Mdekok3000

The approximate distance between the two locations on the planet can be determined with their geographic coordinates and this formula

$d={\sqrt {\left({\frac {r\pi ({\mbox{Lat}}_{2}-{\mbox{Lat}}_{1})}{180}}\right)^{2}+\left({\frac {r\pi ({\mbox{Long}}_{2}-{\mbox{Long}}_{1})}{180}}\right)^{2}}}.$

The radius r in this instance is the radius of the earth. The units that the final distance d is measured in is the same as that you used for the radius.

The formula above is not 100% accurate. That would be impossible, because the earth is not a perfect sphere and the exact radius of the earth is not known. The radius of the earth has been estimated to be about 6,378.135 km ($\approx$3,963.189 mi; $\approx$3,443.917 nm).

Derivation of the Formula

First, all you should have are the sets of coordinates. The latitudinal angle between each location is ${\mbox{Lat}}_{2}-{\mbox{Lat}}_{1}$ and the longitudinal angle is ${\mbox{Long}}_{2}-{\mbox{Long}}_{1}$.

If you were to slice a thin layer of the earth out at the equator, you would have a circle. To find the arc length on a circle given an angle and the radius, the following formula can be used to find the latitudinal and longitudinal distances

${\begin{matrix}s=r\theta .\end{matrix}}$

These distances also form the legs of a right triangle on a flattened surface. To use this formula, your angles must be in radians. To convert the angles from degrees to radians the concept

$\angle ({\mbox{radians}})={\frac {\pi \angle ^{\circ }}{180}}$

will work.

Since the following equations summarizing the above equations are the formulas for the lengths of legs of a right triangle

${\begin{matrix}s&=&r\theta \\s_{1}&=&{\frac {r\pi ({\mbox{Lat}}_{2}-{\mbox{Lat}}_{1})}{180}}\\s_{2}&=&{\frac {r\pi ({\mbox{Long}}_{2}-{\mbox{Long}}_{1})}{180}},\end{matrix}}$

the distance formula will give the length of the hypotenuse, or the geographic distance between each location.

Earth Distance Formula

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