# Why Haversine formula and Web Mercator give different length between two latlng points?

I am calculating the distance between two points given by latlng. However, Google Maps (i.e., web mercator projection) gives me a longer distance than Haversine formula.

Which is the most accurate measure? I can read in some answer that Haversine formula gives it.

So... Is Google Map lying when telling me distance in meters. e.g., in this webpage? http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection/

Edit:

Example: In a small area around (37,0), if I calculate area (width,height), haversine results in (7750m*7753m) while Google results in (9784m*9784m).

• How large are the differences you experience? Since the Haversine uses a spherical earth model, it will err slightly, depending on the configuration of the endpoints: see gis.stackexchange.com/questions/25494 for an analysis. Please give us a link to any answer that claims the Haversine formula is the "most accurate measure" so that we can help correct it. May 19, 2015 at 12:04
• I edited the question to give an example. Sorry, I can not provide real coordinates. Hope it helps. May 20, 2015 at 9:14
• Clearly those "Google results" are using the Mercator-projected coordinates, which will inflate distances at 37 degrees latitude by 25%. But Google Maps provides various ways of computing distances and some of them--such as its measurement tool--appear to be accurate. Exactly how are you using Google Maps to obtain these distances? May 20, 2015 at 13:22
• Only slightly related, but why are you using Haversine and not Vincenty? May 20, 2015 at 14:16
• @Mikkel Presumably because Google uses a spherical earth model for its "Web Mercator" projection. Even so, your question is pertinent because this thread is wondering about "most accurate measure" of distances, and surely a calculation using an ellipsoidal model will be more accurate than using a spherical model: see gis.stackexchange.com/questions/25494. May 20, 2015 at 14:36