# Map Scale – Measuring Distance on a Map

## Measuring Distances on a Map: Map Scale

A map represents a portion of the earth’s surface. Since an accurate map represents the land, each map has a “scale” which indicates the relationship between a certain distance on the map and the distance on the ground. The map scale is usually located in the legend box of a map, which explains the symbols and provides other important information about the map. A map scale can be printed in a variety of ways.

A ratio or representative fraction (RF) indicates how many units on the earth’s surface is equal to one unit on the map. It can be expressed as 1/100,000 or 1:100,000. In this example, one centimeter on the map equals 100,000 centimeters (1 kilometer) on the earth. It also means that one inch on the map is equal to 100,000 inches on the land (8,333 feet, 4 inches or about 1.6 miles). Or even 1 paperclip on the map is equal to 100,000 paperclips on the ground. Other common RFs include 1:63,360 (1 inch to 1 mile) and 1:1,000,000 (1 cm to 10 km).

A word statement gives a written description of map distance, such as “One centimeter equals one kilometer” or “One centimeter equals ten kilometers.” Obviously, the first map would show much more detail than the second because one centimeter on the first map covers a much smaller area then on the second map.

The first two methods of indicating map distance would be ineffective if the map is reproduced by a method such as photocopying and the size of the map is modified. If this occurs, and one attempts to measure an inch on the modified map, it’s not the same as an inch on the original map.

A graphic scale does solve this problem because it is simply a line marked with distance on the ground which the map user can use along with a ruler to determine scale on the map. In the U.S., a graphic scale often includes both metric and U.S. common units. As long as the size of the graphic scale is changed along with the map, it will be accurate.

Maps are often known as large scale or small scale. A large scale map refers to one which shows greater detail because the representative fraction (e.g. 1/25,000) is a larger fraction than a small scale map which would have an RF of 1/250,000 to 1/7,500,000. Large scale maps will have a RF of 1:50,000 or greater (i.e. 1:10,000). Those between 1:50,000 to 1:250,000 are maps with an intermediate scale. Maps of the world which fit on two 8 1/2 by 11 inch pages are very small scale, about 1 to 100 million.

# scale

scale, in cartography, the ratio of the distance between two points on a map to the real distance between the two corresponding points portrayed. The scale may be expressed in three ways: numerically, as a ratio or a fraction, e.g., 1:100,000 or 1/100,000; verbally, e.g., “one inch to one mile” (not “one inch equals one mile”); and graphically, by marking distances on a sample line. The last method has the advantage that the scale remains true even if the map is enlarged or reduced mechanically. The first method is particularly useful since any unit of measurement may be used; e.g., if one uses metric units, a scale of 1:100,000 would mean that one centimeter on the map represents one kilometer on the earth’s surface (since 100,000 centimeters equals one kilometer). The more the size of features on the map approaches the features’ actual size on the earth’s surface, the larger the scale of the map is said to be. A large-scale map usually shows more detail than does a small-scale map, but covers a smaller area than does a small-scale map of the same size.

MAP SCALES & UNITS

This handout was designed to help you understand the relationships between different map scales, map units, distance, and area. You should understand the logic behind how these are used and how they should appear on real topographic maps. On your upcoming lab exam, you should also be able to convert one type of map scale into another, and calculate size differences (scale factor, area factor) between different maps.
A. Review of Common Types of Map Scales

All map scales are an expression of the numerical relationship between the MAP and the LAND that is represented. The MAP unit is always mentioned first.

1. Verbal Scale: The verbal scale is just a sentence stating that “1 Map Unit = X Land Units”. For reasons of convenience, a mixture of units is commonly used, such as

1 inch  = 1 mile

However, there are NO requirements that the units must be different! The expression “1 inch = 63,360 inches” is still a verbal scale. A mixture of map and land units makes the verbal scale difficult to compare between different maps – it must be converted first to a Representative Fraction (see below).
2. Representative Fraction (R.F.): An R.F. scale is a ratio, or fraction, that expresses the mathematical relationship between MAP and LAND, such as

1 : 24,000

which means “1 map unit is equivalent to 24,000 land units.” Because an R.F. carries no units (inches, centimeters, etc.), it means that the R.F. scales can be compared between different maps. Converting an R.F. scale to a verbal scale is very easy; simply select ONE unit and apply it to BOTH map and land numbers. The above example can be written as a verbal scale as “1 inch = 24,000 inches” or “1 meter = 24,000 meters,” etc. (Note: YOU CANNOT MIX UNITS in an R.F.! Doing so will change the numerical relationship of the R.F.)
3. Graphic Scale: The graphic scale is a bar chart or “ruler” that is drawn at the bottom of a topographic map. This is the scale that you should use when asked to measure distances on the map. Be Careful: Note that the zero mark is not located at the left end of the graphic scale. For your convenience, the graphic scale extends to the left of the zero mark to indicate fractions of units, such as 1/10 of a mile. You may measure distances by marking off the 2 end points on the edge of a sheet of paper and aligning the edge of the paper against the graphic scale (make sure one of your marks is on the zero).