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.
Next, I press the Rise key, and write that number down: 1 ft. 5 13/16 in.
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)
Once again I feel compelled to comment. The word “Pitch” is often mis-used, as in this and many other articles. One might say that “it’s a 6/12 pitch” This is incorrect. The proper term for expressing the roof angle is “slope” in that instance. Pitch is properly expressed as a fraction, such as 1/4 pitch or 1/2 pitch. The above would be a 1/4 pitch since the unit rise is divisible into 24 by 4.
And I feel compelled to correct you. According to Wikipedia, the most untrustworthy reference source, but a great location for modern usage, pitch is the proper word to use:
“The roof’s pitch is its vertical rise divided by its horizontal span (or “run”), what is called “slope” in geometry and stair construction. It is typically expressed with the rise first and run second, with the run denominated by the number 12, giving a ratio of how many inches of incline there is to each foot of run. For example, 3:12, 4:12, 5:12, and so on.”
You’re right Gary, stairs have a “slope” and roofs have a “pitch”. At least that is exactly how I was taught 40 something years ago. I’ve heard a few guys use the word “slope’ while talking to the framer cutting rafters referring to a roof and all they got was a ‘Huh’? back. And the guy cutting the steps will always correct someone with “you mean slope” it’s not a roof. So there it is there.
I’ve cut a few rooves. I’ll interchange “Pitch” and “Slope” synonymously for both stairs and roofs since the concept behind both terms is basically the same. We’ve all used or heard the term “step-off” to describe rafter layouts and stairs too.
But the terms “Run” and “Span” should not be confused with each other. I have read many books describing “Pitch” as Bill B. has explained it. I have always felt that “Rise to Span” ratios were a confusing use of the term “Pitch”. (How would this usage apply to multiple pitches, or irregular roofs?) I must not be alone on this because so many modern tools and calculators base Pitch on the Rise to Run dimensions of a single sloped surface.
Span is the width of the Roof
Run is generally one half the Span
“Effective Run” is the Run (Span/2) minus the ridge deduction (usually the Ridge board/2), and is the dim used to calculate the Rafter length.
The most basic thing a roof cutter needs to know and understand is a rafter length is simply the Hypotenuse of a right triangle, and the “ER” is the base of the triangle.
Oh, and I thought 6/12 was a fraction, > > > unresolved of course.
And here I thought, pitch was the gunk that collects on my blades and bits…
You are right about the Pitch, it is the relationship between the total span and the height of the ridge. Say a building is 24′ wide and the slope is 6-12 that would be 6 divided into 24 or 1/4 pitch so the height of the ridge would be 1/4 of 24 or 6′ an interesting one is 5-12 slope on this building the ridge height would be 5′ this is called 5/24 pitch
Actually the pitch is in reference to a roof, the pitch is how you get your slope
So pitch is degree of the Slope. The slope is length of degree from point of intercept of rise to run. 3 angles make a rise, run and slope. first angle being 90 degrees of 180
I think that making trivial comments over whether craftsmen call it ‘pitch’ or the ‘slope’ of a roof is pretty much irrelevant and redundant. I believe that if a person understands what you are even talking about is good enough, and that both parties are on the same page. Just an objective point of view.
Agreed.. Its good to know correct terminology to be on the same page with coworkers etc but its probably the least important comment one could make regarding this article.
To the author: i think this was great; simple and informative. Cut my first roof by myself this weekend and used the construction calc and this same method for setting my ridge beam in relation to height prior to swinging rafters.
I was unsure if there was an easier or better method but after reading this i feel reassured. Obviously more than one way to skin a cat but still good to know.
When you deduct your ridge thickness you are not left with
“the overall run” what you are left with is referred to as
the “Span”. The span divided by two equals – the Run.
That caught my attention also. If memory serves, pitch is rise to span, slope is rise to run.
My goodness, we have a lot of linguistics and English majors on board, but I’m not sure if the debate between pitch and slope really adds a lot to this article. :)
You should say the run of the rafter is 1/2 the span of the building, not “the span of the rafter is 1/2 the buildings width.” I know it’s the same but it drives me nuts when a guy holds a bubble on a doorjamb and says- yep, it’s level…. How about proper use of “run” and “span” while we’re at it.
Span is vert I mean horizontal all the time. There is no run of a bridge it’s always span. When we say slope, run or pitch it’s rafters we are talking.
Vernacular is the key —
As I learned Pitch in the Early days , it was the Rise of a building over its entire run , The denominator was not usually 12. More like 1/2 or 1/4 – Quite frankly for the field carpenter, a useless term. Over time the ratio over 12″ (1 foot) was more commonly used as it was easy to reference on the framing square. The term Pitch when used over 12 became to be understood as the standard , and is commonly called the Pitch of the Roof. Just look at the Calculator entry the button is labeled “pitch’ not slope or incline. The Construction Master folks wanted us to know what that key was for, so they used a Vernacular term.
Like my Mom used to say , Ain’t Aint in the dictionary. Sorry Mom it is now……
Just to confirm we need to add the HAP to the ridge height so the pitch does not alter
I’m glad these calculators are available, however, I can step a rafter with a square quicker than I can go to the truck and get the calculator. Double step when you can 5/12 doubles as 10/24
Nice article Mike. I won’t get into the english debate. Suffice to say around here we call a 6/12 ‘pitch’ for example. Article is well written and the sketchup diagrams make it easy for anyone to understand. I still step off my rafter cuts with a framing square and stair buttons like you show. I haven’t got used to using a calculater, even though I bought one a few years ago. I always forget where it’s at in my van.
Perfect timing. Thank you gentlemen. I have a very fancy screened porch to build next week. This will be practiced in shop tomorrow and done on site next Tuesday.
Yannis N. Tsakiris
Thank you for writing a great straight forward article.
I love how you take a complex task and break it down to simple parts. Thanks for sharing your insights.
Will you be at the JLC in Portland, Oregon? If so, looking forward to learning more from you and Gary.
If I’m cutting a simple gable roof, I’ll have a CMC in my nail bags. But, not if I’m cutting a complex roof. Ben at BuildCalc has done an excellent job on the user interface of BuildCalc and it is the best construction calculator for smartphones.
Android tablets are a great alternative to smartphones. I can see android tablets replacing handheld calculators as the price of the android tablets keep going down in price.
For complex roof framing I use my *********************
******************* = Chappell Master Framers’ Square?
Which would make an excellent topic for a follow up article, hint, hint.
I am waiting for the right project to come along to order mine.
I am not a pro carpenter (I am a wood worker), but am considering building a modest-sized house which I call a ‘cabin concept.’ Tremendous article. If I do build the house, the roof will be designed with rafters, for loft space. While the Pythagorean concept is basic, the application to actual roof construction brings a boat-load of questions for someone in my shoes. The article seems to clarify the whole thing.
Sincere appreciation to Gary Katz and all contributors, who make TiC the great web-site it is.
Gary, thanks for setting our English majors straight, keep it coming.
I’ve always used the step off method which has never failed me. What is great though was using the calculator to find the post height. If you can find the book “Residential Carpentry ” by John Capatosto, you will be able to find all the step methods needed for cutting rafters, including shortening the rafter for the width of the ridge, both common and hip. I have referred to this book for years and it hasn’t failed me yet.
Thanks for the great article!
Although I’ve read this in books and done a couple of simple rooves I never quite got the hang of it but now that I am armed with this information things will be simpler on my next project.
The information was presented in a readily digestible manner that helped me to really understand where to go with it.
I know Mike has game, I’ve met him and seen him at the shows. I just can’t believe we are kicking around beginner roof framing, I thought we were past that. Grammer boys and guys that think they can “walk” a framing square faster and more accurate than a calculator, please…
What do you mean by reverse gable though?
The great thing about our trade is that you’re never “past” anything. It’s always good to review the basics in order to avoid “accumulated error” which, amongst other things*, is what you can get when you step off rafters instead of using a calculator.
BTW David Lemke, I believe you’re always free to write and contribute an advanced framing article for TIC to consider publishing. Sure beats complaining.
* accumulated error also occurs when you’ve accumulated a lot of experience and think you know it all…but really don’t.
Don’t mean to complain just felt like subject was getting nitpicked. Screwed up many a rafter and still do. However you get there is how you get there caveman style, calculator, or book. I use a little of all three. Sometimes forget column is for basics to never ending pursuit of perfection. Might try my hand at an article soon, thanks.
While there are a dozen ways to skin a cat, and do rafter cutting,
the best way I have found is the way they did it before phone apps, and that is with the Reichers framing book..
It will give you everything you need, and no worries if you hit the wrong button, (whether it be the (X), or (divide) the only way you could mess this up is incompetence, and then you might look for a job at Wal Mart.
It will also give you lengths on the valleys and jack rafters
This book is bible, and if you spill coffee on it, it will still work, no need to go to Radio shack for another calculator.
Here’s my two cents on the “pitch” debate:
I learned roof framing the hardest, and most maddening, way possible –– from H.H. Siegele’s books. Actually, these were compilations of articles he wrote, about 100 years ago, in the union magazine. He was a xenophobic man with a condescending attitude, but he did know his roofs (or rooves, as a lot of the guys here like to say).
He was way off, though when it came to the definition of pitch, IMO. For him pitch was rise/span, so an 8/12 rafter had a 1/3 “pitch.” Never mind that with a shed roof or a salt-box, you were talking about 1/3 of something that didn’t even exist!
I’m content as long as I know what a guy is talking about –– dictionaries are descriptive, not prescriptive, so we are in charge of the language.
Regardless of the method used cutting rafters is more fun and rewarding than rolling trusses.
I do love the slope/pitch terminology debate. Kind of like the dado vs plow, soffit/plancher and miter/mitre round and rounds I have been in before.
Good article, it might be good to do one on simple rafters using a “regular” calculator.
An old misunderstanding of the code regarding the seatcut is being repeated. If the overhang is <2' there must be at least 3-1/2" of rafter left above the seatcut. The limit at the other end of this is, the level portion of the seatcut should not extend inboard of the wall. The misunderstanding stems from viewing this bearing cut as a "notch"… and I've opened another can of grammer.
The one thing I do different is I use a straight peice of 1X and clamp it to my square instead of using square dogs. I don’t know how many of those things I’ve lost or the screws fell out of them . And I think the straight edge will span any irrregularities in the 2X better. JM2C
Although CM can make roof cutters job easier, it will NOT make you a roof cutter; Learn the square!
Using a CM to figure rafter lengths without knowing the basics can lead to a ton of headaches when cutting complex roofs, especially bastard hips and true valleys. Keep in mind that all the numbers a CM spits out are mathematical points and not the actual measurements. You have to where to add and subtract for material thickness. Ex: For hip jacks you need to subtract half the thickness of the hip on the pitch plus 1-1/16 for then plancher cut. If you don’t do this your “step off” length will be off and the last few jacks will be out of square by a mile.
@ Jay Stein:
I agree with a lot of what you say, although I don’t like to be a member of the “Just Say No” crowd. To clarify one of your points, I assume that by “bastard hip” you mean what I’ve always called an “irregular hip, that is, two different pitches –– say, 4/12 and 12/12 –– meeting at a hip rafter. In that case, you can no longer just assume a hip that runs at 45º to the plate, you have to solve for it in plan view first. This is a bit confusing with a CM, because you have to call one of the runs the “Rise” for the calculator to solve it. Then the “rafter” that the CM gives you will be the actual run of the irregular hip.
Whew! Hard to do this stuff in words! Did I get that right?
But can you clarify what you mean by “1 1/16 for then plancher cut?”
I am not in the “just say no” camp either, however to fully understand roof cutting one needs to learn how to crawl before they can walk.
I will try to better explain what I mean, but please keep in mind that I am a carpenter and writing is not my strongest skill.
For now, lets forget about bastard (irregular) pitch, for simplicity I will use a common gable roof.
For my example I will be using a 20′ structure with a 10 pitch.
Using the CM calc 10′ run 10″ pitch, you end up with a common rafter length of 13′-0 3/16″; this gives the total length from center of the building to the wall line.
Now we have compensate for a 2x ridge board which is 1 1/2″ half of that is 3/4″, if we just take 3/4″ off the mathematical length we end up 12′- 11 7/16″. However if we use the CM to figure how much to shorten the total mathematical length, we end up with a different number.
Using the CM again, punch in 3/4 run (half of the total span of a 2x ridge) than punch 10″pitch, doing this we end up with a hypotenuse of 1″; this is the actual number you would use to shorten the rafter for ridge material.
Using 1″, subtract that from the total gable rafter (13′ -0 3/16) and you end up with the true length of 12′-11 3/16″, now we end up with a 1/4″ difference.
Now I understand this seems minimal, and for a gable roof it is, however when you start getting into hips and valleys, especially bastard pitches, that 1/4″ starts to compound (the same methods should be used to figure shortening for hip and valley jacks) and can add up to inches, causing wasted time and material.
The plancher cut is the 45 cut at the top end of a jack rafter.
If you cut a 2x on a 45 the face of that cut measures 2 1/4″, half that being 1 1/16″. Remembering that all mathematical points are center lines, this is what you would add to get the real length.
When I hand cut my roofs, I take my ridge thickness off of my total span before deviding total span in half. This is the best way I have found to cut a roof in.
As his example states..20′ run-11/2″ for ridge÷2=run.
And it is referred to as a Birds mouth or seat cut in many places. And as far as “Bastard” or “Irregular ” roof pitches aredone, I have found a much simpler way of doing those on the CM ,which aso gives your degrees for your compound miter . It hasn’t failed me yet.
Approaching the calculating of the diagonal ( being the rafter length less overhang ) using the CM, rafter length is 12′ 11 1/4″.
Your method of arriving at 12′ 11 3/16″ is a tab bit confusing but unfortunately I haven’t seen anyone try to disagree or agree.
When cutting. Common rafters using CM calc I enter run as half the span with no deduction for ridge then when my rafter is layed out I simply measure half my ridge thickness square of my first plumb cut line to get my plumb cut
The only laudable smartphone app for unequal pitched gable roofs, that will give the correct length of the rafters, is Rafter Tools for Android. Deducting 1/2 the thickness of the ridge for the rafter framing lengths for unequal pitched roofs is wrong. See my help file for the correct way to deduct for the thickness of the ridge for unequal pitched gable roofs.
Yes! That is what I was trying to get at,
I used a common gable with regular pitch for simplicity. I felt that getting too much into bastard pitches took away from the original article. I was also trying to make the point that a calculator while a great tool, it is just that, it won’t replace basic training.
The first step to a good house is a good foundation, the same philosophy goes for skills to build it!
The stepper the roof the greater the thickness of the ridge becomes–ex 12/12 you should us 7/8ths for half the ridge , simply think about it-to reach the center(which is the goal) is a longer distance -all calculations are from plumb cut to plumb cut, if you use the actual length on your first common then your jack will lay out perfect. Just my experience
Wow! After reading the article and all of the comments, I know why I’m a finish carpenter.
@ Jay Stein:
By “plancher,” I thought you meant what I call the “soffit.” But I understand now. Never heard it called a “plancher cut,” though. I like your trick of measuring the cut face of a jack to find the length at 45º. Good trick, as long as your hip stock is the same as your rafter stock.
I caught a guy making a related mistake when we were building a timber frame with a hip roof. This guy was marking the top edge of a jack with the 45º edge of a Speed Square. I showed him how to square around to the other side, step back the thickness of the stock to mark a plumb line, then connect the dots on the edges. That’s the safest way, although if you know how, you can mark the edges with a rafter square.
Yes, the risk of measuring along the wrong plane is greater when using a calculator –– the rafter itself is such an excellent visual aid. I’m still in the habit of marking the plumb cut full length, then measuring back at 90º to that line to shorten for the ridge.
By doing that, a guy could catch himself if he made the mistake of measuring along the top edge. But if you see the “end grain” of a piece of “1x” staring at you, you know you’ve done it right.
Gary please pull out your Audel’s Carpenters and Builder’s Guide from 1939 and turn to the “roof slope vs. roof pitch” chart.
This was and still is my bible, dating back to 1972. I’m quite surprised that you and many others are unfamiliar with this fact. I enjoy these historical tidbits and pay homage to them daily. Maybe “This is Carpentry” should explore this 4 book set and write some articles on it.
I respect your experience–the years you’ve invested in the trade and all that you’ve learned over four decades as a carpenter.
I too have a set of Audel’s books and–being short on experience and lacking instruction–I used them a lot when I started out working as a carpenter. But the problem is, they were published in 1939. That means some of the information may still be applicable and some may not: terminology, building materials, and tools have changed a lot over the years. In 1939 there were no circular saws, no nail guns, no cordless drills, no Titebond II, no power miter saws, and no construction calculators that are far more accurate and efficient–especially when you consider cumulative error. Construction
Calculators do not have a key that says “Slope.” They have a key that says “Pitch.” If we had used terminology from 1939 in this article, at the very least it would have confused all directions connected with using a modern calculator. The purpose of this magazine is to provide comprehensive articles that help carpenters improve the quality of their work, speed productivity, and hopefully add a little enjoyment to a sometimes difficult career.
I think some articles on Audel’s would be welcome, but I suspect they’d be more about how things used to be done and how they’re done today.
Some really detailed instructions here. A great guide.
I have to say that my biggest pet peeve in forums and blogs are the guys who want to bring up insignificant details and argue how the author is wrong and they are right. Like they are trying to show how much better they are than the author and want everyone to know it. When it comes to terminology most framers I worked with used pitch and slope as the same. Maybe they are using incorrect terminology but everyone on the crew knows what each other means. The article is titled Common Rafter Framing not the definition of pitch.
Well said, great article!
And on a lighter note from a finish carpenter who cuts a roof now and then; “pitch” is that material you get on your hand when you pick up a board to cut it into a rafter!
I taught carpentry for a few years. I don’t claim to be a skilled roof cutter like many who frequent the forums. What I did find out was that it really didn’t matter what the definition of pitch was, or is. Knowing that definition wasn’t necessarily a help in explaining how to cut a rafter. I taught stepping off with a square, reading from a rafter book and using a calculator. Each has it’s advantages. What’s really inportant is what happens at both ends of the rafter after you know the length. For that a good understanding of a framing square is invaluable. I always taught there’s only two cuts on any rafter – level and plumb. The level cut is always marked on the unit run side of the square (12″ for a common rafter) The plumb cut is marked on the unit rise side of the square (varies with the pitch/slope angle or whatever you want to call it.) You can use the i/s, o/s , top or bottom of the square when marking your cuts as long as you’re consistent. In other words you can’t use the i/s for the rise and the o/s for the run.
Great article. Wish I’d had the information before my last porch build. :)
Thanks for taking your valuable time to put together all the information; it’s very much appreciated.
This is the first article that makes sense to me. Everything I have read about using the Pythagorean theorem was so aggreivating because when using the outside of the wall and the rise from top plate to ridge is not where the rafter actually sits because there is not a seat cut yet and of you did use the exact measuremts than you would have no tails as they would be removed. Now please I cant wait for your ” matching raftter heights article”. Thanks
Hi everyone, can someone please elaborate on the use of wooden shims between the ridge beam and the rafters? Specifically, I understand the need to make minor adjustments without having to cut some length off but I have received mixed reviews on this from a number of people. We are having new construction done and several of the rafters are not laying flush to the ridge beam. I’ve attached one photo as an example. I thank anyone in advance who can offer some commentary on my question.
A shim is a quick fix
If the rafters aren’t working out its because the wall is out of plumb or the ridge is off center. one shim ok. multiple…
Quick, hire a better carpenter.
I was putting a gable roof on a dog house that has an outside measurement of 32 1/4”(16 1/8 run). I laid out a 2×4 with a 45 degree angle for the ridge and pulled down 22 1/16 and 1 1/2 up from the bottom of the ridge cut and the bird’s mouth. I subtracted for the ridge ahead of time. When I put everything together with the ridge the span is still 1 1/2 inches to long. I believe I did everything correctly. If I take out the ridge it is 32 1/4″. What did I do wrong? Is this some mathematical anomaly?
I figured it out….
I have a hip roof with a 12-12 pitch on the main side of the roof while the end is an 18-12 pitch. How do you figure the length and angles of the cuts on an uneven roof for the hip rafter ???
Billy hope this helps you
Construction master pro calculator
Building is 30′ wide Main roof 12/12 end cap is 8/12
1. Enter run 14′-11″1/4 ( this measurement will also be where your 8/12 common rafter starts)
2. Enter pitch 12 inch
3. This will give you rise height, rafter length for 12/12 side
4. Then push 8 inch conv hip/Val this will give you the irregular hip/Val length plumb cut/cheek cut
5. Then clear calculator
6. Enter the rise height from above
7. Then enter 8 inch pitch
8. This will give you the run which is where your first 12/12 common rafter will start and pushing diag next will give you the common rafter for the 8/12 side
Hope this helps
Thanks for the response! I’ve been hoping that Mike would respond to that question, but….it’s been hanging there for a LONG LONG time!! :) Glad you cleared it up! I would have answered it if I could but I couldn’t…no way.
Hello Ben, you gave a very good example here! and I’d like to ask you a question. I’m from across the pond in Ireland where we use degrees and metric for calculating rafter lengths and I would like to ask you is it possible to calculate in metric using the “construction master pro” for an irregular hip roof having a main roof 35° and hip end 55°.
Why is the full 1.5″ width of the ridge deducted to get the length of the rafter and not only 3/4″? I don’t understand how the rafter can reach the center of the wall by taking the complete 1.5″ off. The ridge board being dead center has 3/4″ on each side of the center line.
This kind of made me think about this one too but the method of deducting the overall width of the ridge beam from the span will actually have the same output when subtracting just 1/2 also of the beam’s total width.. because for everything else you will just be computing for the “deducted” length of the span already.
If you follow the procedure carefully – Notice the Ridge is deducted from the ENTIRE width of the structure first , than the result is divided in half to get the actual rafter run. This eliminates the need to deduct 1/2 the ridge . it also tells you where to put the edge of the ridge post as measured from the Outside of the building.
Thanks Mike. I see what you mean.
I have struggled with getting rafters right forever! I have also read everything I can find and watched countless videos but never fully understood the processs untill now. This is the best video on rafter cutting in existence. I got the calculator and followed the video instructions with perfect results!! Thank you for settting me straight.
I’ve attached a pic of how the rafters on the shed looked.
Is your shed open ceiling? What size is the shed? And what pitch is your roof? I’m planning on building a 12×12 shed with an open ceiling. This looks like what I want to do except I want 2 ft. gable overhand and eaves.
Thanks for your comment!
I struggled for way too many years myself .. It really is pretty simple , I wish my math teacher had told me what I was going to use all that math for ……
Thanks for the Photo too !
Thanks so much for the rafter video… it makes laying them out a breeze.. thanks again..
Calculating roof geometry was made much more simple for me after reading “A different Approach to Rafter Layout” by John Carroll. The article is in Taunton’s book “Framing Roofs. Rather than outside the wall to ridge, the author made calculations from inside the wall for effective run of rafter at ridge. This eliminates extra addition (or subtraction) with regard to seat cut. Also puts seat cut in the correct position intersecting inside edge of stud wall (Gary might say, “see the triangle”). Height to bottom of ridge intersecting with bottom face of common rafter also easy. Bottom of ridge board for common gable roof can be set to bottom face of rafters. This combined with Gary’s regard and guidance that lead me to construction calculators really improved my game as a contractor and novice roof cutter.
Thanks For your Comment Mike
Unfortunately Johns Approach has some significant drawbacks. You can’t always set the seat cut at the edge of the Plate. On wide plates it will create a code violation, In addition, when dealing with differing HAP’s it gets really confusing. The method we show here is the most common in use, and it does require a little understanding of where the triangle is. I tried his method but found it to be more confusing than the traditional methods. In addition, you become the only guy on the jobsite measuring to the inside of the plate – to me its like switching the gas and brake pedals on my car ( how do you hook your tape ?)
We chose a simple Traditional approach using the modern Calculator. Better to speak the language of your trade than have to explain yourself ..
So… Your triangle is fixed; your roof pitch angle is 22.67deg; your plum cut on the rafter top against ridge is 22.67deg; then the height of the ridge depends on how deep your seat (birds mouth) cuts are? And what size (width) rafters are used? I’ve been using the wrong triangle!
I meant 26.57 deg.
Mike, I actually need to read your matching rafter heights article, have you written it yet?
How do you find pitch when total rise and run are known?
Read this article Sawyer
What adjustments in layout are made when the bearing walls are of two different widths but you want the pitch the same on both sides?
The Seat cut remains the same for both sides –
The center of building is determined from outside to outside – so the ridge from the perspective of the Interior will be slightly off center
On a room addition I am using 2×10 rafters for a 3/12 pitch.
This is for a cathedral ceiling so my seat cut depth is 1.5″ and seat width is 6″(2×6+1/2″sheathing).
I can not see how to get the “plancher” cut level for a 6″ fascia
without eliminating the birds mouth.
The rest of the house uses a 6″ fascia
Your seat cut does not need to be full width of plate.
Additional info –
The rest of the house was at 5-1/4 on the fascia width.
I now have approx. 6-1/4 and am going to go with it.
I had thought about a deeper seat cut – but that makes a wider seat which extends inside the wall and doesn’t work with the cathedral ceiling. If the ceiling was not cathedral (i.e. flat) then that would have worked.
Thanks for the article. It has made my life simpler. I especially like getting the ridge thickness issue out of the way right up front.
Perfect, absolutely perfect, I have spent two days searching my screen for a straight forward “how to cut rafters” and every thing I found was missing something for me, untill I found you, Thanks a great deal!
Question: If calculating the cuts for a flat sloped roof, is the run measured then from the outside of the down slope wall to the inside of the up slope wall?
If a roof is flat , it has no slope.
Better off drawing a Picture so we can understand what you are trying to describe .
Flat as in no peak. Assume a straight connection between an 8′ high wall and an 11′ high wall 12′ apart. I can easily calculate pitch and the angles for the cuts, but the formula requires span and translating the span instructions above to a non-peaked roof seems to indicate that you use the outside of the down hill wall and the inside of the up hill wall.
What a beautiful illustration and in layman’s terms. Extremely easy to understand. I too was always mystified in my dad’s skill with a using a framing square in construction. I wish I had taken the time in my youth to have learned from him. Thanks much.
I have a question… if you are say using a 2×6 as your ridge whcih are generally 1 1/2 wide… wouldn’t you take 1/2 of that to reduce the overall run of your rafter? In the video you you compesated the 1 1/2in from each side of the rafters giving you a total of 3 total inches of compensation. I am confused why your wouldnt take 3/4 from each rafter so that in total you have achieved the 1 1/2 width you need from each side
Disregard I just re-read above you deducted it from the width if the building not from the run of the rafter
Don’t subtract from the rafter.Always subtract from overall span prior to calculations.
I agree with Andrew of 11/09/2012. 40 plus yrs of carpentry & never used a cal to lay out rafters.I use the framing square & double check it with myFull Length Roof Framer book by A.F.Riechers.
I know that this is an older post, but I was hoping that you could assist. I am putting together a timber frame barn and the roof trusses are half lapped at the peak. The beams are 4×8 and the roof pitch is 40 degrees or 10/12. My question is that I am going to have an overhang of 10 inches and I can’t figure out the distance from the top plumb cut to the bottom plumb cut in order to mark my seat cut, any thoughts? The plate is a 8×8 and the building dimensions are 16′ x 24.’ Any help would be appreciated.
The overall width of the building in S.Cal would be the span.Half the span is the run.Learned to cut roofs in the 70’s from a master roof cutter.
Great article and videos, very informative and easy to understand. I did find in my research that the maximum seat cut depth for a roof rafter is no longer 1/3 the beam depth (D/3) but the 2012 International Residential Code (Figure R802.7.1.1) limits it to 1/4 of the beam depth (D/4).
Building an A frame rabbit hutch/run. I’ve already built one, have difficulty with the angle cuts and knowing what they should be. The rise is 22″, the run is 17 1/4″. What should my cut angles be? I do not have one of those nifty stair squares.
I’ve built three houses in my life. Stick built every roof. When it came time to do the roof rafters, I marked out the roof profile on the floor of the house with a chalk line, draw in the center plate, lay a 2×6 on top of it, mark it, cut it and voila, I have my template.
There are Many ways to frame – that method was used before the framing square & modern calculator , I will use it for the very complex intersections of Radius forms and Roof intersections,
I feel any method you use is perfectly fine as long as the results are achieved. The calculator has shaved off framing time exponentially,
I’m in the business to make a living, the faster and more accurately I can accomplish this, the more time I have for Family :)
Thats where the calculator comes in .
little help for calculations http://myrooff.com/hip-roof-calculator/
This is well detailed and extremely informative! The world needs more experts who can teach effectively! Thanks for keeping this info on the web for so long.
Why is he showing the rise as meeting in the middle of the ridge. The rise is from the TOP of the ridge to the outside of the plate
Overall rise , yes technically it is- but you can’t calculate it that way – Overall rise changes with the Depth of the seat cut , size of the lumber . Calculators & framing squares don’t know this.
Therefore you go from outside of plate to face of Ridge beam – the rise gets calculated , Than the HAP has to be added to get Overall finish . If you layout from the Outside of the plate to the top of the ridge and calculate , your pitch will be wrong. Your forgetting about 3 dimensions of Framing
Laying out from outside of plate to a fixed ridge height is another set of calculations not discussed here . See my article in JLC 7/10
Ok first off i want to say i do not use a construction calculator at all.
I’ve seen some arguments above on what to subtract for a ridge. The way i prefer is to pull my span outside/outside the walls the rafter are sitting on. For example say my span is 300″, i would take 300″-1.5″/2 which gives you a run of 149.25″. Lets say the pitch is a 10/12. On a piece of paper I write 10 over 12 on one side and to the right of that i write 149.25″ with a line drawn above it, the rise sits above that line. I then cross multiply and divide to find the rise. For example 149.25 x 10 / 12 = 124.375″. Then use Pythagoram, A=149.25 B=124.375 A squared plus B squared = C.
A squared = 22275.562
B squared =15469.14
22275.562 + 15469.14 = 37744.702
But you want the square root of 37744.702
Square root of 37744.702 = 194.27995
I would cut the rafter 194 and 3/16 from top to top with a 7″ stance on a 2×8.
Thanks for the nice explanation for us layman. Works for me. Thanks.
How do you calculate the what the pitch of a roof should be?
This article is good, but it doesn’t comply with the book, “Carpentry and Building Construction” that has been a standby text for many years. The confused use of pitch and slope on the internet is really annoying. Always have to read closely to determine which it actually intended.
There is no ultimate authority on framing – Language changes constantly , therefore terms take on different meanings ( when was the last time you ‘dialed’ a phone ? ) The Calculator uses the term Pitch because it is now the most common usage of the Term. I travel all around the country teaching carpenters and I am always amazed at the different terminology used. Trimmer – Jack – Packer -Cripple all regional terms for the same element ( the stud under the header ) If you ask for a Cripple measurement in South Louisiana you might have to clarify what you want. Ask for a Packer & they will know what you’re talking about ..
How about this – Know what a Pork Chop is ? SO if I write a book on framing Only part of the country will know what Im talking about
I totally agree, in fact, most of the country WILL know what you’re talking about even if you occasionally use language that isn’t identical to some regional areas–it’s not like the difference between Greek and English, there is still a significant similarity, enough so that the meaning can be easily inferred by readers from any region. One thing is certain, there is no need for the word police here, at least not yet. Let’s wait until a real crime has been committed before blowing that whistle!
The most important thing obout rafter cutting: the stick fits the first time it’s installed.
If you intend to have the seat 4″, which includes the sheathing, then should the overall run be adjusted to add 1 inch?
I think I qualify to add my 2 cents. I cut my first roof well before there were calculators on the job. However, they are handy especially when calculating stair rise. Once you have determined the run; stepping off with a square and a sharp pencil and attention to accuracy is a no brainer. In order to eliminate the “accumulative” affect, make a pair of rafters (leaving the allowance for the ridge intact) and dry fit them. Make adjustments if necessary, cut off the allowance for the ridge and then use that one as a pattern to scribe the rest.
I had a similar approach to that in the “old ” days as well.
That was when I had a fold out road map trying to find a job site and stopping at a phone booth to call the homeowner for directions.
Than I got one of those new fangled GPS thingys and a flip phone. That saved me a lot of time.
Thats how I view the calculator , less effort smoother and faster. I calculate, cut and install – no need to dry fit – even set the ridge first – saves me dragging the stock up to the roof for a dry run.
Gotta love technology .
You subtract the total width of the ridge beam from both sides. Shouldn’t you only subtract half of it, since the run is determined from the center line of the main ridge beam?
If you follow the Math as it was presented , deducting the entire ridge Before you divide the Span in half is the same thing as cutting the span in half than deducting half of the ridge .
Your rafter only goes to the face of the ridge —
Either way works.
I enjoyed scanning through your article. If it is there I missed it, but how do you use this information to determine the cuts for a gambrel roof? I am trying to find the correct formula or method to place a gambrel roof on a shed I am building this coming year. Is the method for framing a 4/12 top portion the same but shorting the length and then adding the lower portion to create the desired form of the roof?
To not make a pun, you totally nailed it! I was so confused looking at different Youtube videos where details and the pictures were lacking. I find when trying to learned from these open information sources that I have to incorporate multiple explanations from different sources. I believe some videos I watched left out the outside thickness when figuring span. Your explanation has been best so far from what I can see.
Let’s make it really simple.
PITCH = RISE/SPAN.
Always expressed as a fraction.
I taught for 20 years in a state prison. I had to use the KISS method. It worked for me and all my students.
Keep it simple stupid.
This is super helpful thank you for posting this.
How do I find out the anlge to cut my rafter when it plains onto another pitch? With out drawing it out. Let’s say I’m cutting a rafter for a 4 pitch but it’s tying into an 8 pitch roof already there.
While this is a bit outside the scope of the article, the converging pitch angle can be calculated by using the following formula:
Major Pitch angle – Minor Pitch angle = Converging Pitch angle
33.69°(8:12) – 18.43°(4:12) = 15.26°(3 ¼:12)
To find the required information on a CM Pro calculator:
Major Pitch — 8 [Inch] [Pitch] [Pitch]… 33.69°
Minor Pitch — 4 [Inch] [Pitch] [Pitch]… 18.43°
Converging Pitch — 33.69 [-] 18.43 [=]… 15.26 [Pitch] [Pitch] [Pitch] [Pitch]… 3 ¼ in.
Hope that helps,
Wm. Todd Murdock
Art Director, THISisCarpentry.com
There is a simpler formula for calculating ridge height and rafter length. The way I learned is Ridge Height= Unit Rise x Total Run+HAP – 3/8″ (ridge drop). Rafter Length = Hypotenuse x Total Run – 3/4″ (half the thickness of Ridge board. A simple feet and inches app or calculator is all you need for this method.
Simple is good, but your method will give you proximity, not precision. How do you determine you HAP without first laying out your rafter? That would be step 1 of your formula. The further away from a 6/12 pitch in either direction your ridge drop changes too much. For instance, a 3/12 pitch ridge drop for a 1.5″ thick ridge is only 3/16″ whereas a 22 pitch drop is 1 3/8″ – I believe the method we show here is by far the most accurate and cuts out the most chance of error. Yes, I have framed 22″ pitch roofs, not fun –
I always say, whatever method works best for you that you can get consistent results in the shortest period of time.
hi there Tom
I have just come across your article and you tube video on how to lay out and cut a common rafter, I was wondering if you have considered compiling a similar video on how to lay out and cut a hip rafter ?
The article and video on the common rafter lay out is very informative, prcise and a joy to watch.
many thanks Shane
Hi All, I am new to this rafter lingo and techniques but am building a shed that is 16’x16′. I plan to have 2×10 joists so there will be a second floor. From the second floor, I have added another 2′ framing around on which the roof rafters will sit. I plan to support the ridge beam with support beam in the middle and the ends. My question is how do I determine the rafter cuts and the support beam height if I want the bottom of the ridge beam to be 72″ high (so I can stand without hitting my head walking down the center) with respect to the second floor?
Hello, I have a question. Since the Illustration is base on a 2×6 for the rafters, is it the same as using a 2×4 for rafters. Can you do the same Illustration? but this time on a 2×4 . If it’s feasable. I’m just confused.
Yes, you can, but a 2×4 won’t leave you much material at the seat cut, and 2×4’s won’t span very far. Even a 2×6 isn’t often used for rafters.
Just a quick question, I’m building a shed using a 2×6 ridge and 2×4 raffters, will your method work? And loved the video, just like most comments here BEST EVER easy to follow.
Yes it will work with 2×4 rafters. Just don’t cut a full seat cut if you are going to have an overhang . I would suggest a 1 ½ “ seat cut on a 2×4.
MIKE: LOVE YOUR VIDEO VERY DETAILED. THANK YOU.
Wow! This is one of the best articles I have read on how to do something. I did not watch the video until after I followed the instructions outlined. Made a couple mistakes as I was trying to go off memory, but when I followed step by step in using the framing square, I got it marked and cut with no problem. I then came back and watched the video, the video was just as detailed and step oriented as the instructions!
I am contemplating building a shed, and was apprehensive about putting on the roof. But now, I feel confident I can do it!!!
First off, thank you for the great information. For a handyman, but inexperienced in roof framing DIYer like me I found your presentation to be one of the best I found online. I understand the concepts of roof pitch, span, run and ris. However, I’m still confused. I’m building a small gable roof over a front stoop. In your presentation, the top of the rise falls somewhere in the bottom 3rd of the rafter width. I understand how you calculate the Ridge post length, taking into account the HAP, which makes most sense. Your red triangle’s hypothenusis is somewhere within the thickness of the rafter. My confusion comes from other presentations where (in all, except yours) the rise is at the very top of the Ridge board. In that scenario, the slope of the rafter can vary, depending on the depth of the bird mouth cut. In those presentations the hypothenusis is the top edge of the rafter. Cutting the seat of the bird’s mouth 1″ or 2″ deep for example will alter the length of the seat cut, but more importantly, will alter he slope of the rafter. The top point of the rafter in this case, where it meets the top of the ridge board is like a pivot point in that scenario. How do I reconcile the two scenarios? Which way is the right way to do it? I hope I managed to explain where my confusion is coming from.
Thank you very much for your help.
Cutting the seat cut at varying lengths does not alter the pitch of ( or as you callout slope ) the rafter i. It changes the height above plate which in turn will adjust the height of the ridge .No angles or pitch change
The HAP is adjusted by how deep the seat cut is – That is why we showed the Red triangle so you can visualize what the calculator “sees” – Don’t over think this – lookback at the HAP illustration – THEN go layout some theoretical rafters – It will gel …
Maybe I’m being too precise but it seems like you have to start with a guesstimate before cutting the rafter.
For example: say your run is 15’ (span is 30’3”) I have a 3”x8” ledger beam. My rise is 10’. So I have an 8:12 pitch (slope whatever, new to this and not arguing terminology). BUT I have a 3”x3” wall plate. So I feel I need to adjust my previous pitch to accommodate the rise from the floor. So now I need to know the measurement from the corner of the bird mouth to the top of the rafter. Since my original angle has changed I don’t know what angle to draw either plumb line to give me any measurement.
No guestimate – Roof pitch doesn’t change regardless of the “bird mouth ‘ – Seat cut . what changes is the height above plate –
That will in effect change the height of the roof, but not the pitch.
NOW – if you are framing to a fixed elevation with an unknown pitch – that a different story – This article doesn’t address that –
If you are framing to a fixed elevation do a google search for my article – Framing to a fixed elevation .
You can’t know the exact angle unless you know exactly where the rafter will sit on the plate. You can’t know exactly where it’ll sit on the plate without knowing the angle you need to cut. I think everyone just picks a number that is close on the depth of the birds mouth… and goes from there. That’s what it looks like to me. Don’t get me wrong I’m not arguing, I’m brand new to this but have a strong background in math. I’m trying to understand how it works out with the math…
Thanks for doing this. I’m a backyard DIYer. I built a 6-12 roof over my chicken coop, but it was a struggle. I build a jig for round two and that went better. This is much much better. This is was some high falutin people would call a methodological argument.
For someone walking in cold this is spot on. I know how much effort it takes to put these together, so for those who criticize please be respectful.
I’m building an 8×12 shed with a simple roof. I set the first set of rafters on the floor and made a jig once the top was aligned and the birds mouths were flush with the shed floor. I was having problems with subsequent rafters fitting in the jig and then realized the reason is that my 2×4’s are not the same width. While the one I’m using as the standard is 1.5×3.5 as expected, some others are actually one or two eighths wider and this is messing up the fit. Should I:
1. Make sure the birds mouth is flush and just cut off the tip of the rafter to make it the same height as the others.
2. Make sure the top is the same height as the others and just cut the birds mouth a bit longer which will reduce it in size by about two eighths.
3. Or….just take all this lumber back to Lowe’s and not only check for straightness but also measure every single board for its dimensions?
This is nothng new – We deal with this all the time –
personally – +or – ⅛ is perfection in rough carpentry ¼” is considered acceptable & not needing correction – THe most important part of your frame is the roofline at the fascia board – , make it look nice & straight – Me thinks you are sweating too much over eigths of an in inch which – most framers figure is dead on …
Get the Hap consistent by cutting into the birdsmouth if you are a perfectioinist . Make the fascia straight & Level.. Its a shed , not a library in the White house …..
SOrry for the sarcasim –Long day in the field … :)
Seriously . email me & we can chat on the phone —
Honest question should the ridge be increased in depth for the wider rafter?
It is best to have the entire plumb cut of the rafter bear on the ridge , SO yes it should be increased –