Updated:  21 May 2015

Geodetic Calculations - Vincenty's Formulae, Direct Method

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).

  • The calculations are performed using GRS80 ellipsoid values which is used for Australia's new coordinate system (The Geocentric Datum of Australia - GDA).
  • These values are also compatible with the WGS84 system used by GPS. (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). They can be used to calculate lines ranging from a few cm up to half way around the earth (approximately 20,000km) with millimetre accuracy.
  • Latitude must be between 0° and ± 90°. South Latitude is negative (eg -35° 55' 56.12"').
  • Longitude must be between 0° and ± 180°. West Longitude is negative (eg -148° 56' 25.12"').
  • NOTE: Given latitude and longitude of two points, to calculate the ellipsoidal distance, forward and reverse azimuths between the points use the inverse method.
POINT 1 Latitude: Deg. Min. Sec.
Longitude: Deg. Min. Sec.

POINT 2 Forward azimuth: Deg. Min. Sec.
Ellipsoidal distance:

  Forward azimuth:   
If these values are correct, press "Submit Data" to receive the results.

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For more information contact: geodesy@ga.gov.au
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