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

Determining Scale Using a Representative Fraction

It is also possible to determine an unknown scale by using the representative fraction from a source with a known scale, such as a map.

A black and white image of an oxidation pond
The oxidation pond in this image provides a good feature to reference.

For example, suppose you acquired an old aerial photograph but were unsure of the scale. You could use the scale from a known source, such as a map, to determine the scale of the photo.

An image of the Oxidation pond on the Arcata South Topographic Map
The Arcata South USGS Topographic Quadrangle contains the same feature as the photograph.

Recall the definition of scale. In this course, the ratio of map distance over ground distance defines scale.

A definition of scale
Scale is the relationship between a distance measured on the map, and the corresponding distance in the real world.

To determine the scale of the old photograph, you need to know how the distance on the photo relates to the distance on the ground.

An image of photo scale
The definition of scale for the photograph is photo distance over ground distance.

To start, measure the distance of a prominent feature on the photo that you could also identify on a map. In this instance, the let us assume that the width of the divide in the oxidation pond, when measured on the photograph, is six inches.

An image of the oxidation pond.
The oxidation pond is six inches on the old photograph.

By measuring of the distance on the photograph, you have half of the ratio for determining scale, the photo distance.

Next, determine how far this distance represents on earth, which we call ground distance. Let us assume that the same distance, when measured on the Arcata South USGS Topographic Quadrangle is one inch.

An image of the oxidation pond on the map.
The oxidation pond is one inch on the map.

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

In the previous step, you learned how to convert map distance to ground distance using a Representative Fractions (RF). The RF for the Arcata South USGS Topographic Quadrangle is 1:24000.


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

  1. What is the ground distance of the width of the oxidation pond, given that the distance on the map was 1 inch and the map RF is 1:24,000?
An image of photo scale
  1. Based on your answer to question 8 and the definition of scale, what is the scale of the photo? Be sure to reduce the fraction so that you have the number 1 in the numerator and can represent the ratio as 1:x.
  2. What would be the best way to express the scale of the old photograph as a word statement?
  3. Is the old photograph larger or smaller in scale than the Arcata South USGS Topographic Quadrangle?