Cartography

Maps present geographical information at a reduced scale. In order for the information to be useful to the map user, the relative proportions of geographic features and spatial relationships must be kept as accurate as possible. Cartographers use various types of scales to keep those features and relationships in the correct proportion.

Scale is the mathematical relationship between a distance between two points on the map and the distance between two corresponding points on the ground. The relationship is expressed as a ratio, the first number being the distance between two points on the map and the second number being the actual distance represented. The number indicating map distance is always one. Thus, a map with a scale of 1:125,000 tells the map user that every unit of distance on the map equals 125,000 of the same units of distance on the ground. The units of distance used are not important as long as they are the same on both sides of the ratio. One centimeter on the map would equal 125,000 cm on the ground, 1 ft on the map would equal 125,000 ft on the ground, and 1 m on the map would equal 125,000 m on the ground.

Maps showing a large area are called small-scale maps. This is because the ratio between map distance and actual distance is a small number. The number is small because one distance unit on the map represents a large number of distance units on the ground. For example, a map showing North America at a scale of 1:40,000,000 would use one unit of map distance to depict 40,000,000 units of actual distance. One centimeter on these maps equals 40 km of actual distance. Such a map fits on a piece of paper only 9 in wide and 8.25 in high (23 cm by 21 cm).

Maps showing a small area are called large-scale maps. The ratio between map distance and actual distance is a large number. It is large because each unit of distance on the map represents a relatively small number of distance units on the ground. City maps are good example of large-scale maps. A city map of Portland, Oregon with a scale of 1:38,000 fits on a piece of paper 41.75 in by 35.5 in (106.5 cm by 90 cm). One centimeter on this map equals 0.38 km of actual distance and one inch equals six tenths of a mile.

Every properly prepared map has a statement of its scale. This statement can take many forms, and many maps express scale in more than one way. The scale may be indicated by a ratio, such as 1:100,000 or 1/100,000 (the latter is less common). This ratio is called the representative fraction. Representative fractions are not particularly easy to use in everyday situations, so cartographers have developed other ways to communicate the scale of a map to its users.

Sometimes cartographers use a graphic scale, also called a bar scale. A graphic scale is a line or bar subdivided to show how many actual miles fit into a particular measurement on the map. In most parts of the world the graphic scale shows how many actual miles or kilometers are represented by a particular number of inches or centimeters on the map.

Two other means for expressing scale are the area scale and the verbal statement. Area scales are used for maps based on equal-area projections, that is, maps that present all areas shown in the same proportion to one another as they occur on Earth's surface. These scales tell the reader that one unit of area on the map represents a certain area on the ground. The scale can be written 1:250,000², although 1:250,000 is more common. The latter expression assumes the reader is aware that the number represents a ratio of square units. A verbal statement of scale uses words, rather than numbers or graphic symbols. "One inch equals one mile" is a verbal statement of scale equivalent to the representative fraction 1:63,360 (there are 63,360 inches in one mile).