5.2 Map Scale

The map scale is printed in the map legend. It is given as a ratio of inches on the map corresponding to inches, feet, or miles on the ground. For example, a map scale indicating a ratio of 1:24,000 (in/in), means that for every 1 inch on the map, 24,000 inches have been covered on the ground. Ground distances on maps are usually given in feet or miles. 
 

Map Scale Conversion Factors

 

Scale Representative Fraction Map in/mi Map in/ch map ft/in
1:253,440 253.44 0.25 0.0031 21,120
1:126,720 126.72 0.50 0.0063 10,560
1:63,360 63.36 1.00 0.0125 5,280
1:62,500 62.50 1.01 0.0127 5,208
1:31,680 31.68 2 0.025 2,640
1:24,000 24.00 2.64 0.033 2,000
1:21,120 21.12 3 0.038 1,760
1:15,840 15.84 4 0.05 1,320
1:7,920 7.92 8 0.1 660

Table 5.1. Map Scale Conversion Factors

Example 1 - Convert the map scale of 1:24,000 (in/in) to (in/ft).

Step 1. Set up the cancellation table so all units will cancel, except the desired unit, ft/in.

cancellation table

On the map 1 inch is equal to 2,000 feet on the ground, 1:2,000 (in/ft).

Example 2 - Convert the 1:2,000 (in/ft) to (in/mile).

Step 1. Set up the cancellation table so all units will cancel, except the desired unit, miles/inch.

cancellation table

On the map 1 inch is equal to 0.4 miles.

Example 3a - The map distance between two points is 6 inches. The map scale is 1:24,000 (in/in). What is the ground distance in feet?

Set up the cancellation table so all units will cancel, except the desired unit, feet.

cancellation table

The ground distance is 12,000 feet.

USING THE MODIFIED ACREAGE GRID (TRANSPARENCY)

To use the acreage grid transparency, follow these steps:

acreage grid
 

Map Scales and Equivalents

Scale Inches per mile Acres per square inch Conversion factor that each dot equals
1:20,000 3.168 63.769 1.736 Acres
1:24,000 2.640 91.827 2.500 Acres
1:62,500 1.014 622.449 16.946 Acres
1:63,360 1.000 640.000 17.424 Acres

Table 5.2 Acreage Grid Overlay, Map Scales, and Equivalents.

  1. Place the acreage grid transparency over the area to be measured.
  2. Count dots inside the sketched area. Count every other dot when dots fall on the boundary line.
  3. Multiply the total number of dots by the conversion factor on the map scale to determine the total acreage. (See Table 5.2.)
  4. Example 3b - Using the information in Example 3a, find the ground distance in chains, miles, and inches.

    Step 1. Set up the cancellation table so all units will cancel, except the desired unit, chains.

    cancellation table

    12,000 feet = 182 chains
     

    Step 2. Set up the cancellation table so all units will cancel, except the desired unit, miles.
    cancellation table

    Step 3. Set up the cancellation table so all units will cancel, except the desired unit, inches.
    cancellation table
    12,000 feet = 182 chains = 2.3 miles = 144,000 inches

    Occasionally, a map may not provide a scale. The scale can be calculated by knowing the distance between two points on the map, and measuring the distance on the map. Also, if a map has section lines, the distance between section lines is typically 1 mile.

    Example 4 - The distance between point A and B is 6 inches on the map. The known ground distance is 3,600 feet. What is the scale in units of inches/foot?

    The map scale is 1:600 inches/foot.

    Example 5 - Use the map scale in example 6. The known ground distance between points B and C is 1/2 mile. How many inches is does this distance correspond to on the map?

    map scale = known distance / measured distance

    Rearrange terms by multiplying each side by the measured distance and dividing each side by the map
    scale.

    measured distance = known distance / map scale

    Step 1. Set up the cancellation table so all units will cancel, except the desired unit, feet.

    cancellation table

    Step 2. Use the map scale from Example 6 to find the map distance.

    measured distance = known distance
    map scale
    measured distance = 2,640 feet 1 inch = 4.4 inches
    600 feet

    On the ground one-half mile is the same as 4.4 inches on the map.



    5.