# Latitude and Longitude Coordinate System

The latitude and longitude coordinate system, used in GPS systems, is presented with examples.
An online calculator to calculate the >distance between two Points on earth is also included.

## The Prime Meridian and the Equator

It is internationally agreed that the prime meridian is an imaginary great circle that divides the earth, supposed to be a sphere, into two hemisphere (half the sphere Earth): the eastern and western parts as shown below in figures 1 and 2 below. The prime meridian circle runs through Greenwich in England.
The equator is also an imaginary circle that is equidistant from the North and South poles and divides the earth, supposed to be a sphere, into two hemisphere: the northen and southern parts as shown below in figures 1 and 2 below.

The
latitude is an angular measurement between the plane of the equator and the radius from the centre of the earth to the location considered. Therefore locations on earth with the same latitude form a circle and they are called lines of latitude in figure 2 below.
The
longitude is a an angular measurement of the angle between the plane containing the prime meridian and the plane containing the North and South poles and the location considered. Points with the same longitude form a circle called line of longitude or meridians .

Example 1
Write the latitude and longitude of points A, B, C and D (in figure 2) using North (N), South (S), East (E) , West (W).
1) Point A in figure 2 is at the intersection of line with latitude 30$^{\circ}$ North and the line with longitude 60$^{\circ}$ East.
Hence the latitude and longitude of A is written as:   30$^{\circ}$ N , 60$^{\circ}$ E
2) Point B is at latitude 45$^{\circ}$ N and longitude 15$^{\circ}$ W.
Hence the latitude and longitude of B is written as: 45$^{\circ}$ N , 15$^{\circ}$ W
3) Point C at latitude 15$^{\circ}$ S and longitude 75$^{\circ}$ W.
Hence the latitude and longitude of C is written as: 15$^{\circ}$ S , 75$^{\circ}$ W
4) Point D at latitude 45$^{\circ}$ S and longitude 30$^{\circ}$ E.
Hence the latitude and longitude of D is written as: 45$^{\circ}$ S , 30$^{\circ}$ E

## Range of Values of Latitude and Longitude

The latitude of the Equator is equal to zero. The longitude of the prime meridian (through Greenwich) is equal to zero.
The longitude takes values from $0^{\circ}$ to $180^{\circ}$ East and $180^{\circ}$ West.
Negative and positive signs may also be used to express the longitude such that longitude to the east is positive and a longitude to the west is negative
The range of longitudes may be written as: $[-180^{\circ} , 180^{\circ} ]$

The latitude takes values from $0^{\circ}$ to $90^{\circ}$ North and $90^{\circ}$ South.
Negative and positive signs may also be used to express the latitude such that latitude to the North is positive and a latitude to the South is negative
The range of latitudes may be written as: $[-90^{\circ} , 90^{\circ} ]$

Example 2
Write the latitude and longitude of points A, B, C and D (in figure 2) using North (N), South (S), East (E) , West (W) and negative and positive signs.(Note that the positive sign + is omitted)
1) A :    30$^{\circ}$ N , 60$^{\circ}$ E   or   30$^{\circ}$ , 60$^{\circ}$
2) B :    45$^{\circ}$ N , 15$^{\circ}$ W   or   45$^{\circ}$ , - 15$^{\circ}$
3) C :    15$^{\circ}$ S , 75$^{\circ}$ W   or   -15$^{\circ}$ , - 75$^{\circ}$
4) D :    45$^{\circ}$ S , 30$^{\circ}$ E   or   -45$^{\circ}$ , 30$^{\circ}$

## Examples of Latitude and Longitude of Capital Cities in Decimal Degrees

We give some examples of latitude and longitude using either the negative/positive signs and South/North (S/N) for latitude and east/west (E/W) for longitude.
The latitude and the longitude are separated by a comma.
Washington DC(latitude and longitude):     38.8938672 , -77.0846157   or   38.8938672 N , 77.0846157 W
Algiers(latitude and longitude):     36.7391355 , 3.0692912   or   36.7391355 N , 3.0692912 E
London UK(latitude and longitude):     51.5287718 , -0.2416802   or   51.5287718 N , 0.2416802 W
Moscow (latitude and longitude):     55.5815245 , 36.8251409   or   55.5815245 N , 36.8251409 E
Tokyo (latitude and longitude):     35.5090627 , 139.2093892   or   35.5090627 N , 139.2093892 E
Beijing (latitude and longitude):     39.9390731 , 116.1172792   or   39.9390731 N , 116.1172792 E
Cape Town (latitude and longitude):     -33.914651 , 18.3758812   or   33.914651 S , 18.3758812 E
Kuala Lumpur (latitude and longitude):     3.138675 , 101.6169495   or   3.138675 N , 101.6169495 E
Kampala latitude and longitude:     0.3132008 , 32.5290854   or   0.3132008 N , 32.5290854 E

## Format in Writing Altitude and Longitude

Being angles, the latitude and longitude may be written into one of the following forms.
1 - Decimal degrees (DD) format
Example 3
3.138675 $^{\circ}$ , 101.6169495 $^{\circ}$     or     3.138675 $^{\circ}$ N , 101.6169495 $^{\circ}$ E

2 - Degrees, minutes and seconds (DMS)
Example 4
3$^{\circ}$ 34' 45.3'' , 23$^{\circ}$ 55' 23.7''     or     3$^{\circ}$ 34' 45.3'' N , 23$^{\circ}$ 55' 23.7'' E

3 - Degrees and decimal minutes (DDM)
Example 5
-32$^{\circ}$ 34.67' , - 43$^{\circ}$ 55.67'     or     32$^{\circ}$ 34.67' S , 43$^{\circ}$ 55.67' W

## Convert Between Different Formats

Knowing the rates of conversion
1 degree = 60 minutes or 1 minute = (1/60) degree
1 minute = 60 seconds or 1 second = (1/60) minute = (1/3600) degree
conversion from DD to DMS to DDM and vice versa can be done using simple calculations.

Example 6
a) Convert 3.138675 $^{\circ}$ to DDM and DMS
b) Convert 45 $^{\circ}$ 55' 23.7'' to DD and DDM
Solution
a) 3.138675 $^{\circ}$ = 3 $^{\circ}$ + 0.138675 × 60 minutes = 3 $^{\circ}$ 8.3205'       DDM
= 3 $^{\circ}$ + 8' + 0.3205 × 60 seconds = 3 $^{\circ}$ + 8' + 19.23 '' = 3 $^{\circ}$ 8' 19.23 ''       DMS
b)
From the rate given above, we can write that 1' = (1/60)$^{\circ}$ \) and 1'' = (1/3600)$^{\circ}$ \)
Hence
45 $^{\circ}$ 55' 23.7'' = 45$^{\circ}$ + 55' + 23.7'' = 45$^{\circ}$ + 55 (1/60)$^{\circ}$ + 23.7 (1/3600)$^{\circ}$ = 45.92325 $^{\circ}$       DD
45.92325 $^{\circ}$ = 45$^{\circ}$ + 0.92325 $^{\circ}$ = 45$^{\circ}$ + 0.92325 × 60' = 45$^{\circ}$ 55.395'       DDM