Direct and inverse problem for geodesic on a reference ellipsoid is commonly used for many geodetic applications. Direct problem formulas are used in order to find the geodetic coordinates of the second point of the geodesic line and backward azimuth if geodetic coordinates of the first point, the length of geodesic and forward azimuth are given. It has been common to use iteration in order to calculate such coordinates, however, in this paper; we introduce applicable formulas that do not need iteration in order to be calculated with moderate accuracy. The research formulas results have been compared with the corresponding results of Vincenty’s iterative formulas. The comparison showing agreements to within 0.0000004 km of geodesic length (or 4.0 mm) and 0,0001" of azimuth in the range of 4560 km.
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