Map Scale

Topographic maps are drawn to scale.  This means that distances on a map are proportional to distances on the ground.  For example, if two cities 20 miles apart are shown 2 inches apart on a map, then any other locations that are two inches apart on the map are also 20 miles apart. This proportion, the map scale,  is constant for the  map so it holds for any points on the map.  In our example the proportion between equivalent distances on the map and on the ground is expressed as a scale of 1 inch = 10 miles, that is 1 inch on the map is equal to 10 miles on the ground. Map scales can be expressed in three forms. We will look at all three.

The simplest form of map scale is a VERBAL SCALE.  A verbal scale just states what distance on a map is equal to what distance on the ground, i.e. 1 inch = 10 miles from our example above. Though verbal scales are easy to understand, you usually will not find them printed on topographic maps.  Instead our second type of scale is used.

Fractional scales are written as fractions (1/62500) or as ratios (1:62500).  Unlike verbal scales, fractional scales do not have units.  Instead it is up to the map reader to provide his/her own units. Allowing the reader of the map to choose his/her own units provides more flexibility but it also requires a little more work.  Basically the fractional scale needs to turned in to a verbal scale to make it useful.   

First lets look at what a fractional scale means.  A fractional scale is just the ratio of map distance to the equivalent distance on the ground using the same units for both.  It is very important to remember when we start changing a fractional scale to a verbal scale the both map and ground units start the same.  The smaller number of the fractional scale is the distance on the map.  The larger number in the scale is the distance on the ground.

So if we take our example scale (1:62500) we can choose units we want to measure distance in.  Lets chose inches.  We can rewrite our fractional scale as a verbal scale:

1 inch on the map = 62500 inches on the ground.

We can do the same thing used with any unit of length.  Some examples of verbal scales produced using various units from a 1:62500 fractional scale are given in the table:

UNITS	VERBAL SCALE
inches	1 inch on the map = 62500 inches on the ground.
feet	1 foot on the map = 62500 feet on the ground
cm	1 cm on the map = 62500 cm on the ground
m	1 m on the map = 62500 m on the ground

Notice the pattern.  The numbers are the same, only the units are changed.  Note that the same units are used on both sides of each of the verbal scale.

While these verbal scales are perfectly accurate, they are not very convenient.  While we may want to measure distance on a map in inches, we rarely want to know the distance on the ground in inches.  If someone asks you the distance from Cleveland to Columbus they do not want the answer in inches.  Instead we need to convert our verbal scale into more useful units. 

Lets take our example (1 inch on the map = 62500 inches on the ground).  Measuring map distance in inches is OK, but we need to come up with a better unit for measuring distance on the ground.  Lets change 62500 inches into the equivalent in feet (I choose feet because I remember that there are 12 inches in 1 foot).  If we multiple 62500 inches by the fraction (1 ft / 12 in) inches in the numerator and denominator cancel leaving an answer in feet. Remember, since 1 ft = 12 inches, multiplying by (1 ft / 12 in) is the same as multiplying by 1. The result of this multiplication gives:

62500 inches  x  (1 ft / 12 in)=  5208.3 ft

So we can rewrite our verbal scale as  1 inch on the map = 5208.3 feet on the ground. 

This is also a perfectly valid verbal scale, but what if we wanted to know the distance in miles instead of feet.  We just need to change 5208.3 feet into miles (we could change 62500 inches into miles but I never remember how may inches are in 1 mile).  Knowing that there are 5280 feet in a mile:

5208.3 ft x (1 mi/5280 ft) = 0.986 mi.

So our verbal scale would be: 1 inch on the map = 0.986 miles on the ground.  For most practical purposes we can round this off to 1 inch on the map ~  1mile on the ground, making this scale much easier to deal with.

We can do the same type of conversions using metric units.  One of the ways to express a fractional scale of 1:62500 as a verbal scale using  metric units is 1 cm on the map = 62500 cm on the ground (see table above).  As with inches, we really do not want ground distances in cm's.  Instead we can convert them into more convent units.

Lets convert our ground distance from cm's into meters.  Recall that there are 100 cm in a meter.  So:

62500 cm x (1m / 100cm) = 625 m. 

So we can write a verbal scale of 1 cm on the map = 625 m on the ground.

What if we want our distance in kilometers (km).  We just change 625 m into km by multiplying by (1km/1000m).  The result is a verbal scale of 1 cm on the map = 0.625 km on the ground.

So for any fractional scale we can choose the same units to assign to both sides and then convert those units as we see fit to produce a verbal scale.  Given all of the possible map scales and all of the possible combination of units that can be used it may seem that scales on topographic maps a very complicated.  In fact there are only a few scales commonly used, and each is chosen to allow at least one simple verbal scale.  The most common fractional scales on United States topographic maps and equivalent verbal scales are given in the table below.

After all this, why would anyone want to deal with fractional scales.  Well, first as the table above shows its not that bad, and second, they allow us to get the most precise measurements off a topographic map.  If we are not that concern about being precise we can use the third type of scale, discussed below.

A bar scale is just a line drawn on a map of known ground length.  There are usually distances marks along the line.  Bar scales allow for quick visual estimation of distance. If more precision is needed just lay the edge of a piece of paper between points on the map you want to know the distance between and mark the points.  Shift the paper edge to the bar scale and use the scale like a ruler to measure the map distance.

Bar scales are easy to use, but there is one caution.  Look at the typical bar scale drawn below.  Note that the left end of the bar is not zero.  The total length of this bar is FIVE miles, not four miles.  A common error with bar scales is to treat the left end of the line as zero and treat the whole bar as five miles long.  Pay attention to where the zero point on the bar actually is when you measure with a bar scale.

In addition to their ease of use, there is one other advantage of a bar scale.  If a map is being enlarged or reduced, a bar scale will remain valid if it is enlarged and reduced by the same amount.  Fractional and verbal scales will not be valid (unless they are adjusted for the enlargement or reduction, more fun calculations we will not worry about). This is a problem with the maps you are looking at on this web site.  The actual scale of  the map will vary depending on your computer monitor and its setting.  For the maps on this site only bar scales are included since the size of the bar will also change with the size of the map.

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Last Updated: 03/11/2008

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