How to Calculate Distance Between Two Points on a Map
- 1). Read the longitude and latitude coordinates for the start point and the destination point. Although not necessary, it is a good idea to write the coordinates down for easy reference. The coordinates will most likely be in degree/minute/second (DMS) format. Some maps may have them in decimal format.
- 2). Convert the seconds in the DMS coordinates to minutes. Divide the seconds by 60 and add the value to the minutes. Then convert the minutes to degrees by dividing by 60. Finally, convert "W" and "S" values to a negative number since west longitude and south latitude are negative by definition.
Example:
Start point: 104 deg. 42' 03" W : 38 deg 48' 21" N
Destination: 104 deg 40' 23" W : 39 degrees 51' 42" N
104 42' (03/60)" W = 104 (42.0001/60)' W = 104.7 W = -104.7 degrees
38 48' (21/60)" N = 38 (48.35/60)' = 38.806 N = 38.806 degrees
Start Point
longitude: -104.7 degrees
latitude: 38.806 degrees
Destination:
longitude: -104.673 degrees
latitude: 39.862 degrees - 3). Convert angles of longitude and latitude to distance measurements. The conversion factor is 10,000 kilometers per 90 degrees or 111.111 km per degree.
Start Point
longitude: -104.7 * 111.111 = -11,633.322 km
latitude: 38.806 * 111.111 = 4,311.773 km
Destination:
longitude: -104.673 degrees = -11,630.322 km
latitude: 39.862 degrees = 4,429.107 km - 4). Use the Pythagorean Theorem to calculate the distance between the two points.
(lon2 - lon1)^2 + (lat2 - lat1)^2 = c^2
(-11,630.332 - (-11,633.322))^2 + (4,429.107 - 4,311.773)^2 = c^2
8.94 + 13,767.268 = c^2
117.37 km = c
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