percent grade to angle degree

[Unregistered]

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

[JohnS]

Re: 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?

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)

[Unregistered]

Re: percent grade to angle degree

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

[Unregistered]

Re: percent grade to angle degree

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

[Larry]

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?

[JohnS]

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?

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.

[Unregistered]

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

[Unregistered]

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

[Unregistered]

Re: 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?

14% grade= 14' rise for every

Cos = (√ 100 SQ - 14 SQ ) / 100
Degree = -Cos

[Unregistered]

Re: 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?

18 degree grade what is the angle of degree

[That1Guy]

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 "get-me-by". 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 "NASA-accurate" - 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?

[JohnS]

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 "get-me-by". 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 "NASA-accurate" - 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?

Use any scientific calculator with the tangent and arctangent functions (usually abbreviated TAN and either ATAN or TAN followed by a -1 superscript)

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.

[wildman]

Re: percent grade to angle degree

if i have a 4 to 1 slope what would that be as a percentage

[JohnS]

Re: percent grade to angle degree

if i have a 4 to 1 slope what would that be as a percentage

If rise/run is 1/4, that is 25%