Geographic coordinate conversion

In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion comprises a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different geodetic datums. Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems.

In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. A geographic coordinate transformation is a translation among different geodetic datums. Both geographic coordinate conversion and transformation will be considered in this article.

This article assumes readers are already familiar with the content in the articles geographic coordinate system and geodetic datum.

Informally, specifying a geographic location usually means giving the location's latitude and longitude. The numerical values for latitude and longitude can occur in a number of different formats:

There are 60 minutes in a degree and 60 seconds in a minute. Therefore, to convert from a degrees minutes seconds format to a decimal degrees format, one may use the formula

To convert back from decimal degree format to degrees minutes seconds format,

where the notation ${\displaystyle \lfloor x\rfloor }$ means take the integer part of ${\displaystyle x}$ and is called a floor function.

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