Rafter Length Calculations Using Span And Pitch Only

 
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Old 11-18-2012, 07:14 AM   #1
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Rafter Length Calculations Using Span And Pitch Only


I know that it is possible to calculate the length of a rafter from the plumb cut at the ridge to the plumb cut at the birds mouth using only the desired pitch and the span of the building.

I used to have a square which detailed numbers for common pitches of rafters which was multiplied by the span of the rafter or half the span of the building to figure out the plumb to plumb dimensions required.

I was just wondering if there was a mathematical formula that can be used to figure out the numbers which were detailed on my square.

maths has never been easy for me to learn so tbh i dont want to sit and read a load of sh** i dont need.

Is Pythagorean theorem what I need???
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Old 11-18-2012, 07:27 AM   #2
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Re: Rafter Length Calculations Using Span And Pitch Only


Yes you can and yes thats what you need

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Old 11-18-2012, 07:44 AM   #3
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Re: Rafter Length Calculations Using Span And Pitch Only


A construction master from the home depot would probably be your best friend then. Make it easy on yourself if math isn't your gig. You don't want to be manually doing the calculations.
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Old 11-18-2012, 08:22 AM   #4
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Re: Rafter Length Calculations Using Span And Pitch Only


pythagorean theorem wont cut it. I would need the height of the ridge as well as the span of the building to use that. it is only very rarely i would need to perform the calculations as most of the work i carry out is for a large engineering firm so i work from their drawings. i only ask because i just built a small timber frame extensionon on a friends house and allthough we managed to finish the roof i would like to have a better understanding of the maths in case the issue arises again. not sure what u mean by home depot ken?
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Old 11-18-2012, 08:25 AM   #5
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Re: Rafter Length Calculations Using Span And Pitch Only


Quote:
Originally Posted by blbm
pythagorean theorem wont cut it. I would need the height of the ridge as well as the span of the building to use that. it is only very rarely i would need to perform the calculations as most of the work i carry out is for a large engineering firm so i work from their drawings. i only ask because i just built a small timber frame extensionon on a friends house and allthough we managed to finish the roof i would like to have a better understanding of the maths in case the issue arises again. not sure what u mean by home depot ken?
Kent means you can buy a construction master calculator at the depot. They sell them. You will find it very useful for many things. You do have to put in some time learning how to use it.
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Old 11-18-2012, 08:38 AM   #6
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Re: Rafter Length Calculations Using Span And Pitch Only


very simple math and no need for a construction master calculator, just a simple calculator with square and square root function.

Figure the hyp of the given Run and rise using Pythagorean theorem (A^2 + B^2 = C^c) then divide that by the unit run and multiply the result by the total run in inches to get the common rafter line length.

8:12 pitch roof with with a span of 120". Adjusted total run =59.25"

Unit run = 12"
Unit rise= 8"
Using Pythagorean theorem: hyp = sqrt 144+64,

Hyp =14.42/run = 1.202

1.202 x total run =71.2185 = 71 3/16" rafter length

Rafter tail @24" projection = 22.5" x 1.202 = 27.045 =27 1/16" rafter tail

Total rafter length 71 3/16" + 27 1/16 = 98 1/4"

common difference @16" OC = 16 x 1.202= 19.23 = 19 1/4"

jacks= 71.2185 - 19.23 = 1st 51.98" 2nd 32.76", 3rd 13.53"

Hip rafter is the same only use 288 (16.97 x 16.97)as the squared run instead of 144

hip rafter LL= 18.76/12 x 59.25" = 92.6357 = 92 5/8"

Don't checK my math. I did this pretty quick just as an example ;-)
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Old 11-18-2012, 08:38 AM   #7
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Re: Rafter Length Calculations Using Span And Pitch Only


ok thankyou i have found a couple of android apps that seem to do similar things i will take the time to sit andlook at them. im from the uk we dont have home depot
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Old 11-18-2012, 08:47 AM   #8
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Re: Rafter Length Calculations Using Span And Pitch Only


Quote:
Originally Posted by blbm
. im from the uk we dont have home depot
Now it makes sense. I couldn't figure why you never heard of home depot.

Build calc imo is the best app for this. Can't go wrong for $20....or pounds....or whatever it is where you are. Is it rubles now?
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Old 11-18-2012, 08:50 AM   #9
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Re: Rafter Length Calculations Using Span And Pitch Only


Quote:
Originally Posted by dave_k
very simple math and no need for a construction master calculator, just a simple calculator with square and square root function.

Figure the hyp of the given Run and rise using Pythagorean theorem (A^2 + B^2 = C^c) then divide that by the unit run and multiply the result by the total run in inches to get the common rafter line length.

8:12 pitch roof with with a span of 120". Adjusted total run =59.25"

Unit run = 12"
Unit rise= 8"
Using Pythagorean theorem: hyp = sqrt 144+64,

Hyp =14.42/run = 1.202

1.202 x total run =71.2185 = 71 3/16" rafter length

Rafter tail @24" projection = 22.5" x 1.202 = 27.045 =27 1/16" rafter tail

Total rafter length 71 3/16" + 27 1/16 = 98 1/4"

common difference @16" OC = 16 x 1.202= 19.23 = 19 1/4"

jacks= 71.2185 - 19.23 = 1st 51.98" 2nd 32.76", 3rd 13.53"

Hip rafter is the same only use 288 (16.97 x 16.97)as the squared run instead of 144

hip rafter LL= 18.76/12 x 59.25" = 92.6357 = 92 5/8"

Don't checK my math. I did this pretty quick just as an example ;-)
I was steering him in that direction because he said right up front, I don't have a need for math and not good at it. That **** you posted is worthless to him. You just short circuited his brain. He needs simple.
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Old 11-18-2012, 09:01 AM   #10
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Re: Rafter Length Calculations Using Span And Pitch Only


I suggest you buy a book on framing and study it. Most basic carpentry books will walk you through how to calculate out and cut rafters. There's a lot more you need to know than just figuring out the length of your triangle. There's several methods to come up with the answer as well. I prefer the framing square method, it's fast and easy, and my stainless steel framing square usually works a lot better than my calculator out in the rain.

I just realized, do carpenters use metric in the UK? I always thought Canadian carpenters used metric along with everything else until I walked into a hardware store there and saw all the tape measures and speed squares in feet and inches.
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Old 11-18-2012, 10:26 AM   #11
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Re: Rafter Length Calculations Using Span And Pitch Only


Quote:
Originally Posted by Kent Whitten View Post
I was steering him in that direction because he said right up front, I don't have a need for math and not good at it. That **** you posted is worthless to him. You just short circuited his brain. He needs simple.
reread his post. That **** I gave him was exactly what he asked for.

Quote:
Originally Posted by OP
I was just wondering if there was a mathematical formula that can be used to figure out the numbers which were detailed on my square.
I have the CM trig calculator and one on my iphone, they are good rugged calculators but truth is I can figure out rafters just as fast on those calculators using LL ratio than inputting the fractional numbers and I can do more with the results.

If I was going to recommend a $100 calculator I would recommend the Chappell square http://chappellsquare.com/product/traveler-1218/ which can do everything the CM calculator can do and a lot more, in metric and imperial, no batteries required and you get a hell of a nice square to boot. hands down the best roof calculator in the world today!
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Old 11-18-2012, 10:26 AM   #12
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Re: Rafter Length Calculations Using Span And Pitch Only


Or you could buy the Construction Master App and use it. I think I paid $20 for mine. I love it.
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Old 11-18-2012, 10:42 AM   #13
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Re: Rafter Length Calculations Using Span And Pitch Only


Pythagorean theorem is going to cut it...What you need is a carpenter who understand the math you dont. That calaculator will save you some thinking but if you know the pitch/slope and the building width/rafter span you can figuire it out like Dave K showed you.

Everybody wants and APP or something else to do something they are too lazy to learn. One day the power will be compromised and no one will know how to communicate.
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Old 11-18-2012, 11:02 AM   #14
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Re: Rafter Length Calculations Using Span And Pitch Only


Quote:
Originally Posted by blbm
im from the uk we dont have home depot
You can buy them on eBay or amazon as well. Construction master 5 is the latest calculator. While its good to know everything in your head, this thing is well worth it. It does a lot of different things to make it easier.
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Old 11-18-2012, 11:20 AM   #15
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Re: Rafter Length Calculations Using Span And Pitch Only


Dave k's post decribes it well, but it might help to break it down to smaller packets of info.

Basically, it's all about ratios. If you have the roof pitch in rise/run, you can get a multiplier to get the slope dimension. All you need is the Pythagorean theorum to get multiplier. The multiplier wil just be the slope divided by the run. Use your known pitch/slope to get that value.

It usually helps to visualize if you draw out two triangles with the knowns, & unknowns 1st.

Using Dave's example of 8/12 pitch or slope, to get multiplier, you get:
8x8 = 64
12x12 = 144
144+64 = 208
sqrt of 208 = 14.42 = slope

Now you just divide the slope dimension by the run to get your multiplier.
14.42/12 = 1.20

1.20 is then multiplied x the needed run, after taking out your ridge.

The above is all you need, but:

In trig terms, this is the secant value. It's the hypotenuse divided by the adjacent side (or in carpenter's use it's the run). It is also equal to:
1/cosine of the slope angle. If using a basic math calculator, you just do somthing like this:
say your slope is 30 degrees, then:
1/cosine 30 = 1.1547
Then you just multiply that x your run dim to get your slope/rafter dim.

For me it's easier to visualize as ratios instead of trig values.

I don't know if this helps, but I figure it's was worth a shot.
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Old 11-18-2012, 11:46 AM   #16
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Re: Rafter Length Calculations Using Span And Pitch Only


When calculating the length of a rafter you are actually finding the length of the hypotenuse (long, slope side) of a right triangle.

A right triangle is any triangle that has one corner that is exactly 90 degrees. In the rafter example that corner is the corner where the rise and the run meet.

There are three important components that make up that triangle;

- The run (distance along the floor)

- The rise (distance the rafter will rise above the plate)

- The pitch (the angle at which the rafter is rising)

The rise and run are the two short legs of that triangle and the pitch is the angle the third side is bisecting those two legs.

The beauty of the construction calculators is that you only need two of those three components to find the length of that rafter.

Once that concept takes root, you can figure out the most complex layout equations that are common to the construction industry. Even a cabinetmaker uses this on a nearly daily basis.

Basic high school math is a very powerful tool.
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Old 11-18-2012, 11:54 AM   #17
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Re: Rafter Length Calculations Using Span And Pitch Only


Quote:
Originally Posted by dave_k View Post
reread his post. That **** I gave him was exactly what he asked for.
Pythagorean theorem to this guy is French. All that calculation that you posted, all of the detailed "how to" is useless to him, as he states

Quote:
Originally Posted by blbm View Post

maths has never been easy for me to learn so tbh i dont want to sit and read a load of sh** i dont need.
You gave him the load of **** he doesn't need, as he states

Quote:
pythagorean theorem wont cut it.
before you even posted.
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Old 11-18-2012, 12:41 PM   #18
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Re: Rafter Length Calculations Using Span And Pitch Only


Back in the late 1980s, and early 1990s I began as a framing carpenter. This was before I had ever used a computer for anything, so when I wanted to document how I learned the mathematical side of framing, I had to draw it on paper.

Here is a scan of what I wrote down regarding calculating the main common Rafter.
Attached Thumbnails
rafter length calculations using span and pitch only-main-common-rafter.jpg  

Last edited by wallmaxx; 11-18-2012 at 12:57 PM.
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Old 11-18-2012, 01:28 PM   #19
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Re: Rafter Length Calculations Using Span And Pitch Only


Quote:
Originally Posted by Railman View Post
I don't know if this helps, but I figure it's was worth a shot.
Joe
Thank you Joe. I did kinda bang that off in a hurry, it's a beautiful day here and I wanted to get out and enjoy it ;-)

Quote:
Originally Posted by Gus Dering
Basic high school math is a very powerful tool.
Absolutely and you're pretty limited in what you can do as a carpenter without basic math.

You can't get into a carpentry apprenticeship up here without grade math and many employers including our program require a high school diploma with grade 11 math. The math we are talking about in this thread is generally covered before you get to grade nine. Not the trig but the rest of it.

That being said I've been to training workshops in the USA and I understand it's not hard to graduate from the public school system without any knowledge of math. We have the same problem up here but it's not a bad. I have a group of carpenters that have finished their apprenticeship ut failed the final exam. They all failed on the math portion of the exam and roof framing. You just have to know this stuff to be a carpenter.
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Old 11-18-2012, 01:33 PM   #20
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Re: Rafter Length Calculations Using Span And Pitch Only


Quote:
Originally Posted by dave_k View Post
Thank you Joe. I did kinda bang that off in a hurry, it's a beautiful day here and I wanted to get out and enjoy it ;-)

Absolutely and you're pretty limited in what you can do as a carpenter without basic math.

You can't get into a carpentry apprenticeship up here without grade math and many employers including our program require a high school diploma with grade 11 math. The math we are talking about in this thread is generally covered before you get to grade nine. Not the trig but the rest of it.

That being said I've been to training workshops in the USA and I understand it's not hard to graduate from the public school system without any knowledge of math. We have the same problem up here but it's not a bad. I have a group of carpenters that have finished their apprenticeship ut failed the final exam. They all failed on the math portion of the exam and roof framing. You just have to know this stuff to be a carpenter.
All throughout my first year of trade school, we had to take a math class separate of any construction related course. Math probably made up 75% of first year. I was appalled at the amount of people there that couldn't add fractions or do a simple ratio and proportion.

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