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I am trying to convert latitude and longitude into meters in polar regions. I am looking for higher accuracy upto 0.00 meters preferably. I tried the haversine formula but it doesnt seem to be accurate enough for small increments in latitude. does anyone know a better formula that can be used near poles?

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The Haversine formula will be extremely accurate, regardless of the latitude increments--for a spherical model. If you're having trouble with accuracy, that means you need to use an ellipsoidal datum. If you possibly can, choose a suitable projection so that ArcGIS does all the heavy calculations behind the scenes. Otherwise, consider changing the spherical parameters to match a typical radius of curvature near the area of interest and apply the Haversine formula. –  whuber Nov 27 '12 at 20:26

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