Geodetic calculation methods
Last updated:7 June 2023
Online calculations and downloadable spreadsheets to perform geodetic calculations
Detailed information about the spreadsheets and formulae used in all calculations listed below can be found in the Geocentric Datum of Australia Technical Manual.
Calculate Great Circle distances using latitude and longitude.
- Online version: Great Circle Calculator - 'As the Cocky Flies'
- Great Circle and Approximate Ellipsoidal [XLS 18.0 KB] which calculates distances using two different simplified methods.
Calculate bearing and distance from latitude and longitude
Use Vincenty's formulae to calculate distance and bearing from latitude and longitude and vice versa.
- Online version
- Vincenty Direct
- Vincenty Inverse
- Vincenty's formulae to calculate distance and bearing from latitude and longitude [XLS 71.0 KB]
Note: Please have the Excel program 'Tools|Options|Calculation|Iteration' box selected so you do not get a circular reference in this file.
Convert from geographic to grid coordinates
Use Redfearn's formulae to convert between geographic coordinates (GDA94, latitude and longitude) to grid coordinates (Map Grid of Australia (MGA94), eastings and northings) and vice versa.
- Online version
Transformation of coordinates
The following are available for download but are not yet available as online calculations.
- High Accuracy Transformation Grids - Recommended method (only available for use within Australia)
- Medium Accuracy 3 Dimensional Similarity Transformation [XLS 31.0 KB] which computes a similarity transformation and converts between geodetic coordinates and Earth centered Cartesian coordinates - (latitude, longitude, ellipsoidal height <-> X Y Z)
- Low Accuracy Molodensky's method [XLS 33.0 KB] which transforms between AGD66 and AGD84 and GDA94
- Low Accuracy Block Shift [XLS 360.5 KB] for average size of the block shifts between AGD66 and AGD84 and GDA94, computed for 1:250 000 topographic map areas across Australia.