected via a great circle arc.

**INSTRUCTIONS:** Enter the following:

- (
**φ**_{1}) Latitude of First Point
- (
**φ**_{2}) Latitude of Second Point
- (
**λ**_{1}) Longitude of First Point
- (
**λ**_{2}) Longitude of Second Point

**Central Angle of a Great Circle Arc (θ): **The calculator returns the angle in radians. However, this can be automatically converted to compatible units (e.g. degrees) via the pull-down menu.

#### The Math / Science

This vCalc equation in three dimensional geometry calculates the central angle of a great circle arc defined by a pair of latitude/longitude pairs.

##### Definition of Great Circle^{1}

The great-circle^{2} is the shortest distance between two points on the surface of a sphere. Through any two points on a sphere which are not directly opposite each other, there is a unique great circle.

Between two points which are directly opposite each other, called *antipodal points*, there are infinitely many great circles. All great circle arcs between antipodal points have the same length, i.e. half the circumference of the circle.

The Earth's shape can be approximated as nearly spherical, so great-circle distance formulas give the approximate distance between points on the surface of the Earth.

A *great circle* arc can be drawn between any two points on the earth's surface.

- ^ https://en.wikipedia.org/wiki/Great-circle_distance
- ^ orthodromic distance

### Great Circle Calculators