### Online geodesic calculations using the GeodSolve utility

Geodesic calculation:
 Inverse: lat1 lon1 lat2 lon2 → azi1 azi2 s12 Direct: lat1 lon1 azi1 s12 → lat2 lon2 azi2

Input (ex. «40.6 -73.8 49°01'N 2°33'E» [inverse], «40d38'23"N 073d46'44"W 53d30' 5850e3» [direct]):

 Output format: decimal degrees degrees minutes seconds Heading at point 2: forward azimuth back azimuth Longitude: reduce to [−180°,180°] unroll Output precision: 1m 0.00001d 0.1" 100mm 0.01" 10mm 0.001" 1mm 0.0001" 100μm 0.00001" 10μm 0.000001" 1μm 0.0000001" 100nm 0.00000001" 10nm 0.000000001" 1nm 0.0000000001" Equatorial radius: meters Flattening:

Select action:

Geodesic (input in black, output in blue):

```    ellipsoid (a f)     = 6378137 1/298.257223563 (WGS84)
status              =

lat1 lon1 fazi1 (°) =
lat2 lon2 fazi2 (°) =
s12 (m)             =

a12 (°)             =
m12 (m)             =
M12 M21             =
S12 (m^2)           = ```

GeodSolve (version 1.48) performs geodesic calculations for an arbitrary ellipsoid of revolution. The shortest path between two points on the ellipsoid at (lat1, lon1) and (lat2, lon2) is called the geodesic; its length is s12 and the geodesic from point 1 to point 2 has azimuths azi1 and azi2 at the two end points. There are two standard geodesic problems:

• Direct:   given [lat1 lon1 azi1 s12], find [lat2 lon2 azi2];
• Inverse: given [lat1 lon1 lat2 lon2], find [azi1 azi2 s12].
Latitudes and longitudes can be given in various formats, for example (these all refer to the position of Timbuktu):
```        16.776 -3.009
16d47' -3d1'
W3°0'34" N16°46'33"
3:0:34W 16:46:33N```
Azimuths are given in degrees clockwise from north. The distance s12 is in meters.

The additional quantities computed are:

• a12, the arc length on the auxiliary sphere (°),
• m12, the reduced length (m),
• M12 and M21, the geodesic scales,
• S12, the area between the geodesic and the equator (m2).

The ellipsoid is specified by its equatorial radius, a, and its flattening, f = (a − b)/a, where b is the polar semi-axis. The default values for these parameters correspond to the WGS84 ellipsoid. The method is accurate for −99 ≤ f ≤ 0.99 (corresponding to 0.01 ≤ b/a ≤ 100). Note that f is negative for a prolate ellipsoid (b > a) and that it can be entered as a fraction, e.g., 1/297.

GeodSolve is accurate to about 15 nanometers (for the WGS84 ellipsoid) and gives solutions for the inverse problem for any pair of points.

GeodSolve, which is a simple wrapper of the GeographicLib::Geodesic class, is one of the utilities provided with GeographicLib. Geodesics can also be computed using JavaScript; see the JavaScript geodesic calculator and geodesics on Google maps. If you wish to use GeodSolve directly, download and compile GeographicLib. The algorithms are described in C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87, 43–55 (2013); DOI: 10.1007/s00190-012-0578-z; addenda: geod-addenda.html. See also the Wikipedia page, Geodesics on an ellipsoid.

Charles Karney <charles@karney.com> (2015-05-14)
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