# Calculating lat/long with range bearing

by michael atlas
Tags: haversine formula
 P: 5,462 ΔAt 300 yards the flat earth approximation will suffice. You need to calculate the latitutes (difference in northings or meridional or N-S distance) and Departures (difference in eastings or parallel or latitudinal distance). Since your are working in range (R) (metres) and degrees you can calculate this in two stages. First calculate the latitudes (ΔN) and departures (ΔE) in metres. Then convert these to the difference in degrees to angular measure to add to your existing lat and long. Using whole circle bearings (wcb) ΔN = Rsin(450-wcb) ΔE = Rcos(450-wcb) Now all circles of longitude have the same circumference so the change of longitude (θn)) is $${\theta _n} = \frac{{360\Delta N}}{{2\pi r}}$$ Where r is the radius of the earth (= 6371000 metres) However the radius of each parallel of latitude varies with latitude , so if your approx latitude is L $${\theta _E} = \frac{{360\Delta E}}{{2\pi r\cos L}}$$