How to figure the angle to cut a shed type porch roof rafter.

This is the easy way to figure the angle to cut a porch roof rafter

Here’s a simple formula to help figure out the angle cut at the top of a shed roof when it lies on the main roof. First you must know the pitch of the main roof and the porch or shed roof.  Usually it can be found on the plans when building a new home. Second you must be able to convert the pitch which is usually expressed as inches of rise per foot of run…. for example a 7/12 roof will be 7” rise to 12” of run. Sometime you can get these numbers from the side of a speed square or from roof slope tables.  Of course once you know the mathematical way it’ll free you from your reliance on these charts.  A 7/12 roof for instance means 7 divided by 12 which will give you the tangent. In this case it’s .583333. Get a calculator and choose the inverse tangent operation and it’ll show 30.2564˚.  Subtract the integer portion and you have .2564, multiply this by 60 (60 minutes in a degree) and you’ll get 15 minutes.  So it’ll look like this 7 ÷ 12 = .583333 next enter inv tan .583333 = 30.2564˚. Convert the decimal portion to minutes by multiplying by 60 and you’ll get 15 minutes which will be added to 30˚ for 30˚15̕.

Now that you know how to convert the pitch simply subtract the high pitch from the low pitch in degrees and the resulting pitch will be the setting to use on the framing square. Simply mark your line with a framing square using the level side(12” side of framing square) If you don’t have a framing square it’s 90 – the This Angle Pitch because there’s 90˚ between plumb cuts and level cuts. So in the example above 7/12 = 30˚15̕ , 4/12 = 18˚26̕ ,  so 30˚15̕ - 18˚26̕ = 11˚56̕ which is about a 2 ½ in 12 …. just use the level cut or if you prefer it’s 90˚ - 11˚56̕ = 78˚04̕ if you like using a speed square.

To learn how to do this with a framing square see this page. How to Mark the Top of a Shed Roof Rafter with a Framing Square.

To figure how long to make a shed type porch rafter see this page.

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