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# angular Distance

Returns the "distance" in radians (about the spheres centre) between two positions.
Controller: will

C++

## AngularDistance

 doubleangularDistance( const Position& start const Position& end )
Calculates the angular distance between two points on the surface of a sphere relative to the centre of the sphere.

This calculation is made using:
$dist&space;=&space;\cos^{-1}&space;\left&space;[&space;\sin(a_{lat})&space;\sin(b_{lat})&space;+&space;\cos(a_{lat})&space;\cos(b_{lat})&space;\cos(b_{long}&space;-&space;a_{long})&space;\right&space;]$
where a and b are the start and end location.

### Example 1

#include <stdio.h>
#include <codecogs/maths/geometry/spherical/angularDistance.h>

int main()
{
Position start(10,-90);
Position end(45,20);
printf("Angular Distance in Radians = %lf", angularDistance(start, end));
return 0;
}
Output:
Angular Distance in Radians = 1.686437

### Parameters

 start the first Position [Latitude, Longitude]. end the second Position [latitude, Longitude].

### Returns

the distance in radian about the center of the sphere.
##### Source Code

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## Distance

 doubledistance( const Position& start const Position& end double radToDist = 3437.7475 )
Applies a simple conversion to the distance calculated by angularDistance to give a more conventional measure of distance according to the specified conversion ratio. This is simple the circumference of the sphere divided by $\inline&space;2&space;\pi$. For example, with the planet earth on degree is divided into 60, which is called 1 minute of arc. This is also one nautical mile. Therefore to convert radian to nautical miles (knots) you multiply by:
$\frac{360.0&space;\cdot&space;60}{2&space;\pi}$
 Description radToDist Nautical Mile on Earth 3437.7475 knots/radian Miles on Earth 3956.0881 miles/radian kilometers on Earth 6366.7070 km/radian

### Example 2

#include <stdio.h>
#include <codecogs/maths/geometry/spherical/angulardistance.h>

int main()
{
Position start(10,-90);
Position end(45,20);
printf("\nKnots = %lf", distance(start, end));
printf("\nMiles = %lf", distance(start, end, 3956.0881));
return 0;
}
Output:
Knots = 5797.543498
Miles = 6671.692101

### Parameters

 start the first Position [Latitude, Longitude]. end the second Position [latitude, Longitude]. radToDist Default Value = 3437.7475

### Returns

the distance to new position.
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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Last Modified: 18 Dec 11 @ 22:53     Page Rendered: 2022-03-14 17:45:39