# Calculating Geodetic Distance

There are many tools in AutoCAD for measuring distances.  With features like Object Snap, it is a simple matter to get a very precise number of units between any two points.  But is this precise measurement accurate?  As I concluded in a  tutorial on Accuracy vs. Precision several years ago, it is sometimes better to be approximately correct, than precisely wrong.

Here are the differences between precision and accuracy, in a nutshell:

Precision is determined by how finely your measuring tools can split hairs. For instance, a grade-school ruler marked in sixteenths of an inch provides less precision than a vernier caliper graduated in thousandths of an inch.

Accuracy is determined, in part, by knowing exactly what you are measuring, and how to measure it.  This becomes more important as we routinely import base map data from a variety of sources.

To accurately measure long distances, you need to know what projection your base map is in , and you need to use a tool that can interpret this projection. Otherwise, you will get a very precise, but inaccurate number.  This is because it is impossible to depict features from the (nearly) spherical surface of the earth onto a flat sheet of paper (or computer screen), without introducing some form of distortion.  Different projections trade-off different types of distortion, for different purposes – for more information on this complex topic, here is a very well written and thoughtfully illustrated introduction to map projections . Most AutoCAD measuring tools, such as Distance, calculate the difference between points using simple coordinate geometry.  They measure the projected map distance, not the real distance that map projection represents over the curved surface of the earth.  This is often close enough for a site map of a few acres, or even a road layout over several miles.  However, if you need to know (for example) the precise distance between microwave relay towers that are many miles apart, you need a tool designed to mathematically correct for the distortion introduced by the map projection.  The real distance betwen mapped points is called the Geodetic distance, and much more advanced mathematics are required to calculate it from a projected map.

The Geo Distance measuring tool in Map 3D, (also available in Civil 3D), calculates Geodetic distance.  It resides on the Analyze tab, Geo Tools panel of the Map 3D ribbon: This tool can also be launched using the actual AutoCAD Map 3D command:  MAPDIST. Just like the AutoCAD  Distance command (DIST), MAPDIST prompts for a first and second point.  It then calculates the actual distance between the points, using the mathematics that were used to create the map projection, and responds with accurate distance and azimuth data, as well as X and Y deltas.

In order to perform this calculation, the tool needs to know what projection the map is in.  This means that the proper coordinate system needs to be assigned to the drawing. How AutoCAD Map 3D manages coordinate systems and map projections is a complex topic, covered in detail in our book A Practical Guide to AutoCAD Map 3D 2012, and in the software help files.

Many other factors can influence accurate measurements between two points on a map, chiefly topography and elevation. Elevation differences certainly add to the distance between two points, and as an alignment traverses hills and valleys, vertical curves add to its length, but an accurate geodetic distance provides a good foundation.

When I studied cartography in the mid-1980s, I learned how to perform calculations like this manually.  Even with the benefit of a sophisticated calculator, this was a tedious endeavor.  It gave me great appreciation for the work of early cartographers in creating maps by hand.  Now, we have tools built right into the software to make it easy.  However, if we don’t know they exist, or how to use them properly, they don’t do much good.  If you are curious about Geodetic (or Geodesic) mathematics, here is what Wikipedia has to say about it.  I encourage you to explore it further.