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keisanHigh-precision calculations for everyday life and work

Distance and Azimuth Between Two Points

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Specify the latitudes and longitudes of two points on Earth to calculate the shortest distance and its azimuth, and indicate the direction from point A to B.
Please specify western longitude and southern latitude as negative values.
The default latitude and longitude values for the B location represent Mecca.
Longitude of A
Latitude
Longitude of B
Latitude
[Earth Radius rkm]
A to B azimuth
Calculations are based on the Earth as a sphere with an equatorial radius of r = 6378.137 km.
Azimuths are measured as North: 0 degrees, East: 90 degrees, South: 180 degrees, and West: 270 degrees.

Location A (longitude x1, latitude y1) and location B (longitude x2, latitude y2)
\(\normalsize\\\hspace{10px} d=r \cos^{\tiny -1}(\sin y_{\tiny 1} \sin y_{\tiny 2}+ \cos y_{\tiny 1} \cos y_{\tiny 2} \cos\Delta x)\\ \phi=90-atan2(\sin\Delta x,\ \cos y_{\tiny 1} \tan y_{\tiny 2}- \sin y_{\tiny 1}\cos\Delta x)\\ \hspace{30px}\Delta x=x_{\tiny 2}-x_{\tiny 1}\\ \hspace{30px} atan2(x,y)=atan(\large\frac{y}{x}) \)

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