converting slope grade to degrees
by lmohara on 10/11/05 at 12:45:05

Hello!

What's the formula to convert a slope grade to degrees? Thanks!

Lisa

Re: converting slope grade to degrees
by Wilfred on 10/12/05 at 00:36:48

If you just want to convert a grade (for example a 100 percent grade) into degrees (in this case 45 degrees), it will help if you understand trigonometry (a branch of mathematics).

The slope or grade of an inclined surface is described by the vertical rise (the height you have climbed) compared to the horizontal run (the horizontal distance you have travelled).

For example, if you travelled a roadway with a 1 in 10 grade, you would have climbed one foot after travelling a horizontal distance of ten feet. The actual length of roadway you would have used would be slightly more, because you are actually travelling along the sloping surface.  This 1 in 10 slope, or 10 percent grade, has an angle of inclination of 5.71 degrees, which can be calculated as shown next.

The relationship between the Angle of inclination, which I will call “a” degrees, compared to the Rise and Run of the slope is as follows:
Tan a = Rise / Run

The website:
http://www.geog.ubc.ca/courses/geog516/talks_2001/slope_calculation.html
gives extensive treatment to this subject.

Re: converting slope grade to degrees
by Robert Fogt on 10/15/05 at 00:43:22

I think I can work up something quickly in Microsoft Excel if that will help.

It is on my to-do list but will be awhile before I have something automated up on the site.

Re: converting slope grade to degrees
by Warren on 10/29/05 at 17:52:16

On my trusty Casio fx-17 Scientific calculator this translates to:
RISE divided by </> RUN equals<=> arctan <arc> <tan>

;)

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