Geography 140
Introduction to Physical Geography
Lecture: Map Scale
III. Map scale is a concept referring to the fact that maps are reductions of
the areas they represent (well, I suppose you could map something under a
microscope, at which point the map would be an expansion of the area it
represents). They should tell you how much they reduce the earth, so you
can do stuff like measure distance and interpret relative size. "Scale"
is the index of reduction, which gives you this information. There are
three basic ways of doing this.
A. The graphic scale or bar scale. This is just a line marked off in
kilometers or miles, so that you can just use a ruler or any other
straight edge to measure the real world distance between any two
places on the map.
1. These bar scales can be given in kilometers or miles or a
combination of the two, as you see here.
2. A nice feature of graphic scales is that they can be reduced or
enlarged and still retain their proportionate meaning. All other
scale types have to be redone if you plan to reduce or enlarge the
map.
3. There are two possible shortcomings:
a. As with any scale, you should trust its accuracy only in the
center of the map and view it only as an approximation around
the edges, especially in maps that depict large areas.
b. The scale can be culture-bound, in the sense that, if you only
provide scale in miles, most of the rest of the world won't be
able to use your map without lots of extra calculations.
Similarly, if you only provide kilometers, most Americans other
than those in the sciences will have trouble reading it without
a lot of extra work. Be courteous and provide both.
B. The verbal scale or stated scale. One inch equals one mile or 1
centimeter equals one kilometer or whatever. Again, you'd use a ruler
to estimate real world differences.
1. An advantage of this is that it is easy for most people WITHIN A
CERTAIN culture to use it.
2. One disadvantage is that it's really difficult to translate into
another numerical culture though (somehow 2.5 cm = 1.6 km doesn't
do it for me, nor would 0.4" = 0.6 mi.).
3. Another minor disadvantage is you need an actual ruler to use it:
You can't just mark off a piece of paper against the graphic scale
right then and there.
4. One BIG disadvantage is you have to recalculate and restate it if
you enlarge or reduce the map.
C. The representative fraction or map ratio shows scale as a fraction or
ratio, in which the numerator is always one. Examples would be
1:500,000 or 1/100,000 or 1/63,360 or 1:62,500. The denominator
stands for the number of the SAME UNITS (e.g., centimeters or inches)
that the map shows in the real world. So, 1:100,000 would mean one
inch on the map equals 100,000 inches in the real world (about
1.6 mi.). It would equally mean one centimeter on the map equals
100,000 centimeters in the real world (1 km).
1. This way, everyone can read your map in whichever measurement
system they're comfortable with. Everybody's happy.
2. Like the verbal scale, the representative fraction has to be
recalculated any time you enlarge or reduce a map.
3. The biggest drawback is it's sort of tough to imagine, oh, 125,000
inches or 125,000 centimeters. We have to convert it from the
dinky units of centimeters and inches into the kinds of larger
units we use in traveling around: kilometers and miles. So, you
have to do a little division to make them sensible to you
a. In the metric system, there are 100,000 cm/km, so just divide
the denominator by 100,000.
i. 1:500,000 is 1 cm=5 km
ii. 1:250,000 is 1 cm=2.5 km
iii. 1:125,000 is 1 cm=1.25 km
iv. 1:100,000 is 1 cm=1 km
v. 1:62,500 is 1 cm=0.625 km
vi. Right there, you can see why scientists like the metric
system -- easy division (we're a lazy bunch)!
b. Most Americans use the English system, even though the English
gave it up for the pleasures of owning the Prime Meridian and
even though the Americans whupped the English in the Revolution
that gave birth to the USA and divorced themselves from all
sorts of other Anglicisms (such as the way they spell stuff like
"honour," "defence," and "amongst"). In the English system, one
mile is, uhhhhhh, how many feet? Hmmmmmm. That's a tough one.
Anyone know right offhand? I never remember it myself, and I
actually actually had to look it up for this lecture <blush>.
One mile is 5,280 feet. Why 5,280? Click here to
find out if you're morbidly curious. So, how many inches are
there in a foot? Twelve. So, how many inches are there in a
mile? Twelve times 5,280 is (are you sitting?) 63,360. Yep,
one mile is 63,360 inches. So, just divide the denominator by
63,360. Piece of cake!!! 1:500,000, then, would be, let's see,
500,000/63,360 = 7.8914 miles. Oh, THAT's a nice round number
we can all vividly picture, right? Not. So, the United States,
to make the English system a little bit more manageable in USGS
maps, fudges a bit. For the purposes of using USGS maps, you
assume that one mile equals 62,500 inches. How come? Because
it's kind of close to the real number of 63,360 and it is easier
to divide into those denominators. So, 1:500,000 now involves
500,000/62,500. So, 1 in. "equals" 8 mi.
i. 1:500,000 is 1 in. = 8 mi.
ii. 1:250,000 is 1 in. = 4 mi.
iii. 1:125,000 is 1 in. = 2 mi.
iv. 1:100,000 is 1 in. = 1.6 mi.
v. 1:62,500 is 1 in. = 1 mi.
vi. 1:63,360 is also 1 in. = 1 mi.
vii. Now you see why American scientists are so aggravated that
most Americans are reluctant to go metric, despite the USA
signing the Metric Treaty back in 1875, despite Thomas
Jefferson and John Quincy Adams urging the new US to
consider the merits of the French system, despite the U.S.
Congress authorizing the US to go metric in 1866, despite
the U.S. Congress (again) passing a Metric Conversion Act
of 1975 to establish an oversight body "to coordinate the
voluntary conversion to the metric system," and despite the
economic and trade costs of our refusal to participate in
the international (and easy to use) system that the country
itself helped develop!!! Eeeek!! Excuse me, I think I've
regained my composure....(end of rant for now).
D. A very confusing concept is the notion of large scale and small scale
maps. You really have to focus here.
1. A large scale map is one that shows a large amount of detail about
a small area. In other words, its representative fraction is a big
number (which means it has a relatively small denominator). Got
all that? Just remember: Large scale equals large DETAIL.
2. A small scale map is one that shows a small amount of detail about
a large area. Its representative fraction is a small number
(which, mathematically, means it has a big denominator). Remember:
Small scale equals small amounts of detail.
3. So, which is the larger scale map? 1:10,000 or 1:100,000? (first
one)
4. Which would be the smaller scale map? 1:250,000 or
1:1,000,000,000? (second one)
5. Which would be the larger scale map? One that shows the whole
world or one that shows California only? (California)
E. If you would like to learn more about these issues, you can visit:
Map interpretation
Conversion: metrics
The next lecture will be on map symbolization.
Document and © maintained by Dr.
Rodrigue
First placed on web: 09/16/00
Last revised: 06/08/07