Comprehensive Edition

## Map Scale

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The scale of a map is critical to the map reader as it may imply how accurate a map can be and how much spatial information can be effectively presented on that map. There has been some confusion about the terminologies that relate to map scale. This section is an attempt to clarify all this confusion.

Since a map drawn on a piece of paper cannot have a one-to-one size relationship with the land, the map is thus a one-to-many size relationship with the real world that it represents. In other words, one unit of measurement on the map is designated to represent many of the same units of in the real world. Thus, the map scale is actually a mathematical ratio. Map scale can be expressed in three ways:
•As a Representative Fraction or a ratio: e.g. 1: 10,000. This expression means that, for example, one inch on the map represents 10,000 inches on the ground. Notice that there is no unit of measurement on a ratio. Because scale expression is a ratio or a fraction, it will work with all units of measurement; therefore, it also works for metric measurements, such as one centimeter on the map represents 10,000 centimeters on the ground. The units of measurement on both sides of the ratio, however, must remain the same.

•As a Verbal Statement: e.g. One inch on the map represents one mile. Notice that units of measurements are different (inch and mile) from a representative fraction. This is perfectly acceptable; but the map reader has to recognize these non-matching units. If a map reader measures the distance of a journey taken from home to work to be 2.5 inches on the map, then it can be deduced that the realworld distance between home and work is 2.5 miles. Verbal statement scales can certainly be converted back into ratios. In this case, it is necessary to find out how many inches there are in one mile since a representative fraction or ratio requires that the units be the same on both sides of the ratio. There are 1760 yards in one mile, 3 feet in one yard, and 12 inches in one foot. From these, we can multiply 1760 by 3 by 12 to derive the number of inches. The result is 63,360. Therefore, the verbal statement of “one inch represents one mile” is the same as 1:63,360. Remember that once it becomes a ratio, it will work for all other units of measurement, even in the metric system. Thus, it is also truthful to say that one centimeter on the map represents 63,360 centimeters on the ground.

•As a Graphic or Bar Scale: See the following example: This graphic scale provides the map reader the opportunity to physically measure a distance on the map and line it up against this graphic scale to read off the real-world distance. Straight line distances can be easily measured with a ruler. Curved line distances can be measured either with a piece of string to simulate the curves on a map or with the straight edge of a piece of paper by holding down at turning points of the curve with a pencil until the entire curved distance is “hugged” by the edge of the paper. Once the curved map distance is simulated on the string or the edge of a piece of paper, they can be lined up parallel to the graphic or bar scale to read off the real-world distance.

There are some misconceptions or confusion about the terms large scale and small scale. Large-scale maps refer to those that cover a small area of land and showing a great deal of local detail. An example would be a cadastral map. Small-scale maps, on the other hand, cover large areas of land and cannot include local details. An example would be a world map on a regular book page.

Since scales are fractions, it is possible to compare the fractions between large and small scales to determine which is a larger scale and which is a smaller scale. A typical large-scale cadastral map may have a scale of 1: 2,000 and a small-scale world map may have a scale of 1: 40,000,000. The fraction, 1/2,000 (0.0005) is a larger number than the fraction 1/40,000,000 (0.000000025). Therefore, the cadastral map has a larger scale than the world map.

The comparison of map scales is always relative. The scales that are in between large and small scales can be considered as intermediate scales. Again, intermediate scale is only a relative term, depending on whether it is compared to a large-scale map or small-scale map.