# What is the "57.29578" that ArcGIS uses in Aspect calculation?

ArcGIS Desktop Help on How Aspect works explains the calculations used, but introduces the for me magic number of 57.29578:

``````aspect = 57.29578 * atan2 ([dz/dy], -[dz/dx])
``````

Where does this number come from and what does it stand for?

• It took me a while and some research to figure out what was going on, so I thought I'll post a question-answer here, maybe it'll help someone :) Apr 22, 2017 at 1:14
• Nice one, I remember the number 1.852 from mapping software I learnt from as a student. Realizing what it was was very educational and provides a mental shortcut that I use still. Apr 22, 2017 at 5:40
• Cool! Had to look that one up too, but it's great to see all these numbers making sense: 1.852 -> en.wikipedia.org/wiki/Nautical_mile Apr 22, 2017 at 15:26

In a GIS aspect is generally shown in radians.

`57.29578` is 1 radian in degrees - ArcGIS is using this number when converting to radians.

A simple way to remember how to convert from degrees to radians and vice versa, is to keep in mind that 180° = π rad (check out the corresponding section on Khan Academy) - therefore:

Here's a great visualization that explains this relation well: (Credit - Lucas V. Barbosa - Own work, Public Domain)

And here's some python code for converting one way and the other:

``````import math

# pi radians = 180 degrees -> 1 radians = 180/pi degrees

``````print(radians_to_degrees(1))