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

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• Francis Bacon
Thanks again for your help.In summary,To calculate the slope of a linear line, you need to know the angle of the line in radians. To do this, you need to convert the angle to degrees and then multiply by 180 degrees.

#### Francis Bacon

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

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

Francis Bacon said:
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.

Francis Bacon said:
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.

pbuk said:
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.

Francis Bacon said:
... 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 ##
Francis Bacon said:
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 ##\ ##

BvU said:
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...).

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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BvU said:
To me it makes sense, because the 45 degree interpretation involves hefty surveying
Absolutely. Whether you are talking about cartography, architecture or setting out e.g. plumbing, you are working to a horizontal datum. So I think it is not good to introduce doubt: run is always horizontal and rise is always vertical.

• BvU