Earth Distance Formula
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 (≈3,963.189 mi; ≈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 Lat2 − Lat1 and the longitudinal angle is Long2 − Long1.
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.