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.

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.

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.

The ground distance is 12,000 feet.

### USING THE MODIFIED ACREAGE GRID (TRANSPARENCY)

To use the acreage grid transparency, follow these steps:

**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.

- Place the acreage grid transparency over the area to be measured.
- Count dots inside the sketched area. Count every other dot when dots fall on the boundary line.
- Multiply the total number of dots by the conversion factor on the map scale to determine the total acreage. (See Table 5.2.)
**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.

12,000 feet = 182 chains

__Step 2.__Set up the cancellation table so all units will cancel, except the desired unit, miles.__Step 3.__Set up the cancellation table so all units will cancel, except the desired unit, inches.

12,000 feet = 182 chains = 2.3 miles = 144,000 inchesOccasionally, 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.__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.