Journal of Geodesy

, Volume 85, Issue 8, pp 475–485

Transverse Mercator with an accuracy of a few nanometers

Original Article

DOI: 10.1007/s00190-011-0445-3

Cite this article as:
Karney, C.F.F. J Geod (2011) 85: 475. doi:10.1007/s00190-011-0445-3


Implementations of two algorithms for the transverse Mercator projection are described; these achieve accuracies close to machine precision. One is based on the exact equations of Thompson and Lee and the other uses an extension of Krüger’s series for the mapping to higher order. The exact method provides an accuracy of 9 nm over the entire ellipsoid, while the errors in the series method are less than 5 nm within 3900 km of the central meridian. In each case, the meridian convergence and scale are also computed with similar accuracy. The speed of the series method is competitive with other less accurate algorithms and the exact method is about five times slower.


Geometrical geodesy Map projections Conformal mapping 

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.SRI InternationalPrincetonUSA

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