Updated:  21 May 2015

Geodetic Calculations - Vincenty's Formulae, Inverse Method

Given latitude and longitude of two points, calculate the ellipsoidal distance and forward and reverse azimuths between the points.

  • The calculations are performed using the GRS80 ellipsoid which is used for Australia's new coordinate system (The Geocentric Datum of Australia - GDA) and is also compatible with global coordinate system (a = 6,378,137.0 metres; 1/f = 298.25722210)
  • Vincenty's formulae are used (T. Vincenty, Survey Review, 23, No 176, p 88-93,1975) to calculate lines ranging from a few cm to nearly 20,000 km, with millimetre accuracy.
  • Latitude must be between 0° and ± 90°. South Latitude is negative (eg -35° 55' 56.12"').
  • Longitude mast be between 0° and ± 180°. West Longitude is negative (eg -148° 56' 25.12"').
  • NOTE: "The inverse formulae may give no solution over a line between two nearly antipodal points. This will occur when the difference between two latitudes is greater than 180 Deg. in absolute value" (Vincenty, 1975).
  • NOTE: Given the latitude and longitude of a point (1) and the forward geodetic azimuth (1-2) and ellipsoidal distance to a second point (2), calculate the latitude and longitude of the second point and the reverse azimuth (2-1) using the direct method.
POINT 1 Latitude: Deg. Min. Sec.
Longitude: Deg. Min. Sec.

POINT 2 Latitude: Deg. Min. Sec.
Longitude: Deg. Min. Sec.

YOUR ENTERED VALUES Latitude (Pt 1):   
  Longitude (Pt 1):   
  Latitude (Pt 2):   
  Longitude (Pt 2):   
If these values are correct, press "Submit Data" to receive the results.

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