Working with Scale

Table of Contents

  1. Working with Scale
  2. Measuring Distance Using a Graphic Scale
  3. Calculating Slope When Determining Distance
  4. Converting Map Distance to Ground Distance Using a Representative Fraction (RF)
  5. Determining Scale Using a Representative Fraction

Converting Map Distance to Ground Distance Using a Representative Fraction (RF)

As you learned in this chapter, a representative fraction (RF) is the ratio between distance on the map and the distance on the ground. An RF is written using the notation 1/x or 1:x, where 1 represents the distance on the map and x represents the distance on the ground. Because the RF is a ratio, it is independent of any units of measurement.

For a review of this concept, read the Chapter 4 section on representative fraction.


On a separate piece of paper, write down the answers to the following question:

An image of the scale bars on the Arcata North USGS Topographic Quadrangle.
On a USGS Topographic Quadrangle, the RF is usually printed near the bottom of the map, just outside the neatline.
  1. What is the RF of the Arcata North USGS Topographic Quadrangle?

Calculating the Ground Distance

You can use a representative fraction to estimate distances between two points on the map. For example, suppose you had a map with an RF of 1:48,000. On the map, you marked two points. Using a ruler, you measured that the distance on the map between the two points was 6 inches. You could use this information to find out the distance between the two points in miles.

An image of an RF calculation.
Though we are using inches as an example, it is important to remember that an RF has no units. It is the ratio between map distance and ground distance.

An RF of 1:48,000 means that 1 inch on the map is equal to 48,000 inches on the earth (ground inches). Therefore, 6 inches on the map is equal to 288,000 inches on the earth (6 x 48000 = 288000). There are 63,360 inches in 1 mile. To find out how many miles there are between the two points, convert inches to miles by dividing 288000 by 63360. The answer is that there are approximately 4.5 miles between the two points.


On a separate piece of paper, write down the answers to the following question:

An image of the scale bars on the Arcata North USGS Topographic Quadrangle.
On a USGS Topographic Quadrangle, the RF is usually printed near the bottom of the map, just outside the neatline.
  1. Using a ruler, you found that the distance between two points on the Arcata North USGS Topographic Quadrangle was 13.2 inches. How many miles are there between the two points?