There are services to project from one coordinate system to another, GIS software packages that perform projections, but it is all black box, as far as I've been able to find.

I want to see the calculations/equations necessary to calculate the reprojection from NAD 83 Michigan GeoRef (EPSG:3078) to WGS84 (EPSG:4326). Does anyone know where I can find the equations?

I am aware, that one is a Projected Coordinate System and the other is a Geographic Coordinate System, so my use of "project" may not be the correct word choice.

  • 1
    Thank you both very much. For my needs, the EPSG Geomatics Guidance Note 7 Part 2 is what I was looking for, as it provides the equations. I want to pull the Michigan GeoRef coordinates from our ESRI SDE (SQL table, a view table, specifically) and reproject them to WGS84 in an Access report without having to invoke an ESRI product. I will have to put the execution of my plan on hold until I have more time. Again, thank you both. Sep 17, 2019 at 11:55

2 Answers 2


According to spatial reference.org, EPSG:3078 is a Hotine Oblique Mercator projection.

The equations for converting between (E,N) and (lat,lon) using a Hotine Oblique Mercator projection may be found in the EPSG Geomatics Guidance Note 7 part 2.


You can check the coordinate transformation pipeline with the gdaltransform utility https://gdal.org/programs/gdaltransform.html#gdaltransform starting from GDAL version 3.0 that is using new Proj library version 6 or higher.


gdaltransform -s_srs epsg:3078 -t_srs epsg:4326 --debug on 

10 30
OGRCT: Selecting transformation +proj=pipeline +step +inv +proj=omerc
+no_uoff +lat_0=45.3091666666667 +lonc=-86 +alpha=337.25556 +gamma=337.25556 +k=0.9996 +x_0=2546731.496 +y_0=-4354009.816 +ellps=GRS80 +step +proj=unitconvert +xy_in=rad +xy_out=deg +step +proj=axisswap +order=2,1 (Inverse of Michigan Oblique Mercator (meters) + NAD83 to WGS 84 (1))
-91.8821927734989 40.4018436536371 0

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