Q:

Convert UTM northing and longitude to latitude

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?

A:

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.

