There are many ways to approach cutting and installing common rafters; this is the one I’ve used most often, using math, geometry and a calculator (even though there are online calculators that will do all the math for you, it’s important to understand how the geometry works. I’ll start with the traditional longhand method first).

I start by measuring the overall width of the building (the outside faces of the wall sheathing plywood), checking to be sure that the dimension is the same at the front, middle and back of the building (give or take 1/4” or less). If you have some variation in your measurements, record the largest dimension.

The next required part of the equation is either the height at the peak of the roof that you want to achieve, or the ‘pitch’ of the roof that you’re wanting to achieve, expressed as units of rise per units of run: for this roof I want the peak to be At least 83 inches above the loft floor, giving it a pitch of around 14 inches of rise for every 12 inches of run.

Here’s the long-form calculation:

To find the run of the rafter:

144 inches (the width of the building)

- 3/4 inch (half the thickness of the 2x10 ridge)
- __________________

143.25 inches / 2

=71.625 inches (71-5/8”)

To find the rise of the rafter when we’re aiming for a particular pitch (angle) for the roof (in this case 14/12) this is the calculation:

Set up a proportion, cross multiply, and divide:

A/71.625 x 14/12

12 x A = 14x 71.625

A = (14 x 71.625) / 12

A = 83.5625 (83-9/16)

To find the dimension of the rafter between the tip of the ridge cut and the crotch of the heel cut we use the Pythagorean theorem a2 + b2 = c2

(83.5625 x 83.5625) + (71.625 x 71.625) = 12059.25

The square root of 12059.25 is 109.81 or 109-13/16” (use the square root function on your calculator to solve that)

That’s the old-school way. Nowadays there are any number of online calculators to give you your angles and dimensions, and I use them to confirm my longhand calculations (all part of a good carpenter’s habit of trust, but verify and measure twice, cut once).

One online calculator that I’ve used is

www.inchcalculator.com/roof-pitch-calculator/

Armed with these figures, I’m ready to lay out the first rafter, which will become my pattern for all the rafters. I select a nice straight piece of rafter stock for the pattern rafter, and mark the direction of the crown, or the bend along the edge, with an ‘X’. The crown ‘X’ is always oriented to be the top of the rafter.

Every common rafter has a ridge cut (or plumb-cut) at the upper end and a ‘bird’s mouth’ and tail at the lower end. The roof pitch determines the ridge cut angle (use the online calculator to easily learn this angle), which I mark using a triangular rafter square, such as a ‘speed square’.

Make the ridge cut (50 degree angle), and then hook your measuring tape onto the tip of that cut and measure down the 109-13/16” that we earlier calculated.

Because I am measuring diagonally along the length of the rafter, I hold my pencil against the board at the measurement and carefully move the tape measure in an arc, to scribe a short line at that 109-13/16” distance from the tip.

The ‘bird’s mouth’ consists of the seat cut and the heel cut. The heel cut angle is the same as the ridge cut, 50 degrees.

The angle of the seat cut, or the flat part of the bird’s mouth notch, is the complement of the 50 degree ridge cut angle and heel cut, so 40 degrees.

Once the bird’s mouth is cut, use this rafter as a pattern to make just one more: In theory, my pattern rafter is a perfect fit, but before I cut a whole pile of 2x6, I test-fit these two rafters.

Now is also the time to mark each side of the ridge with the rafter positions, marked out for their 24 inch spacing.

The next step is easiest with 2-3 people, but can be done by one. The ridge needs to be temporarily supported in its final position until there are at least 2 pairs of opposing rafters. If I’m working alone I build two T-shaped props that support the ridge at its exact height above the loft floor while I do the test fit and then to place those first 4 rafters.

With the 2x10 ridge supported in place, trial fit the two test rafters, checking that all points are a good fit.

If everything checks out, take the pattern rather back down and use it to carefully trace the cut lines on to all your rafters (remember to have the crowns all facing the same direction. Don’t use a board that has excessive crown or bow.

When installing your rafters, it’s best to fasten the bird’s mouth first, with two 3” nails or screws on an angle into one side of the seat cut, and one nail into the other side. Then fasten the ridge end, using 5 nails or screws, 3 on one side of the ridge cut, 2 in the other.

This roof has a dormer, and the rafters on each side of it are doubled, the rest are singles.

Next up: building the dormer, cutting dormer rafters and creating the skylight opening.