Check my math

1. ## Check my math

Minnesota Dave, and anyone else;

Is my math correct?

We express roof pitches as 6:12, 3:12 12:12 For 12' measured horizontal, how much rise, or fall?

We express grades as % A 10% grade falls away 10' in 100' of horizontal.

Both of these are ratios. We can convert.

Also inclines are expressed in degrees. We can measure an angle, in this case deviation from horizontal with a protractor, but how do we turn that number into percent, or ratio?

A circle 200 feet in diameter has a circumference of 200x Pie, or 3.1416, or 628.32 feet. As a circle has 360 degrees, each degree is 628.32/360 or 1.7453333333333......

Therefore, a 10% grade is 10x1.7453333333333333.......or a 17.4533333333... degree angle.

A circle 24' in diameter has a circumference of 24x3.1416 or 75.3984' As this circle is also 360 degrees, we can divide. 75.3984/360= .20944. therefore a 6:12 pitch is 6/.20944=28.6478 degrees.

I have a new phone. It tells me the angle as a deviation from level. I always need it expressed as ratio, or percent for it to make sense to me.

I understand this won't work very accurately as my units of measure are circular, and these measurements need to be straight.

What is the proper way to convert?

Willie

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## Re: Check my math

Willie,

The math you are doing gives you the length of an arc. If you are looking for the rise of a 10% grade at a distance of two hundred feet it's 10% of 200. What are you trying to calculate? Maybe I'm reading it wrong, but it looks like you are trying to calculate the vertical rise from horizontal at the intersection of that vertical line and a 10 degree arc angle? I think to do that you will have to resort to the old school angle calc's with a sine/cosine table?

Maybe I'm just confused.

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## Re: Check my math

Alternatively you could calc the long side of a 10% triangle with a base (horizontal run) of 200' and a rise of 20' :

20x20 = 400. and 200 x 200 = 40000. and 400 + 40000 = 40400. Square root = 200.9975'

Then do a ratio of long side to rise for a radius of 200' :

200 / 200.99751 = .99503 and ... 20 x .99503 = 19.9007'

So, if my guess at the math is correct the rise of a 10% rise arc angle for a 200' radius is 19.9007'

Clear like frikkn mud ...
Last edited by John Bartley; 11-16-2017 at 08:51 PM.

4. ## Re: Check my math

Originally Posted by Willie B

Therefore, a 10% grade is 10x1.7453333333333333.......or a 17.4533333333... degree angle.

Willie
This part is incorrect.

A 10% grade is a 5.71 degree angle (also a 1.2 pitch roof is 5.71 degrees)

100% grade would be 45 degrees

When you took your 10x1.7453 from your example, it's still a 10 degree angle.

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## Re: Check my math

Willie
You are trying to convert a ratio into an angle and can't do it the way you are attempting to with your use of a circle. What a roof ratio of say 3/12 or 6/12 is in trigonometric terms is the tangent of an angle- or rise over run. If you take a calculator and divide 3 by 12 and take that answer hit the inverse function key- and then the tangent key-you'll get 18.43 degrees. So if you had a slope of 10% that is telling you for a rise of 1 you go out out a ratio of ten. Or again 1 divided by 10 take the inverse tangent of that and get 5.73 degrees. So a 10% slope equals almost 6 degrees.

So if you are holding your phone and it tells you the angle- take the calculator function and enter that angle in degrees and hit the Tangent key -it gives you a value- lets use 45 degrees the tangent is 1 so that is saying for every 1 value UP- you also moved out 1 value which is what a 45 degree angle is one inch or one mile up to one inch or one mile of run produces an angle equal to 45 degrees.

If you are with me so far- let's assume that you tilt the phone and the new angle is 30 degrees- go to the calculator and put in 30 and hit tangent- it comes back as 0.58 if you decide you want to know how far UP that 30 degree angle would be, you pick a distance let's use 10 feet-since it makes the math simple- 10 x .58 =5.8 feet- so your rise is 5.8 feet over a run of 10. You can also do it the other way-you know that you are 5.8 feet high- and want to how far from that point on a wall you would have to go out to give you an angle of 30 degrees 5.8 feet divided by .58 equals ten which again is saying a ratio of 5.8/10

Hope this makes sense if not will give it another shot.

6. ## Re: Check my math

Originally Posted by John Bartley
Willie,

The math you are doing gives you the length of an arc. If you are looking for the rise of a 10% grade at a distance of two hundred feet it's 10% of 200. What are you trying to calculate? Maybe I'm reading it wrong, but it looks like you are trying to calculate the vertical rise from horizontal at the intersection of that vertical line and a 10 degree arc angle? I think to do that you will have to resort to the old school angle calc's with a sine/cosine table?

Maybe I'm just confused.
Hills are expressed as percent grade. A 10% grade is 10' of rise per 100' of horizontal run. In my attempts to calculate grade in percent, i was imagining 10' as a portion of the circumference of a circle 100' in radius. A 100' radius circle would be 628.32feet in circumference. Each increment of one degree or 1/360 of its circumference is 1.74533333333'. a 17 degree tilt would be approximately 29.67 feet of rise per 100' of run, or 29.67% grade.

My son suggests that a 45 degree angle would be 100%, or 12/12 as roofs are described. Divide the angle by 45. 17/45 is 37.777%. I believe he is mistaken.

7. ## Re: Check my math

Originally Posted by MetalMan23
This part is incorrect.

A 10% grade is a 5.71 degree angle (also a 1.2 pitch roof is 5.71 degrees)

100% grade would be 45 degrees

When you took your 10x1.7453 from your example, it's still a 10 degree angle.
Yeah, I got it all wrong. A 17 degree angle is near 30% grade.

8. ## Re: Check my math

I like a pencil and pictures

Also, look at the trig table below (tangent only)

The fraction 4/12 is 0.3333... which is between 18 and 19 degrees.

The fraction 10/100 is 0.1000 which is between 5 and 6 degrees.

The angle always corresponds with the fraction (written as a decimal).

Last edited by MinnesotaDave; 11-16-2017 at 10:49 PM.

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## Re: Check my math

Originally Posted by Willie B

My son suggests that a 45 degree angle would be 100%, or 12/12 as roofs are described. Divide the angle by 45. 17/45 is 37.777%. I believe he is mistaken.
Hmmm .... I think he's correct. A 45 degree angle is an equal rise and run.

10. ## Re: Check my math

Originally Posted by John Bartley
Hmmm .... I think he's correct. A 45 degree angle is an equal rise and run.
I know he's not mistaken about the 100%, and 12/12 being 45 degrees. I just think his dividing the angle by 45 will not yield the correct answer in %.

11. ## Re: Check my math

I like a pencil and pictures

Also, look at the trig table below (tangent only)

The fraction 4/12 is 0.3333... which is between 18 and 19 degrees.

The fraction 10/100 is 0.1000 which is between 5 and 6 degrees.

13. ## Re: Check my math

A little algebra (moving stuff around).

The right hand column I just used the calculator.
On the left I took the 4 digit number from the table.
Basically a calculator is a fancy electronic trig table

Last edited by MinnesotaDave; 11-16-2017 at 11:17 PM.

14. ## Re: Check my math

Originally Posted by Willie B
I too like pencil & pictures now that my 11 year old military spec cell phone died. I'm starting to gain early proficiency with the camera on my new, already obsolete I phone 8. Does this make me a millennial?

15. ## Re: Check my math

Here is a grade-angle chart you can use for checking your trig practice

16. ## Re: Check my math

Originally Posted by Willie B
I too like pencil & pictures now that my 11 year old military spec cell phone died. I'm starting to gain early proficiency with the camera on my new, already obsolete I phone 8. Does this make me a millennial?
Using pencil and paper and then taking a pic is faster than typing anyway

...more understandable too - for me anyway

Was my 17 degree explanation workable for you?

Basically there are always 3 possible spots to write numbers. The angle, the numerator and the denominator.

As long as you have 2 of them, the 3rd can always be found pretty quickly.
Last edited by MinnesotaDave; 11-16-2017 at 11:28 PM.

17. ## Re: Check my math

Thanks guys. I guess i should have failed high school math. ...........Then again, what teacher was going to risk having me in their class a second year?

Willie

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## Re: Check my math

Here's a link to both an online calculator and the formula to convert % of slope to degrees of angle

https://www.calcunation.com/calculat...conversion.php

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## Re: Check my math

Originally Posted by Willie B
Thanks guys. I guess i should have failed high school math. ...........Then again, what teacher was going to risk having me in their class a second year?

Willie
Hey Willie,

I should probably say the same thing as you said above, but ..... every time I have to go to the web or a book to re-learn something I think to myself ... "how often do I use this stuff?" Its a wonder that we can even remember the math terms, never mind how to use them. I enjoyed this thread. It was a math refresher - thanks!

20. ## Re: Check my math

Mrs. B is a first grade teacher. I posed my math question to her. She was no help. She showed me the sort of math, and the sort of students she deals with.

21. ## Re: Check my math

Originally Posted by Willie B
Mrs. B is a first grade teacher. I posed my math question to her. She was no help. She showed me the sort of math, and the sort of students she deals with.
My students love kid snippets videos

22. ## Re: Check my math

Originally Posted by Willie B
Minnesota Dave, and anyone else;

Is my math correct?

We express roof pitches as 6:12, 3:12 12:12 For 12' measured horizontal, how much rise, or fall?

We express grades as % A 10% grade falls away 10' in 100' of horizontal.

Both of these are ratios. We can convert.

Also inclines are expressed in degrees. We can measure an angle, in this case deviation from horizontal with a protractor, but how do we turn that number into percent, or ratio?

A circle 200 feet in diameter has a circumference of 200x Pie, or 3.1416, or 628.32 feet. As a circle has 360 degrees, each degree is 628.32/360 or 1.7453333333333......

Therefore, a 10% grade is 10x1.7453333333333333.......or a 17.4533333333... degree angle.

A circle 24' in diameter has a circumference of 24x3.1416 or 75.3984' As this circle is also 360 degrees, we can divide. 75.3984/360= .20944. therefore a 6:12 pitch is 6/.20944=28.6478 degrees.

I have a new phone. It tells me the angle as a deviation from level. I always need it expressed as ratio, or percent for it to make sense to me.

I understand this won't work very accurately as my units of measure are circular, and these measurements need to be straight.

What is the proper way to convert?

Willie
Trig is where you should be
Last edited by Laggy; 11-25-2017 at 06:26 PM.

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## Re: Check my math

Originally Posted by Willie B
Thanks guys. I guess i should have failed high school math. ...........Then again, what teacher was going to risk having me in their class a second year?

Willie
I have taken a lot of math in my life but it is just like everything else. Use it or lose it. I have forgotten way more math then I would like to admit.

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## Re: Check my math

This might help

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## Re: Check my math

Willie,
If your phone gives you the angle from level in degrees, try this. If the angle is 17 degrees, enter 17 into a calculator then press TAN. Tan is "opposite over adjacent", but forget about that. Sounds like 11th grade trig class (I didn't like it much but took it twice anyway). Tan is really Rise over Run. This I can get my head around. Ok, 17 Enter, TAN, =.3057..., x 100= 30.57. So, 17 degrees drops or rises about 30 1/2 ft along 100 ft. Three strokes on a calculator.

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