# Which spatial-reference system is used by the Haversine formula?

I've been reading Pro Spatial with SQL Server 2012. It discusses the various spatial-reference systems (SRS) that can be used when defining a coordinate system. According to the book, Google uses WGS 84.

Prior to my exposure the SQL Server's functionality (i.e. `Geography` data type), I've used the Haversine formula to calculate distances between two lat/lng pairs. I'm assuming that it (the Haversine function) makes some assumptions about the Earth's geoid (perhaps the `great-circle distance`), which suggests that it is using a particular SRS. Is this correct? Could one make use of other SRS (at least ones that use lat/lng pairs) with the function just by changing the `great-circle distance`?

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Said another way, does the Haversine formula care is the coordinates are WGS84, NAD83, or another other geodetic datum?

• The haversine formula computes great circle distances on a sphere. The 'r' in the equation (if using Wikipedia's formulation) is the radius of the sphere. Sep 11, 2015 at 18:05
• A more accurate formula is Vincenty's Formula which factors in the fact that the earth is an ellipsoid Sep 11, 2015 at 18:43
• The errors made when using the Haversine formula to compute geodetic distances are analyzed in the closely related thread at gis.stackexchange.com/questions/25494. Their magnitudes are so enormous compared to the differences between WGS84, NAD83, or any whole-earth geodetic datum, that one could justify answering this question in the negative. Sep 11, 2015 at 20:26
• So, the errors from using a spherical datum (Haversine) when compared to the other shapes (WSG84,NAD83) far outweigh the errors that are introduced by using a lat/lng pair from any of these other datum with the Haversine function. Is this correct? Was the Haversine function designed w/ a particular coordinate system in mind? Sep 11, 2015 at 20:36
• Haversine is correct only for spherical coordinates (latitude or colatitude, plus longitude) on a perfect sphere. Haversine is a formula: it's not a datum. It is inappropriate to apply it to geodetic coordinates relative to an ellipsoidal datum, but it is a decent approximation to the extent the ellipsoid can be considered to be perfectly spherical. Sep 12, 2015 at 20:16