percent grade to angle degree

How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?

[JohnS]

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)

thanks, you just helped me with my performance assesment for my physics class.

Thanks JohnS, your simple explanation is exactly what I needed for my surveying homework.

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?

[JohnS]

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.

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

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