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How to Calculate Fractional Map Scale?

Published in Cartography 2 mins read

To calculate a fractional map scale, you need to express the ratio between a distance on the map and the corresponding distance on the ground as a fraction. The numerator is always 1, and the denominator represents how many units on the ground are equivalent to one unit on the map.

Here's a breakdown of how to calculate it:

Steps to Calculate Fractional Map Scale:

  1. Measure a distance on the map. Choose two distinct points and measure the distance between them using a ruler. Note the units (e.g., centimeters, inches).

  2. Determine the corresponding ground distance. Find the actual distance on the ground between those same two points. This may be provided in the problem, or you might need to use another resource, such as a known distance between landmarks. Make sure to note the units (e.g., meters, kilometers, feet, miles).

  3. Convert both distances to the same unit. This is crucial! Choose a unit and convert both the map distance and the ground distance to that unit. Centimeters are often convenient for smaller maps, while meters are often convenient for representing larger distances.

  4. Create the ratio. Write the map distance as the numerator and the ground distance as the denominator. So, it will look like:

    Map Distance / Ground Distance

  5. Simplify the fraction so that the numerator is 1. Divide both the numerator and the denominator by the original map distance (the numerator). This will give you a fraction in the form of 1/x, where 'x' is the fractional scale.

Example:

Let's say you measure a distance of 2 cm on a map. The corresponding distance on the ground is 100 meters.

  1. Map Distance: 2 cm
  2. Ground Distance: 100 meters
  3. Convert to the same unit: Let's convert 100 meters to centimeters. 1 meter = 100 cm, so 100 meters = 100 * 100 = 10,000 cm.
  4. Create the ratio: 2 cm / 10,000 cm
  5. Simplify: Divide both the numerator and denominator by 2: (2/2) / (10,000/2) = 1 / 5,000

Therefore, the fractional scale of the map is 1:5,000. This means that 1 unit (e.g., centimeter, inch) on the map represents 5,000 of the same units on the ground.

Key Considerations:

  • Accuracy: Ensure accurate measurements for both map and ground distances.
  • Units: Always pay close attention to units and convert them appropriately.
  • Understanding: The smaller the denominator in the fractional scale, the larger the scale of the map, and the more detail the map shows.