At first glance the rafter table stamped into the side of a framing square can be a bit tricky to understand. But it is not so difficult once you get the hang of it. The first thing to understand is that it is based on roof pitches expressed in amount of rise (vertical) over a 12 inch run (horizontal). The table is constructed with values underneath the inch markings on the top of the square. In the picture above I have highlighted in green the rafter length for a 16/12 roof pitch. Because the rafter forms the long side of the the right triangle it needs to be 20 inches for every foot of run, or 20 feet for every 12 feet of run.
The math behind this is pretty simple. Using the pythagorean theorem we know that the square root of the hypotenuse (long side) of a right triangle is equal to the sum of the square of the sides. There a few right triangles where the math works out smoothly. a right triangle with sides of 3 and 4 will have a hypotenuse of 5. (3x3)+(4x4)=5x5. In the case of a 16/12 slope you can see that it follows the same ratio but is just 4 times bigger so the long side will be 5x4or 20.
It gets a bit more complicated when you get to hip or valley rafters. Because they are at a 45 degree angle to regular rafters they have to be longer. You can use the second line of the table to determine their length, or you could also use the pythagorean theorem again, but lengthen the horizontal dimension by 1.414 times since it is now the hypotenuse of a right triangle with even sides (look down at the roof from above to see this).
The next thing the rafter table shows is the difference in length for jack rafters. Jack rafters are those that meet either a hip or a valley rafter. They start out being the same length as regular rafters - so you use the common rafter table to determine this length - but as they work their way along the hip or valley they get shorter and shorter. The "difference in length of jacks" row shows how much shorter each one will be than the previous one based on either a 16 or 20 inch spacing.
The final thing the rafter table shows is how to cut the bevel on the ends of the angled rafters (hip, valley, jack). This is the bevel looking from above. To do this set the square along the top of the rafter with the 12 inch mark on one leg at the end point of the rafter and the "length" given by the rafter table on the other leg the edge of the rafter. Drawing a line from the end point of the rafter will give you the angle you need to cut.
In measuring rafters you need to keep a few things in mind. First is the thickness of the ridge rafter and the top plate. Neither should be included in your calculation of run. In other words, measure run from the inside of the wall and the outside of the ridge rafter. The second thing is that you don't want to have to measure and layout each rafter individually. Make one which fits and then use it as a pattern for all the others. Check the fit first at a few different places as your measurements may be a bit out or you may have a wall which is not quite square to the ridge.
Comments (13)
How do i convert pitch or grade to degrees. Thanks
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Pitch is usually noted as rise over run (5/12 for example). Using a bit of trigonometry we can find the angle. The tangent of an angle of a right triangle = the opposite side over the adjacent side. This is the same as the pitch. To convert the tangent to an angle, we take the arctangent. So for a pitch of 5 in 12 we are looking for the arctangent of 0.41666 which equals 22.6 degrees. Use a computer or calculator to do this. But in case you don't have one available, here are the pitches converted to angles:
Posted by Michael Stannard | June 21, 2007 1:20 AM
Posted on June 21, 2007 01:20
If your laying out your lines on a fountation or floor you want to have a square line to pull all your mearsurements off of. We call it three four five. There a mathmatical way of doing it. I just can't remember. Like if you have one line thats 40 feet 4 inchs and another line thats 25 feet 5 inches. How do you find the number that makes thoughs lines square to eachother?
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The Pythagorean Theorem says that for a right triangle (that is a triangle with one corner which is 90 degrees), the sum of the squares of both sides is equal to the square of the hypotenuse (the longest side). So with a 3-4-5 triangle squaring both sides and adding gives (3x3)+(4x4) = 25. 25 = 5x5 of course. The measurements you give are a bit difficult to do in your head, but a calculator gives (40.333x40.333)+(25.416X25.416) = 2272.784 so the long side will be 47ft 8in. You are better off marking one side at 24 ft, the other at 32 ft and measuring the diagonal. It should be 40ft. 3 yards, 4 yards, 5 yards.... Hope that helps. Simplifying the problem is easier than doing the complicated math. -Jack
Posted by Chris | August 17, 2007 2:12 AM
Posted on August 17, 2007 02:12
In measuring rafters you need to keep a few things in mind. First is the thickness of the ridge rafter and the top plate. Neither should be included in your calculation of run. In other words, measure run from the inside of the wall and the outside of the ridge rafter.
This information is not correct. There will be most often a Difference in the thickness of the ridge board and the wall plate width. The correct way is to measure the run from the outside of the wall to the center of the span, then subtract 1/2 the thickness of the ridge board.
Posted by Ray Trawick | August 28, 2007 3:18 PM
Posted on August 28, 2007 15:18
Thanks guys. I am a carpenter by trade. I live in alaska and about to begine building my retirement home in the wild. I am 42 years old. I have been in the field for 22 years. There is no power where I am at, so it's back to the basics. This was a great refresher course for me.Funny what you forget when don't use it.
Scott G.
Posted by Scott Gladieux | January 15, 2009 11:17 AM
Posted on January 15, 2009 11:17
I'm having trouble figuaring out the room size from what you are describing? If it is a 6/12 what size is the room?
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6/12 refers to the roof slope. Size of the room may or may not apply. Measure the length from the side of the ridge to the plate. Then add what you need for eaves. -Jack
Posted by Buck B. | March 21, 2009 4:56 AM
Posted on March 21, 2009 04:56
how do you determine location and length and angle cuts on valley rafters when you have 2 different intersecting roof pitches? Example: main roof is 10/12, and opposing gable is 11.25/12.
Posted by Ed Grossman | August 31, 2009 10:08 AM
Posted on August 31, 2009 10:08
I'm 56 years old. Decently educated. I worked as a surveyor for 15 yrs and now build custom houses for almost 20 yrs.Until recently I have never new what all the numbers on a framing square were! I am now working with a young fella 35 who knows more about a framing square than I ever did. Both of us are wondering, if there is a book, just explaining the theories of a framing square. Thanks
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Sure, look for "A Practical Treatise on the Steel Square" by Fredrick Thomas Hodgson. It is quite old, but things have not changed since then. -Jack
Posted by potts | November 7, 2009 11:59 PM
Posted on November 7, 2009 23:59
I was working with a 8/12 slope for my rafters. As mention of the inch marks, and below is the length of hypotnuse for the 8/12 is 14 42. Is that 14.42 inch?
As of the 18/12 coming out to be (from your 16/12 picture) 21 63 for the 18/12 that is 21 point 63 hundreths?
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There are no units associated with that number. If you are measuring your run in inches then that is the factor you will multiply by so the result will be in inches too. Same would go for feet, meters or miles.
The number for 18/12 is indeed 21.63.
-Jack
Posted by Robert Timmermann | December 1, 2009 9:49 AM
Posted on December 1, 2009 09:49
Help please - i have the measurments for the common rafters BUT where at the birds mouth to where at the ridge angle cut do i measure?
Thanks for the help.
Posted by Michel Mitchell | December 14, 2009 1:55 AM
Posted on December 14, 2009 01:55
Simply follow this basic pythagorean for any pitched roof .1-12 for the hip: (hip must be supported On a framing square it's X/17 vs X/12 (X=roof pitch)
Use Rafter RUN X Coeffient for HIP:
1/12: sq.rt. 145 = 12.04
2/12 148 = 12.17
3/12 153 = 12.37
4/12 160 = 12.65
5/12 169 = 13
6/12 180 = 13.42
7/12 193 = 13.89
8/12 208 = 14.22
9/12 225 = 15
10/12 244 = 15.62
11/12 265 = 16.28
12/12 288 = 17 (sq.rt of 3 @ 45 degrees)
And for the Mountain Climbers:
13/12 313 = 17.7
14/12 340 = 18.44
15/12 369 = 19.21
16/12 400 = 20
17/12 433 = 20.81
18/12 468 = 21.63
19/12 505 = 22.47
20/12 544 = 23.32
21/12 585 = 24.19
22/12 628 = 25
23/12 673 = 26
24/12 Figure it out Mansart/Wall/Steeple Men
Posted by Handyman | February 5, 2010 7:17 AM
Posted on February 5, 2010 07:17
Hi, I'm building an A-frame cottage.24ftx24ft the roof pitch is 18/12, using your calculations..(Thank-you)
The angle is 18/12 = 56.3 degrees
and the hip is 18/12 468 = 21.63
What my question is ... What is the angle of my cuts for the rafter.
floor angle:?
peak angle: ?
Any help is appreciated,
Julie
If I understand you correctly, the angle at the peak is 56.3 and the angle at the floor would be 90 - 56.3 = 33.7 degrees. -Jack
Posted by Julie | April 5, 2010 3:50 PM
Posted on April 5, 2010 15:50
I need to cut an angle for my pitch of 1 and 12 for a 21 foot span. what is the angle cut on the end of the rafter which is being attached to the header?
Thanks in advance!
Keith
Posted by Keith W. | May 3, 2010 11:39 PM
Posted on May 3, 2010 23:39
I was just wandering if the common rafter conversions could be used to also layout steps.If not what would be the procedure using the framing or speed square.
Posted by Joe Hickman | May 17, 2010 7:11 PM
Posted on May 17, 2010 19:11