Latitude Maps

How do I show mathematically that 1 degree of latitude is 111 km anywhere on earth?

Show mathematically that, if you move due north or south, one degree of latitude equals approximately 111 km (69 mi) everywhere on earth. Assume that the earth is a perfect sphere with the radius of 6378 km.

Public Comments

1. with a scale
2. You can't because latitude changes as you move away from the equator. Longitude does not change with latitude. The circumference of the earth would be 2PI times radius = 40,074 kilometers. Divide that by 360 degrees and you get 111 km per degree. So 1 degree of longitude is 111km. For latitude 1 degree of latitude = 111km times the cosine (latitude). At 60 degrees north or south, 1 degree latitude is about 55 km.
3. Glad you ask, I have been waiting to give someone the answer. Ready: The Formula for Latitude Distance at a Given Latitude (theta) in Km: 1° of Latitude = 111.13295 - 0.55982 * cos(2 * theta) + 0.00117 * cos(4 * theta) Now take it and run.