How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
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Re: percent grade to angle degree
Originally posted by UnregisteredHow do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
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)

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Re: percent grade to angle degree
thanks, you just helped me with my performance assesment for my physics class.
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Re: percent grade to angle degree
Thanks JohnS, your simple explanation is exactly what I needed for my surveying homework.
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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?
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Re: percent grade to angle degree
Originally posted by Larry View PostSo 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?
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.
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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
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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
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Re: percent grade to angle degree
My employer is unwilling to fork out the cash to purchase a couple of "slope meters" so I'm considering the generic alternative of using an angle meter (such as the Johnson Level & Tool 700 Magnetic Angle Locator as a "getmeby". I will be measuring slopes in the 2 to 8 percent range.
How do I convert the angles to get the corresponding slopes for each percent of slope (2, 3, 4, 5, 6, 7 and 8 percent)? It doesn't have to be "NASAaccurate"  obviously since I plan to use an angle gauge. But I'm hoping it will give me a close enough idea as to what percent slope my guys are setting.
Is this even possible or am I wasting my time?
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Re: percent grade to angle degree
Originally posted by That1Guy View PostMy employer is unwilling to fork out the cash to purchase a couple of "slope meters" so I'm considering the generic alternative of using an angle meter (such as the Johnson Level & Tool 700 Magnetic Angle Locator as a "getmeby". I will be measuring slopes in the 2 to 8 percent range.
How do I convert the angles to get the corresponding slopes for each percent of slope (2, 3, 4, 5, 6, 7 and 8 percent)? It doesn't have to be "NASAaccurate"  obviously since I plan to use an angle gauge. But I'm hoping it will give me a close enough idea as to what percent slope my guys are setting.
Is this even possible or am I wasting my time?
As a decimal fraction slope = rise/run = tan(angle). If you want percent multiply the decimal by 100%
Example 4° angle is meaured. Slope = tan(4°) = 0.0699
In percent, this is 6.99% (or about 7%)
In reverse, take the slope in percent and divide by 100 so it is a decimal fraction. Take the arctangent
7% = 0.07
ATAN(0.07) = 4.004° or about 4° with sensible rounding.
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