Latitude and Longitude

It is important when using topographic maps to have some way to express location.  You may want to tell someone where you are (i.e. help we are sinking at this location), or where to go (meet me at this location), or even just what map to look at (look at the map showing this location).  In  each case  you need to be able to express your location as precisely as possible.

There are many systems for expressing location.  We will start by looking at one you are already familiar with: latitude and longitude. 


Latitude and longitude lines form a grid on the earths surface. Latitude lines run east to west, longitude lines run north to south.  Latitude lines run parallel to the equator and measure the distance north or south of the equator.  Values for latitude range from 0 at the equator to 90 N or 90S at the poles.  Longitude lines run parallel to the Prime Meridian (arbitrarily set to run through Greenwich, England) and measure distance east and west of this line. Values of longitude range from zero degrees at the Prime Meridian to 180E or 180W.

The basic unit of latitude and longitude is the degree (), but degrees are a large unit so we often have to deal with subdivisions of a degree.  Sometimes we just use a decimal point, such as 35.789N . This format referred to as decimal degrees.  Decimal degrees are often found as an option on Global Position Systems (GPS) or with online topographic maps, but decimal degrees are not used on printed maps.  On these topographic maps the latitude and longitude units are expressed in degrees, minutes, and seconds.  Each degree is subdivided into 60 minutes(').  Each minute is divided into 60 seconds('').  Note the similarity to units of time which makes these relationships easy to remember.  If we are interested in a general location we may just use degrees.  For more precision we specify minutes, or even seconds.  Note that we always need to specify the larger unit.  You can't specify your latitude or longitude with just minutes or seconds.  A coordinate such as 25' is meaningless unless the degrees are also given, such as 45 25'. 

North-south running lines of  longitude, and east west running lines of latitude, combine to form a grid on the earth surface. This grid is used to define the boarders of topographic maps.  Each rectangle in the grid (like the one shown in red) would represent topographic map covering a certain area, referred to as a quadrangle.  Each quadrangle has a name based on a feature found within its boarder.  For example the Alliance quadrangle contains the city of  Alliance, Ohio.  



The area covered by the quadrangle depends on the spacing of the latitude and longitude lines used in the grid.  For maps of roughly the same size closer spaced lines produce maps that cover less area, but show more detail.  Lines that are spaced further apart produce maps that cover much larger areas, but are not as detailed.  Quadrangles are often referred to by the spacing of these lines.  For example we distinguish 7 minute quadrangles, that cover an area of 7 minutes of latitude by 7 minutes longitude,  from 15 minute quadrangles, which cover an area of 15 minutes latitude by 15 minutes longitude.  For standard topographic maps each type of quadrangle is associated with a specific map scale as shown in the table below.


Quadrangle Type

Coverage (Latitude x Longitude) Common Scale
7 minute* 7'  by 7' 1:24000
15 minute 15' x 15' 1:62500
30 minute 30' x 30' 1:125000
60 minute 60' x 60' (or 1 x 1) 1:250000
1/2 degree by 1 degree* 30' x 60' (or x 1) 1:100000
1 degree by 2 degree* 1 x 2 1:250000

*   Maps commonly available in continental U.S.  Other scales found on older maps, though 15' maps are still used for Alaska.


Lets look at how we can determine location in terms of latitude and longitude from a topographic map.  The diagram below is a very simplified version of a topographic map.  While no features are shown on the map, the marking for latitude and longitude found in the margins of topographic maps are shown.


First lets determine what the numbers on the map mean.  The numbers on the left and right side of the map are latitude. (As always we are assuming that north is to the top of the screen).  The numbers across the top and bottom of the map are longitude.

Lets determine what type of quadrangle this map represents.  Longitude on the left of the map is 118, longitude on the right side of the map is 117 45'.  The difference between these two is 15'.  Latitude of the top of the map is 40 30' and the latitude of the bottom of the map is 40 15'.  The difference between these two is also 15'.  This map, which covers an area that is 15' x 15' would be referred to as a 15 minute map (see table above).

Notice that latitude and longitude is only fully written in the corners of the map.  Along the edges of the map only the minutes are written.  The map reader must realize that 20' latitude on this map is actually 40 20', because 20' lies in between 40 15' and 40 30'.

We can also use latitude and longitude to give the location of points on a map.  Estimate the location of each of the red letters on the map in terms of latitude and longitude.  The answers are below.

POINT Latitude Longitude Explanation
A 40 30' N 118 W

Point A is in the upper left corner of map so its coordinates are the printed coordinates of this corner.  The one thing that needs to be added are the direction notations of each coordinate.  They are not printed on the map because it is assumed you can tell what hemisphere you are in.  When you are asked for latitude and longitude you must add these letters.  It is easy to tell where you are by which direction the numbers for latitude and longitude increase.  Latitude increase going north on this map so we are in the northern hemisphere.  Longitude increases going to the west, so this map is located west of the Prime Meridian. 

B 40 25' N 117 55' W To determine the location of point B we need to read across to the side of the map (to determine latitude) and up to the top of the map to determine longitude. Point B lines up with labeled tick marks labeled 25' and 55', but we know these numbers are incomplete. looking at the corner of the map we see that the latitude is 40 25' N (north because of same argument for point A) and the longitude is 117 55' W.
C 40 20' N 117 50' W  

Follow the same procedure as point B above.


D 40 27' 30" N 117 47' 30" W Point D does not line up directly with tick marks. Instead we need to estimate its location. Point D looks like it is half way between the 25' and 30' marks for latitude and half way between the 45' and 50' marks for longitude.  Half way for each of these is 27'30" and 47'30".  Remember one half a minute is 30 seconds.  Adding the remaining parts of the coordinates as we did above give us the answer.
E 40 16' N 117 52' 30" W Solved the same as point D above.  The only difference is in estimating the minutes for latitude. Point E seems to closer to 15' that to 30' so I have estimated it as 16'.  This is only an estimate so the answer can vary, but it should be greater than 15' and less than 17' 30"



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Last Updated: 01/18/2014