In polygon mode, Planimeter calculates the perimeter and area of a polygon whose edges are either geodesics or rhumb lines on the WGS84 ellipsoid. Counter-clockwise traversal of a polygon results in a positive area. Only simple polygons are supported for the area computation. There is no need to close the polygon. Polygons may include one or both poles. In polyline mode, Planimeter calculates the length of the geodesic path joining the points.

Give the vertices in terms of latitude and longitude, 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 16:46:33NThe coordinates can also be given in UTM, UPS, or MGRS coordinates (see the documentation on the GeoConvert utility). A blank line or a coordinate which cannot be understood causes the reading of vertices to be stopped.

The result for the perimeter is accurate to about 15 nm per
vertex. The result for the area is accurate to about
0.1 m^{2} per vertex.

Planimeter,
which is a simple wrapper of the
GeographicLib::PolygonArea class,
is one of the utilities provided
with
GeographicLib.
Geodesic areas can also be computed using JavaScript; see the
JavaScript geodesic
calculator.
If you wish to use Planimeter 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.

Charles Karney <charles@karney.com> (2014-11-06)