Scale factor

A scale factor is a number which scales, or multiplies, some quantity. In the equation:

$$y=Cx\;$$

$$C$$ is the scale factor for $$x$$. $$C$$ is also the coefficient of $$x$$, and may be called the constant of proportionality of $$y$$ to $$x$$. For example, doubling distances corresponds to a scale factor of 2 for distance.

Applications
Scale factor plays an important role in GIS and cartography. Knowing the scale factor of the map allows the reader to calculate distance and more efficiently guide himself. However, it is important to understand that scale factors are not always accurate in every area of a map due to the distortions of the selected map projection. "Every map of even a portion of the earth involves at least some distortion, some compromise in the representation of the earth’s features ". It is important to note that the map scale depends on the projection used and how the projection distorts the world. While obvious on world or country scale maps, these distortions are minimized on large-scale maps, such as a map of a city. In these cases, understanding scale factor can be very useful in using map information in a relatively accurate manner. For instance, on a 1:24,000 scaled map, the scale factor is 24,000. If a road segment appears to be 2 inches long on the map, you can multiply that by the scale factor to find its distance on the ground. In this case, the road segment would be 48,000 inches or .75 miles long.

Calculations
Here are several useful formulas for determining distance, area, and scale factor. These are simple versions that do not take into account inconsistencies due to map projections.

GD = Ground Distance: the distance between two points in real life MD = Map Distance: the distance between two points on a map SF = Scale Factor

$$GD = MD * SF\;$$

$$MD = GD / SF\;$$

$$SF = GD / MD\;$$

GA = Ground Area MA = Map Area CF = Conversion Factor

$$GA = (MA * (SF ^ 2) )/ CF\;$$