## State Plane <-> Latitude and Longitude Conversions

The following example was provided by a GeogTools user.  To check the accuracy of GeogTool’s State Plane conversion, the user compared the conversion of the following State Plane coordinates from western Missouri (state code 2403):

Easting:     853372.6 ft
Northing:  107266.2 ft

These coordinates are known to correspond to:

Latitude:      37.13333353
Longitude: -94.46202253

To check the accuracy  of GeogTool’s State Plane conversion, we use the “StatePlane to LatLon” function:

This function requires that the State Plane coordinates be in units of meters (following the official policy of the National Geodetic Survey).  Converting from feet to meters using the standard SI conversion (1 ft = 0.3048 m) and then using the converted State Plane coordinates with the "StatePlane to LatLon" command gives the following:

The converted latitude and longitude are very close to the known coordinates, differing only in 4th decimal place, in this case corresponding to a distance of a few meters.  In many cases, this is sufficient.  But in some cases greater accuracy is required.

The discrepancy between the converted and known coordinates is not due to an inaccuracy in GeogTools, but rather due to the conversion from feet to meters.  This is because State Plane coordinates are often in U.S. survey feet (3937 yards = 3600 meters) rather than international feet (1 ft = 0.3048 m).

Reconverting the State Plane coordinates into meters using the U.S. survey feet conversion and then converting to latitude and longitude using the “StatePlane to LatLon” command gives

This time we see that the conversion is, for practical purposes, effectively exact.  The difference between the U.S. survey foot and international foot is very small.  In most cases the difference will not matter.  But this small difference can cause problems in some cases, so it's advisable to always know which units are being used.

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