Map Scale: Calculating Representative Fractions

When a map provides a note on scale

In the following example, the cartographer provided a simple note defining the scale of the map. This does not state the ratio of map to ground, however, it does provide enough data for the cataloger to make an approximation of the ratio.

In the map at left, the cartographer noted the map scale with a phrase:

"The Squares are Square Miles"

From this we can measure the length of a "square" to use in calculating the map's "Scale."

The length of the square equals 1 inch. Since the map states that the square is equal to 1 mile, we can determine scale by the following:

• divide 1 mile (5,280 feet) into inches = 63,360 inches.
• Since 1 inch on the map = 1 mile on the ground
• the scale is 1:63,360.

Enter the 255 as follows:

Scale is always determined by taking map and ground measurements and breaking them to a common denominator (in this case, inches), to arrive at a comparable set of numbers.

The first number (map measurement) is always "1" (which could be 1 cm., 1 m, 1 foot, 1 inch, etc.).

The second number (ground measurement) is always calculated so that the resulting number equals the same unit of measurement as the "1" on the ratio (in the above example, ground scale needs to be converted to inches). This provides the representative fraction.

Handy calculators are available online. Here are several examples:

• Scale Finder (Nigel James, Bodleian Library, Map Room). Convert linear scales to representative fractions and vice-versa.
• Common Length and Distance Conversions
• Length or Distance Converter
• Martindale's Calculators On-line Center (more calculators than you may ever need).

David J. Bertuca, Map Librarian, University at Buffalo.
Created by 26 October 2000

Last Modified: 25 April 2013
URL: http://www.DavidBertuca.net/maps/cat/scale-measuring.html
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