As a young carpenter (or should I say, “helper”) I was always amazed at the skill of the roof framers. They made it seem effortless to cut and fit roof rafters with only the aid of a framing square. The whole process mystified me. In those early years, I tried several times to do it myself, but I never had success. In time, an older carpenter named Rich Murphy took me up on a roof and helped me lay out and cut a reverse gable using a framing square and his roofer’s pocket reference or “bible.” That experience sent me on the quest to master the art of roof cutting. I can’t say I ever mastered it, but I’ve come a long way since Rich graciously took the time to help me understand what was going on.
Of course, that was decades ago. Today, I use a calculator to find rafter lengths and angles. Without a doubt, a construction calculator is the quickest way to find your way around a roof.
Construction calculators are pre-programmed with Pythagorean formulas for finding the values of right triangles—and roofs are all about right triangles. These calculators eliminate some of the memorization, and all of the charts. They put all the information in a nice, clean, easy-to-understand interface.
There are also two laudable software versions available as smartphone apps: one from Calculated Industries, and one from BuildCalc. They essentially do the same thing as an actual construction calculator, but I prefer the real thing—if I’m going to drop a calculator in the mud, I’d rather it not be my pricey smartphone!
Using a Construction Calculator
The values on the calculator that we use for common roof framing are: Pitch, Rise, Run, and Diagonal. If you have any two of those values, the calculator will quickly figure out the rest of the right triangle—which means it will tell you everything else you need to know about a rafter.
Most of the time, the two values I have are the run of a building and a specified pitch, which is why I used these values for the example in this online tutorial:
Looking at our model roof, I need to find the two elements that will give me all the information needed to frame the roof.
The building width, in this example, is 6 ft. 3/4 in., including the sheathing.
Each rafter only spans half the width of the building, and they start at the face of the ridge beam. For simplicity, and to prevent error, the first thing I do is deduct the full width of the ridge beam from the building width: in this example 6 ft. 3/4 in. – 1 ½ in. = 5 ft. 11 1/4 in.
I write this down on my template rafter as the adjusted overall run. Then, I divide that by 2 to get the actual run of each rafter. The result on my Construction Master calculator is 2 ft. 11 5/8 in. Next, I press the Run key, instructing the calculator to use that dimension as the ‘run,’ which is the first element of the right triangle I am working with.
I need one more element, and in this case I know the pitch of the roof, which is 6/12. So I enter the number 6 into the calculator, followed by the Inch key, and then press the Pitch key. Note: It’s important to remember to press the Inch key when entering the roof pitch—without it, the calculator treats the number entered as ‘degrees of pitch’ instead of the rise/run ratio of the roof.
Now the calculator has all the details it needs, and it can provide me with every bit of information about that triangle. For instance, I’d also like to know the diagonal measurement, which will help me layout the seat cut. All I have to do is press the Diag key, and the calculator displays the measurement: 3 ft. 3 13/16 in. I write this measurement down on the template rafter, too.
Be sure to go through all the calculations a few times, clearing the calculator in between. If all the results match, you can rule out any keystroke errors.
The next step is to layout and cut the rafter. First, I attach a set of stair gauges to my framing square, so I can make precise, repetitive marks. In this case, I attach the gauges for a 6/12 pitch—6 in. on the tongue of the square and 12 in. on the body of the square. I carefully align those measurements along the edge of the rafter material, and then set the gauges.
Laying the square on the top of the rafter material, I start by scribing the plumb cut at the peak of the rafter. Keep in mind that, for most framing jobs, the tongue (the skinny side) is the vertical cut, and the body (the wider side) is the horizontal or seat cut.
I make this plumb cut at the peak with my saw before marking my seat cut (or “bird’s mouth,” in some vernacular). This way, I have something to hook my tape measure on, which is very handy for long rafters.
Measuring from the tip of the rafter, I mark off the diagonal measurement along the top edge of the rafter.
Then, using my framing square (some carpenters choose to use a speed square, but speed squares aren’t as precise, especially on fractional pitches), I draw the parallel plumb line across the rafter, marking along the tongue of the square. This line represents the plumb line on the rafter at the edge of the building.
The seat cut (or “bird’s mouth”) is referenced from this line. If you are framing from scratch, and not matching rafter heights (which will be explored in a future article), you will need to decide on what size the seat cut should be. Most codes require a minimum of 1 ½ in. of seat bearing on the top plate. I like to keep the seat cut the same width as the wall, including the sheathing.
In my model here, and on most of my jobs using 2×4 walls, the seat measures 4 in. with the sheathing. With wider plates, you cannot cut into the rafter more than a third of its overall width—this would weaken the structure too much. I generally go with 4 in., and it works well with most roofs.
To do a 4-in. seat cut, I rotate the square 180 degrees from the plumb cuts I’ve marked so far—this way the stair gauges will be referenced against the bottom edge of the rafter. I then slide the square along the bottom edge until the 8 in. mark on the body intersects the parallel plumb line I drew earlier; you’ll see that the line I trace will be exactly 4 in. long.
To me, that’s the quickest way to draw the seat cut.
Then, while I have the square there, it’s easy to slide the square over to mark for the rafter’s overhang (if I have an overhang less than 12 in.). In my case, that’s 6 in., and I draw another plumb line so I can start to cut the rafter.
Setting the Rafters
Before I set my rafters, I like to set the ridge in position first. That’s why I recorded the Rise measurement of our rafter.
I could calculate this on my construction calculator, but honestly, I find it easier to draw it out—it’s much safer, since drawing makes it easier to keep track of the numbers. By drawing it out on a story pole, I find the post elevation, and I can then cut the story pole to post the ridge.
|To do that, I start with my calculated Rise of the rafter, and measure up that distance from the bottom of my post. I mark that on the post, and label it. In this case, that measurement is 1 ft. 5 13/16 in.|
To get to the top of the ridge, I need to measure the rafters HAP, or “Height Above Plate.” Looking at the illustration (below), you can see the triangle that our construction calculator calculated. The calculator has no idea about the depth of the seat cut, or the size of the rafter material—it’s easiest to measure from the seat cut to the top edge of the rafter I’ve cut, and that is the HAP.
|I add that measurement to the Rise and label it. The post height will now be at the top elevation of the ridge. In this example, my rafter has a 4-in. HAP.|
Next, since I want to post the ridge, I measure the depth of the ridge beam (in my example, 5 ½ in.), and measure down from my HAP line mark. This line represents the height of the post. I now know if I cut that, it will fit.
|Mathematically: (RISE + HAP) – Ridge Beam depth = Post Height|
In real life (not mathematics), not everything is perfect. I usually deduct a 1/4 to 1/2 in. more, to allow me to shim the ridge into position perfectly. It’s a lot easier to shim a 1/2 in., than to have to cut a 1/2 in. off after the ridge is on the post.
The process is pretty straightforward—no complex charts or tables. And as Tom Brewer says, we all love it when a plan comes together and actually works!
(SketchUp drawings by Wm. Todd Murdock)