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I am doing some work with the Military Grid Reference System (MGRS), which is based on Universal Transverse Mercator (UTM).

I find that I need to convert from UTM northing and longitude (actually, delta angle between desired longitude and appropriate UTM central meridian) to latitude. I've searched for days and cannot find this conversion.

I need an algorithm. Can anyone point me to a reference to such an algorithm, or to open source software that does this conversion?

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    I have used this website before and the excel spreadsheet you can download from it: uwgb.edu/dutchs/usefuldata/utmformulas.htm
    – dklassen
    Commented Feb 11, 2014 at 22:41
  • Did you find an answer? Your'e trying to find the coordinates of where a line of constant UTM northing crosses a given line of longitude, right?
    – Marc Pfister
    Commented Aug 24, 2016 at 3:20

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GeographicLib (written by me) includes a utility GeoConvert to convert between UTM/MGRS/Lat+Long. If you want to try it out before downloading it, use the online version of GeoConvert.

The algorithm used by GeographicLib is an extension of Krüger's 1912 series. The derivation is given in this 2011 paper in the Journal of Geodesy. You can download a preprint of this paper here and here are some addenda.

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    GeographicLib is available on (at least) recent Ubuntu-like distributions from repositories, which makes it easy to install. The user tools are in "geographiclib-tools".
    – BradHards
    Commented Feb 12, 2014 at 3:18
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Welcome to GIS.SE.

The go-to tool for MGRS is usually GeoTrans. If you want a nice map viewer that supports display in both MGRS and Lat/Long (and UTM), try FalconView (which uses GeoTrans underneath).

If you are on Windows, there are pre-built installers. Make sure you get the version that matches your host operating system (32 or 64 bit) and that you have the Java Runtime Environment for that machine as well.

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Kind of surprised that everyone recommended a software tool over what you wanted

I need an algorithm. Can anyone point me to a reference to such an algorithm, or to open source software that does this conversion?

Fairly well written is a lat/long to UTM conversion function written in Python - https://github.com/Turbo87/utm/blob/master/utm/conversion.py#L171

Let me know if there is a line you need translated from python to basic math, but it should be fairly readable already.

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