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#1
03-05-2008, 07:14 AM
 Unregistered Guest Posts: n/a

How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
#2
03-05-2008, 12:01 PM
 JohnS Double Ultimate Supreme Member Join Date: Dec 2007 Location: SE Michigan, USA Posts: 9,225 Rep Power: 18
Re: percent grade to angle degree

Quote:
 Originally Posted by Unregistered How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
Make sure it is the ratio of vertical rise to the horizontal run, not the slant length, Then angle = arctan(rise/run).

In this case, express as the percent as a decimal and plug in

angle = arctan(0.14) = 7.97°

(If it is rise/slant_length, use the arcsin function)
#3
10-08-2008, 01:43 PM
 Unregistered Guest Posts: n/a
Re: percent grade to angle degree

thanks, you just helped me with my performance assesment for my physics class.
#4
11-11-2008, 12:32 PM
 Unregistered Guest Posts: n/a
Re: percent grade to angle degree

Thanks JohnS, your simple explanation is exactly what I needed for my surveying homework.
#5
07-30-2009, 05:14 PM
 Larry Guest Posts: n/a
Re: percent grade to angle degree

So a 100% grade is a 45 degree climb. As the grade goes from zero to 100, the angle goes from zero to 45 degrees. Is that relationship linear? If it was, then 1 degree would be 1/45 of 100, or 2.222%.

Or did I miss something? Also, what's a 50 degree grade (assuming we might find it in, say, San Francisco?
#6
07-30-2009, 06:32 PM
 JohnS Double Ultimate Supreme Member Join Date: Dec 2007 Location: SE Michigan, USA Posts: 9,225 Rep Power: 18
Re: percent grade to angle degree

Quote:
 Originally Posted by Larry So a 100% grade is a 45 degree climb. As the grade goes from zero to 100, the angle goes from zero to 45 degrees. Is that relationship linear? If it was, then 1 degree would be 1/45 of 100, or 2.222%. Or did I miss something? Also, what's a 50 degree grade (assuming we might find it in, say, San Francisco?
The relation is nonlinear, angle = arctan(rise/run)
or rise/run = tan(angle)

tan(1°) = 0.01746 = 1.746%
It is pretty linear for small angles (under 6°) but gets quite non linear for larger angles.
tan(50°) = 1.19175, the rise is larger than the run. You might find it on a roof, probably not on a road.
#7
07-31-2009, 02:18 PM
 Unregistered Guest Posts: n/a
Re: percent grade to angle degree

Yes. It's clear if you look at the tangent graph. Leaving zero it moves in a direction up and to the right. But it's rate of climb increases as it goes, passing 1 at 45 degrees, and heading for straight up and infinity at 90 degrees.

Thanks for the comeback,
Larry
#8
05-24-2010, 06:43 PM
 Unregistered Guest Posts: n/a
Re: percent grade to angle degree

Thanks for the conversion formula. I ride a road bike and have wondered when fellow road bikers tell their stories of how hard the hill they just rode was and it was a (XX) % grade just what angle of rise it was, thanks.

Bob
#9
07-20-2011, 07:46 PM
 Unregistered Guest Posts: n/a
Re: percent grade to angle degree

Quote:
 Originally Posted by Unregistered How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
14% grade= 14' rise for every

Cos = (√ 100 SQ - 14 SQ ) / 100
Degree = -Cos
#10
08-14-2011, 04:32 PM
 Unregistered Guest Posts: n/a
Re: percent grade to angle degree

Quote:
 Originally Posted by Unregistered How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
18 degree grade what is the angle of degree

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