Applications

You’ve got a USGS 1:24000 “Quad” map that shows the road you’ll drive in on and two ponds you need to survey for Western Toads (Anaxyrus boreas). The road is 0.75 inches from the first pond. How many miles will you walk to get to this site? The pond is roughly round and measures 1.25 inches across. What is the pond’s area in acres? We are going to add scales to our unit conversion skills in order to solve problems like this!

You’ll most frequently use a map scale to figure out how far a distance you see on the map will be on the ground. Calculate this by measuring the distance on the map (you can use an inch or a millimeter/centimeter ruler), and using it as the first factor in a dimensional analysis. The second factor will be the scale. The ground distance (GD) will be in the numerator and the map distance (1) will be in the denominator. (This makes sense because a small distance on the map needs to become a big one on the ground – so we multiply by the GD.) You’ll then use one or more factors to convert from the units you measured on the map (in or cm) to something that makes sense for a ground measurement (mi or km).

What about calculating area using measurements from the map? We’ve got two options. One, convert each of the map measurements individually to ground distances and calculate the area using these ground measurements. Two, calculate the area using the map measurements, and then convert this to a ground area using the map scale SQUARED and the conversion factors for area.