Distance Between Degrees of Latitudes and Longitudes

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With the specification of latitudes and longitudes, it has become very easy to exactly pinpoint a location anywhere on the surface of this Earth. The grid system that makes up latitudes and longitudes divides the Earth into neat little sections making it quite easy for anyone to either explain to someone or for someone to understand the position one is talking about. It is much much easier to explain and infinitely simpler to understand a set of numbers representing a particular position rather than going into a virtual verbal diarrhoea - near the bridge, across the river, in front of the tall building, where the cow grazes every morning ... no, no, no, not where your uncle lives, where my sister's boyfriend (the second one) used to work before he moved to where there is a river flowing into the ocean. Whoopie!!! It is so much simpler to say N 22°11'25" E 79°23'42" representing the latitude and longitude of the location we are trying to explain.

What we need to remember is the fact that latitudes and longitudes are not squares, though they might appear so on an atlas.

Latitudes are parallel lines to each other. There are 180° of latitude from Pole to Pole, with the Equator being at 0° and the North and South Poles at 90°N and 90°S respectively. Longitudes on the other hand are not parallel. They start and converge at the Poles with them being at the widest distance from each other at the Equator.

AT THE EQUATOR, the distance between two corresponding degrees of latitude and two corresponding degrees of longitudes are roughly the same - about 111 km. So, if were lost at sea, at the Equator and were able to signal your coordinates in a Mayday call, and were correct to within 1° of latitude and longitude, the search would be looking at an area of over 12,000 sq km! The more accurate you are, the greater the chances of your being rescued quickly. The sea is a very big place to be going out on a wild goose chase.

Let us take a look at the distances between various degrees of latitudes.

0 -1°
9 - 10°
19 - 20°
29 - 30°
39 - 40°
49 - 50°
59 - 60°
69 - 70°
79 - 80°
89 - 90°
Distance in Kms

Longitudes are a different matter altogether since they are not parallel, but converge at the two Poles. The distance between two degrees of longitude is maximum at the Equator, about 111 km, and the minimum at the Poles, 0 km. At every place in between the Equator and the Poles, the distance between two corresponding degrees of longitude will change. Actually, you do not need to know your longitude at all, you need to know your latitude.

The distance between two degrees of longitude equals the cosine of the latitude in decimal degrees, multiplied by the distance at the Equator. So, if we are trying to find the distance between longitudes at N 22°11'25", we need to first convert the latitude into decimal degrees, using the formula:

Decimal Degrees = degrees + (minutes/60) + (seconds/3600)

22 + 11/60 + 25/3600.
22 + 0.18333333 + 0.00694444 = 22.19027777 decimal degrees

and then this to radians...

22.19027777° × π / 180° = 0.12327932094π rad = 0.38729340902 rad

If we multiply this result with 111 (the distance in kilometres at the Equator), we get 42.99, and this is the distance between two degrees of longitude at N 22°11'25" latitude.

One can use this resource to convert latitudes into decimal degrees ... https://www.latlong.net/degrees-minutes-seconds-to-decimal-degrees and this to convert decimal degrees to radians ... https://www.rapidtables.com/convert/number/degrees-to-radians.html