I am working on a shed (12x12, 7.5 tall). I have done a fair bit of amateur framing before, so it’s coming along well. However, I need to make the rafters, and I want to seek math guidance here. Despite working in a STEM field, geometry makes my head spin.
I want a 4 foot peak with 6 inches of overhang. So, applying pythagorean, I get 6^2 + 4^2 = 52, square root of 52 = 7’ 2 3/8", + 6" overhang = 7’ 8 3/8" total length of one side of the roof, and therefore what I should be cutting. So the first question is whether or not my math holds up.
OK, the part that I struggle with: Each end of the rafter needs to be cut at the appropriate angle so that at the peak the two will make an appropriate miter, and at the eave will have a neat, plumb line. I believe that this will be the same angle, correct? What is that angle?
Finally, I want to “Birds mouth(?)” where the rafters rest on the top plate (thus I plan to use 2x6 for the rafters, even though it isn’t really necessary). Is my best bet to trace the profile of the top plate on the rafter and cut that, or is there a way to calculate the location and angle of the bird’s mouth?
Sorry for the amateur questions, but any help (and unsolicited advice) is welcome.
FWIW, I have a pretty solid set of tools, ranging from miter saw to framing nailer.
The math to figure out the angle is your old sine, cosine, and tangent rules. Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. You could use any one of those.
sin X = 6 / 7.21
cos X = 4 / 7.21
tan X = 6 / 4
Using the last one:
tan X = 6/4 = 1.5
INV TAN of 1.5 = 56.3 deg.
INV SIN (6/7.21) and INV COS (4/7.21) will give you the same answer.
That’s the angle between the rafter and a plum line. You will need to subtract that from 90 to get the angle to cut on your chop saw.
90-56.3=33.7 deg,
So set your chop saw to 33.7 deg and use that to cut the ends of your rafters.
The same angles will be on your birdsmouth. You can use a square using the same 6/4 ratio to mark the birdsmouth on the rafter. The location will be at the 7’ 2 3/4 " mark on the rafter.
This isn’t a very good picture but I hope it will get the point across.
Of the two methods, even for a STEM guy, there a reason the speed square and blue book are found on every construction site. Those job specific tools are faster, more accurate and more goof proof than the most elaborate “detached” calculations.
Use the calculator that Sicks Ate linked to. You have to take into account a variety of other things, like the depth of the birdsmouth, the dimensions of your rafter lumber and the thickness of your ridge board to get it all right. That calculator covers it all, in a way that simplifies things.
I have a speed square, but I never learned how to use it. Then, I have never needed to do rafters before, just remodeling and finishing a few basements.
Mine has been used 99.9997% of the time to mark straight lines for cuts…the rest it’s been used for what it’s actually really good for, and that’s cutting rafters
The speed square (or a rafter square sometimes) is the way its done on site. Usually a standard roof pitch is used such as 8/12, and the speed square lets you mark out your cuts as you need then.
If you go with a 52" rise instead of four feet you get a nice clean 8/12 pitch and maintain your 6" eave. The speed square lets you mark out your rafter cuts at the proper angle quickly. A rafter square layed on 8 and 12 will give you the same angle. That gives you a rafter length of 93 3/4" long to short (think parallelogram). You have to take a horizontal 1.5" off the rafter for fascia or let your eave grow to 7.5 inch. A birdsmouth will drop the final height a couple inches but won’t effect your angles
The fool proof method is to draw the whole deal out on a nice fresh subfloor.
Or, just buy pre-fab trusses and find a healthy back to help hold them in place while you nail gun secures them to the top plates. I have never used them, but, since every tract development seems to use them, can’t be bad.
If you want to be cheap - buy 1 and pick off angles and dimensions from it.
90° or 180°? Shouldn’t the inside angle of a triangle be subtracted from 180°? The two angles should add up to the horizontal line created by the lower board.
I think it would be easier to build trusses. The first one becomes a jig for the remaining units and it takes all the fuss work out making sure everything lines up.
On a typical chop saw, the 0° mark is a perfect 90° cut, and the angle on the saw is the angle away from 90°. That’s why you subtract from 90 and not 180.
I didn’t think about it when I wrote that post, but some chop saws have the center position marked as 90° and not 0°. I’m just used to the way mine is set up. If you’ve got one of these then you just use the angle and you don’t need to subtract.
And once you’ve used one for a few minutes, you’re very unlikely to make all the stupid mistakes carefully calculating and out-thinking chop saw angles. I’ve fucked up miter saw cuts (especially compound ones) after three skilled people helped make the calculations and checked the setup. It’s just too easy to get your visualization or math backwards, not even counting hurdles like “0 or 90 degrees?”
Framing squares make it easy, intuitive and a lot more error-proof.
I probably should invest in one but I draw my plans out in advance and transfer measurements directly to the wood. Even when I have the right measurements I’ll still reverse it on the saw. If it looks correctly drawn on the board to be cut it’s usually right.
I suggest watching this one first. He explains it really well. Even shows how to test the square for square. Even a new square is out a little. He explains how to adjust it.
