APPENDIX C
FINDING YOUR EXACT LOCATION
Notes to Teachers
In many scientific experiments it is important to know exactly where an event took place. The
best way to express this is with latitude, longitude and height. This pinpoints where on the earth’s
surface an event happened. The following exercise allows students to do just that, but much
more. It also emphasizes the need for accuracy when taking measurements and doing
calculations. In the event that a GPS system is available to you, it allows you to compare your
results with a GPS.
USGS MAPS
United States Geological Survey (USGS) maps are line and symbol representations of natural
and selected man-made features of a part of the Earth’s surface plotted to a definite scale. The
type used in this exercise are 7.5 minute, topographic, quadrangle maps.
AVAILABILITY OF MAPS
Maps may be purchased or checked from a map depository. To see a list of depositories go to
www.usgs.gov.
Maps may be purchased from:
US Geological Survey (delivery takes 4-6 weeks) $4 each
http://edcsns17.ev.usgs.gov/EarthExplorer
Illinois Geological Survey $4 each (217) 244-0933
Travelden, Kirkwood, MO $6 each but will mail them to you the next day or can be picked up.
FINDING YOUR EXACT LOCATION
To find your exact location you need to determine:
Longitude, which is measured in degrees east (+) or degrees west (-) of the Greenwich Meridian.
The earth is divided into 360 (degrees)
Each degree is then divided into 60’ (minutes)
Each minute is then divided into 60” (seconds)
Latitude which is measured in degrees north (+) or degrees south (-) of the equator.
The Equator is 0.
The northern hemisphere is divided into 90 as is the southern hemisphere.
Each degree is then divided into 60’ (minutes)
Each minute is then divided into 60” (seconds)
The third component is height, which is normally measured with respect to your position above or
below mean sea level (MSL).
USGS maps are marked with tic marks indicating latitude and longitude. Once you have
determined your location on the map, you then need to measure the distance on the map to the
nearest latitude tic and the nearest longitude mark. (there are four tic marks in the interior of the
map at 2.5’ intervals, in addition to tic marks on the borders)
Use the most precise measuring tool available to you.
USGS maps have a scale of 1:24,000, so 1 cm on the map equals 24,000 cm (240 m).
Once you have determined the distance from your location to the nearest tic mark, you need to
convert this to degrees.
LATITUDE
Conversion factor for cm to degrees latitude
1 degree latitude = 30.922 meters per second
This is determined by
2  R = length
360
R = radius of the earth (6.378 140 x 106 m)
2  (6.378 140 x 106 =
360
111.3195 km/degree
111.3195 km/degree = 30.922 m / second
You then add or subtract the converted value to the value of the tic mark you measured from.
Look at the latitude numbers at the left and right vertical borders of your map. You will notice that
the numbers increase as they go up. If your location is above the tic mark you measured from,
you will add the distance measured to the value of the tic mark. If your location is below the tic
mark, you will subtract the value.
EXAMPLE - LATITUDE
The distance you measured from the tic mark to the 38 47” 30’ tic was 1.234 cm.
You location was above the tic mark on the map.
1.234cm x 240 meters/centimeter (map scale) = 296.160 meters
296.160 m  30.922 meters / second of longitude = 9.5776 seconds
(conversion factor from above)
3847’30” + 9.5776’ = 3847”39.5776’
Your location is 3847”39.5776’ latitude.
LONGITUDE
To calculate the conversion factor for cm on your map to degrees in longitude you must first know
you latitude. This is because the length of a degree of longitude is longest at the equator and
decreases as it nears the poles.
The conversion factor is calculated as follows:
r = R cos 
r ~ conversion factor
R~ radius of earth in km/degree
~ latitude
From our example above:
r = 111.3195 km/degree (cos 3847”39.5776’ latitude)
r = 86.7624 km/degree
Tip: Check your calculator for the correct way to enter value of degrees.
86.7624 km/degree = 24.1006 meters/second
EXAMPLE - LONGITUDE
Your location is to the right of the 8957’30” longitude tic mark. The distance from the tic mark is
0.266 cm.
Look at the longitude numbers at the bottom of your map. If you are in the western hemisphere
the number are decreasing from left to right.
If your location was to the left of the tic mark you measured to, you will add the minutes you
calculated to the value of that tic mark.
If your location was to the right of the tic mark you measured from, you will subtract the minutes
you calculated to the value of that tic mark.
0.266 cm x 240 meters / centimeter (map scale) = 63.84m
63.84 m  24.1006 meters / second of longitude = 2.6488 seconds
(conversion factor from above)
8957’30” - 2.6488’ = 8957”27.3512’
Your location is 8957”27.3512’ longitude.
To determine your height or elevation.
The USGS map has contour marks that indicate height above mean sea level. These are marked
in feet or meters above mean sea level. Check the legend at the bottom of the map to determine
which. Once you have determined your location on the map, measure the distance from your
location to the nearest contour line and using the 1:24,000 scale, determine your height.
An alternative source of elevation information is a blueprint. If, for example, you are interested in
the elevation of a school building, you may be able to determine the elevation from the structural
blueprints of the building.
COMPARING YOUR CALCULATIONS TO GLOBAL POSITIONING SYSTEMS
Your position on the GPS will include latitude in degrees north or south, longitude in degrees east
or west. To compare your values to the GPS, the map values may need to be adjusted due to
Datum revision of the map. See legend, bottom left corner of map. These values should be
close to your calculated values from the map.
The GPS height position is given in meters and some adjustment is necessary here.
Because the Mean Sea Level fluctuates with the topography of the earth’s surface, GPS systems
measure height using the geoid, an arbitrary smooth line drawn around the earth, as a reference
point. The height you determined using the map used MSL as the reference point. To compare
these two values you must adjust for the difference between the geoid reference point and MSL.
First, find your location in reference to the Geoid. To do this, go to the NIMA Geoid Calculator at
http://164.214.2.59:80/GandG/egm96/int.pt
The Geoid calculator will ask for your latitude and longitude in degrees, minutes and seconds.
Tip: Eastern Hemisphere (+)
Western Hemisphere (-)
If you get a negative geoid number it means that the MSL at your location is below the Geoid so
the geoid value needs to be added to the GPS number. A positive number would be subtracted.
Make any necessary English to metric conversions – and compare the height values.