In order to make topographic maps useful for relating the position of features on the map to the actual land surface, conventions of scale have been standardized. The common and standard map scales are:
1:1,000,000 for area of 4° to 6°
1:500,000 for area of 2° to 3°
1:250,000 for area of 1° to 3°
1:125,000 for 30' quadrangles
1:62,5000 for 15' quadrangles
1:24,000 for 7½' quadrangles
A map scale defines the relationship between distance on a map and the corresponding distance on the ground. Such a scale is usually expressed as either a numerical ratio (those listed above are numerical ratios) or shown graphically by bar scales marked in meters and kilometers or feet and miles (Figure 7.4 and the sheet of topographic map symbols). Because the construction of topographic maps still utilizes the English system of measurement (inches, feet, miles), examples and problems relating to topographic maps will use the English system of measurement rather than the metric sytem.
Figure 7.4 - Map scales in form of bar scales corresponding to ratio scales 1:62,500 (1 inch = 1 mile) and 1:1,000000
Ratio map scales were arrived at by allowing one unit on the topographic map (1:) to represent a constant number of units on the ground (e.g., 62,500) and this constant depends on the area covered by the map (e.g., 30', 15', etc.). The convention arrived at was simple and based on the number of inches in a mile
1 mile = 5280 ft = 63,360 inches (5280 x 12)
however, this number proved difficult to work with at larger or smaller scales, and the value of 62,500 inches was chosen to represent one mile. The rational behind this decision is that the difference of 860 inches or 71.5 feet could not be detected under normal circumstances, and the comparison among maps with different scales would be easier. Therfore, a ratio map scale of 1:62,500 is considered to represent a ratio of 1 inch to 1 mile. This ratio was adopted as the standard for all 15' quadrangles. A ratio map scale of a 30' quadrangle (1:125,000) then represents 1 inch to 2 miles, and so on. The scale on the 7½' quadrangle was made even smaller (1:24,000) to allow for greater detail. Notice the ratios listed above will work with any units of measure such that a ratio of 1:24,000 can represent 1 inch to24,000 inches, 1 centimeter to 24,000 centimeters, 1 meter to 24,000 meters, etc. Compare the mile and foot scales for 1:24,000 and 1: 62,500 illustrated on the information sheet of the U.S. Geological Survey publication Topographic map information and symbols, Marck 1978.