# If the Earth was flat, what unit of measurement would distances between geographic points be represented as?

A whole lot of abstraction- given two longitude/latitude points given from a GPS, I'm using the Pythagorean distance formula to find the distance between them. What unit of length would the distance be? Kilometers? Miles?

## 1 Answer

Just like any other function, you will get out the same unit of measurement you put in. In this example you are using lat/long and so will therefore get the distance between your two points (the hypotenuse) in degrees. The number of kilometers/miles/inches/whatever that the output corresponds to depends entirely on where on the surface of the earth the hypotenuse lies.

Also, it does not really matter in this instance that you are "pretending" the earth is flat. Along that note, if the earth was flat we wouldn't use lat/long as, again, those are ellipsoidal (angular) measurements. This is why we have map projections with grid based (cartesian) coordinate systems.

• +1 Re your remarks on projections: the question can be understood as asking how to compute the scale of a Plate Carree projection. – whuber Oct 4 '12 at 15:59