Geographic Coordinates Calculation

A geographic coordinate calculation is the name given to any operation using GPS coordinates (latitude and longitude) to determine another geographic location of an object, place or point.

Calculations are essential for various applications, including navigation and cartography.

dCode calculate the median (middle) point on a sphere with the same radius as Earth (it is not the same than on a plan).

Knowing the starting point $ (\phi_1, \lambda_1) $ (latitude, longitude) the direction $ \theta $ (azimuth from the north) and the distance $ d $ on a sphere of radius $ R $, dCode can calculate the path (calculations in radians) and find the arrival coordinates $ (\phi_2, \lambda_2) $ by the formula:

$$ \phi_2 = \arcsin \left( \sin(\phi_1) \cos(\frac{d}{R}) + \cos(\phi_1) \sin(\frac{d}{R}) \cos(\theta) \right) \\ \lambda2 = \lambda1 + \operatorname{atan2} \left( \sin(\theta) \sin(\frac{d}{R}) \cos(\phi_1), \cos(\frac{d}{R}) − \sin(\phi_1) \sin(\phi_2) \right) $$

NB: this formula uses the atan2 function defined as $$ \operatorname{atan2}(y,x) = 2 \arctan{ \frac{ y }{ \sqrt{x^2+y^2} + x } } = 2 \arctan{ \frac{ \sqrt{x^2+y^2} - x }{ y } } $$

All angles are in radians. The distances $ d $ and $ R $ must have the same unit, the result will be in that same unit (usually meters or kilometers).

Use geocoding / geolocalisation function also available on dCode. It is not a calculation but of an association between an address and coordinates (latitude, longitude) on a map.