# Calculate m (slope) of a line given the angle in degrees

Hi,

I want calculate the m = slope of a linear line WHEN I already know the angle in degrees of the line.

Here is an example: I calculate with Excel the angle with the following function: =+DEGREES(ATAN(0.0874887)) and I get as result the angle of 5%.

But how do I calculate the value 0.0874887 that is m = slope if I already know the angle of the linear line is 5%?

Thanks

BvU
Homework Helper
You simply convert the angle from degrees to radians. Do you know how to do that ?

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Thanks BvU for your fast response.

Unfortunately I don't know how to convert the angle to radians. Please give me the Excel formula.

Thanks a lot.

Hi BvU,
I got it.

Thanks really a lot.

Hi,
In the above example I have calculated the DEGREE of the slope of the line and not as I have written the percent of the slope.
I have written 5% as the angle of the line. That is wrong. It is 5° !!!

Now I have a new question concerning the slope of a linear line: "How do I calculate the PERCENT of the slope of the line?

Lets assume I have a linear line with a slope of m = 0.05. What is the percent of the slope of the line?

Thanks

pbuk
Gold Member
Lets assume I have a linear line with a slope of m = 0.05. What is the percent of the slope of the line?
0.05 x 100% = 5%.

Hi pbuk,

thanks a lot. How simple.

pbuk
Gold Member
thanks a lot. How simple.
Indeed. If you want whatever you are doing with this in Excel to make any sense I think it would be a good idea for you to relearn the basics of triangle geometry - plenty of resources online.

Indeed. If you want whatever you are doing with this in Excel to make any sense I think it would be a good idea for you to relearn the basics of triangle geometry - plenty of resources online.

You are right and I am already searching for some online courses in geometry and trigonometry.

BvU
Homework Helper
... Please give me the Excel formula.
The excel formula isn't good enough. What if your batteries run out ?
Better to understand what needs to be done! :

You know that one revolution is 2##\pi## and also 360 degrees. So

angle in radians = angle in degrees / 180 ##\bf \times## ##\bf\pi ##
Hi,
In the above example I have calculated the DEGREE of the slope of the line and not as I have written the percent of the slope.
I have written 5% as the angle of the line. That is wrong. It is 5° !!!

Now I have a new question concerning the slope of a linear line: "How do I calculate the PERCENT of the slope of the line?

Lets assume I have a linear line with a slope of m = 0.05. What is the percent of the slope of the line?

You should be aware that percent slope isn't all that unambiguously defined:
it is 'rise over run' but 'run' can be actual distance covered or it can be horizontal distance covered.
So 100 % can be 90 degrees or 45 degrees, respectively b/c and b/a in the figure in the link below.

https://communityviz.city-explained...1/Formulas/Function_library/Atan_function.htm

For small angles the difference is very small:
$$\arctan(0.05) = 0.049958396 \qquad \arcsin(0.05) = 0.050020857$$

and now you know what that is when expressed in degrees ##\ ##

pbuk
Gold Member
You should be aware that percent slope isn't all that unambiguously defined:
it is 'rise over run' but 'run' can be actual distance covered or it can be horizontal distance covered.
So 100 % can be 90 degrees or 45 degrees, respectively b/c and b/a in the figure in the link below.
Can you provide any authoritative source for the 90° interpretation? As far as I am aware this is not an ambiguity, it is simply wrong. It is not even a USA/rest of the world thing as you can see from the US Geological Survey and (can't find an international reference...).

BvU
Homework Helper
In short: No. I just copied the warning.
Usually a “25% slope” means that b/a = 0.25 in the figure above...
(Be aware, however, that sometimes people use the term percent slope to mean b/c.##\quad##...)

To me it makes sense, because the 45 degree interpretation involves hefty surveying

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pbuk
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