Convert the two waypoints' longitude and latitude from decimal representation to radians by dividing them by 180/π, or 57.29578. The mathematical constant π, or pi, can be approximated by 3.14. For example, the longitude and latitude measurements for Paris, France, are 48.866667 latitude and 2.333333 longitude, and the measurements for Paris, Texas, are 33.6608333 latitude and -95.5552778 longitude. Dividing each by 180/π results in 0.852884234 radians latitude and 0.0407243434 radians longitude for Paris, France, and 0.58749237 radians latitude and -1.66775422 radians longitude for Paris, Texas.
Subtract the longitude of the second location by the first. For the example, -95.5552778 (Paris, TX) minus 2.333333 (Paris, France) equals -97.8886108. Calculate the cosine of that value, which equals -0.877947371.
Calculate the cosines and sines of the latitudes of both locations. For the example, the cosine of the latitude of Paris, Texas, is -0.624202582 and its sine is 0.781262528, and the cosine of the latitude of Paris, France, is 0.171134331 and its sine is -0.985247705.
Multiply the two sines together. For the example, 0.781262528 multiplied by -0.985247705 equals -0.769737113. Multiply the three cosines together, including the cosine for the difference in longitude. For the example, -0.624202582 times 0.171134331 times -0.877947371 equals 0.0937845254.
Add the combined sines to the cosines. For the example, -0.769737113 added to 0.0937845254 equals -0.675952588.
Calculate the arccos, or arccosine of that number, which is the inverse cosine. For the example, the arccosine of -0.675952588 is 2.31305288.
Multiply that number by 3963, which is the Earth's radius in miles. For the example, 2.31305288 multiplied by 3963 equals 9,166.62856 miles, which is the distance from Paris, France, to Paris, Texas.