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How do I cut that bastard?

tomc5's picture

I have two roofs to worry about on an L-shaped colonial. The L has a hip with 7/12 pitch on either side and the front being 12/12. The other roof is the main being 12/12 with the 7/12 L intersecting square to it.

My first problem, is the cheek cuts on the hip and jacks. Can the compound angle be determined from the scales on the 2-foot square? Or are these scales only good for equal pitch hips? Now that I think about it, I don't even know how to figure the seat cut on this bastard hip. What marks would you hold on the framing square? And how much to drop the seat? (All lumber is 2x and CDX sheathing, so I'm not worrying about backing the hip.) I'd like to learn how to do this without lookup tables, because I know very well, the book will disappear when I need it most.

Second problem is the valley where the 7/12 L intersects the 12/12 main. Am I right in thinking the valley cheek cuts could be figured the same way as the bastard hip jacks? But the bigger problem is a complication I never had to frame for - the both intersecting ceilings under this valley will be cathedral, so the valley rafters can't extend lower than the valley jacks of either the 7/12 or the 12/12. Is there a way to figure the width of the valley w/o putting it up and scribing along a few points of the valley jacks? And what about a bevel on the bottom of the valley, how would you figure these bevel angles? (It seems to me this is going to be a lot of trial and error, but structurally AND cosmetically it has to look right by the time I'm done. I don't want to go into a job having to rely on rockers and tapers to cover my experiments)

I know I'm not the first to have to do this, so all advice and experience is welcome.

(post #160554, reply #2 of 113)

When I run into something like that I figure it mechanically, in other words I lay the squares aside, hold the board up there and eyeball the thing, not as impressive as knowing all the degrees and scales, but just as effective and much faster. Never been stumped this way, but made a lot of firewood cutting on the ground.

(post #160554, reply #3 of 113)

First, your hip and valley is figured as such:

1. 7x12 = 84.

2. square root(7squared + 12squared) = square root(49 + 144) = square root(193) = 13.8924

3. 84/13.8924 = 6.04647

4. 6/12 pitch.

We could give you all the formulas, but your best bet is just to frame the roof with your commons and ridge, then run a string exactly where your hips/valleys go. You can then use your speed square to find heel cut lengths and angles.

If you're going to be doing any more of these, I'd recommend buying a Construction Master IV. If you need more info, contactme, I'll be glad to help.


(post #160554, reply #4 of 113)

Here's a good website to learn more about roofs, too. Forgot about it until after I posted.

(post #160554, reply #5 of 113)

I am installing stairs in a well opening 8'10" and the floor height is 9' exactly.
Stairs can project 8'10".
What's the riser height?
This is my first time attempting this.

(post #160554, reply #6 of 113)

Can you put a landing at the bottom and make a few steps turn an opposite direction off of this? Is the reason you can only have a total run of 8'10" because of 3' clearance at the bottom to a wall or something?

I am having a hard time coming up with a good measurement because you will need 14 or 15 risers and your tread run would be too small. Please give me more info.


(post #160554, reply #7 of 113)

Remember if you think the stairs have to end at the same point as your stairwell opening, they don't. You just need 6'8" headroom. Also, if you have 14 steps, your rise would be 7.714". 15 steps would be 7.2". And also you have to minus the thickness of the finish tread from your bottom riser. Please send more info though and I will try to make the numbers work for your treads.


(post #160554, reply #8 of 113)

Or, just e-mail me with your plans if you prefer (pics or sketch or floorplan, something like that.)


(post #160554, reply #9 of 113)

I am working with limited projection space.
There is a door at the right where the bottom step will be.
The length of the projection will be 106".
The finished floor to floor measurements is 108".
Tread thickness is 1". Do the run determine the width of the tread?
Thanks CD

(post #160554, reply #10 of 113)

The problem is that you need to leave a 36" clearance between the door and the steps to meet code requirement. You could put in 13 risers (even though I don't like that for this total rise) but you will not have a 36" clearance for the door. I responded to your e-mail and will talk with our architect today. I'm busy right now but will get back with you later this evening.


(post #160554, reply #11 of 113)

It sounds like you have a nice project going Tomc.

The bastard hip and valley system that you are describing can indeed be calculated. The tables that are supplied on the framing square will not do it however because they only concern themselves with equal pitched roofs.

I'm going to pass on explaining the steps needed to figure your roof parts. It's not all that complicated if you are an experienced roof framer as I'm sure you are (I can tell you have significant experience because you are asking the right questions). I will however tell you that our resident roof expert is Ken. I'm amazed that he hasn't already swooped in here and did his usual great job of explaining the math and giving precise answers. He's probably too busy wrapped up in those circular stair threads on the main page that Stan has started.

I would advise caution about only using the roof explantion reference website that Allyson suggested. I have extensive experience (including bastard hips) with roofs dating back to the 70's and I get very confused at the suggested site. It might be the perfect site for you however, so give it a look and form your own opinion. It might not provide the explanations that you seek however because the last time I perused the site, the author hadn't finished the section on unequal pitched roofs. I haven't been there in a while however and it might be done now.

If I see Ken lurking or posting, I'll send him in here to educate you. I guarantee you will have good solid explanations with great easy to read graphics. Don't be afraid to seek him out and direct him in here. He loves these roofing challenges although this is just a walk in the park for him.


(post #160554, reply #12 of 113)

Hi devil,
Thanks for the post (good name!),
I hope Ken stops by soon. I'm anxious to hear from anybody on this roof problem. I've cut a few rafters in my time (~25 years) but I'm really stuck on this one. I know the language so Ken won't have to get too elementary.

(post #160554, reply #13 of 113)

Tom: Blue is correct about Ken. He is very unselfish with his knowledge and does his best to explain it. I e-mailed him telling of this interesting problem.

(post #160554, reply #14 of 113)


After those flattering comments by blue eyed devil and Stan, I guess I better come up with some answers for you.

Let's start with an easy one.

1) How do you determine the cheek cut bevels on the jack rafters?

Draw a right triangle as shown in the diagram below. Since the unit rises are 7" and 12", make one leg of the triangle = 7", and the other = 12". Use your "speed square" to measure the angles of the triangle as shown to get the bevels for the jack rafters, as well as the hip and valley rafters.

If you're at the job site, you can do this on a square corner of a sheet of plywood. If you draw the triangle accurately, you'll find that the cheek cut bevels are 30 1/4º and 59 3/4º, or about 30º and 60º.

The smaller angle, 30º, will be the bevel on the 12/12 jack rafters, and the larger angle, 60º, will be the bevel on the 7/12 jack rafters.

This method will work for ANY combination of intersecting roof pitches, provided you are working at a square corner of the building, or a 90º corner.

Another easy way to figure out the bevels is to use a calculator that has trig functions.

Arctan (7/12) = Arctan .5833 = 30 1/4º, and

Arctan ( 12/7) = Arctan 1.7143 = 59 3/4º.

Here's yet another way, if you own a Construction Master IV calculator.

Enter 7" as rise, and 12" as run. Then press pitch. Obviously, the calculator will display 7". Now press pitch again, and the calc will display 30 1/4º. This is the bevel for the 12/12 jacks, and if you subtract it from 90º, you'll get the bevel for the 7/12 jacks, or 59 3/4º.

I have 2 questions for you Tom. Are the common and jack rafters for your roof 2 x 8 and the hips and valleys 2 x 10? If not, what are they? I'll need to know that information eventually.

Also, when are you starting the roof cutting?
< Obsolete Link >

(post #160554, reply #15 of 113)

Thanks for offering to help. The commons and jacks are 2x8 @ 16"O.C. The hips are 2x10. The plans don't call out a size on the valleys, but just a note showing "Double, Minimum". So I'm planning on 2x12's knowing I'll have to trim and bevel them. Woodwork won't start until mid April.

(post #160554, reply #16 of 113)


Let me make sure I understand your last post.

Are you planning on doubling the hips and the valleys, or just the valley that is vaulted?


(post #160554, reply #17 of 113)


Here's a sketch which indicates how the hips and valleys appear when the 2 roof pitches are 7/12 and 12/12. Notice that the angles that the irregular hips make with the plates, is the same as the jack rafter bevels that we have already found, 30 1/4º and 59 3/4º.

Does your roof look anything like this sketch? Perhaps you could use the sketch to describe your roof in comparison.

Here's another question. Do the blueprints show that the overhangs are equal or unequal for the 2 different pitches? If they are equal, the roof plan will show the hips and valleys offset from the corners. If the overhangs are unequal, they will pass directly over the corners of the house.

Do you have a scanner?
< Obsolete Link >

(post #160554, reply #18 of 113)

Your picture is the right interpretation except reversed and the the main roof ends in a 7/12 hip. If you are interested, the lengthwise footprint of the main building is 45' long x 20' wide. The L is 14 wide x 16 long (the long side is square to the main). The soffit detail shows same height throughout, so I'll adjust the overhang width as needed to maintain the straight elevation. In other words, the hips and valley come to the corners. I think your other question was on the valley being doubled, but I'm seeing now that the hip roof which projects into the L may also have to have doubled up hip rafters in order to let me put on the correct bevel for the vaulted ceilings.
Lastly, no scanner.
Thanks again for helping,

(post #160554, reply #19 of 113)


Is this it? If so, which hips are do you think need to be doubled?

< Obsolete Link >

(post #160554, reply #20 of 113)

That is it exactly. The vaulted ceiling lies beneath the area of V1, H3 and H4. The V1 is definitely doubled because that is what the desiner wanted. H3 and H4 I am thinking should be doubled only to easily accomodate bevels on their underside to match the planes of the respective vaulted ceilings. I'm assuming you would extend H4 all the way to the plate (or would you run H4 to R2 and run R2 all the way through?) Maybe I'm assuming too much here, so I'll wait for your advice.

By the way, I'm with you on the angle cuts for the jacks, I don't exactly see why your layout method works mathematically, but I got the same numbers as you on the Construction Master. What will be the settings on the square for the hips and valley?


(post #160554, reply #21 of 113)


I like to use 22" on the body of the framing square when I cut irregular hips and valleys, such as in your roof. The setting on the tongue of the framing square would be 11 1/16" in this case. ( the pitch of the hip and valleys is just slightly larger than 6/12 )

The number 17 has no particular significance when 2 different roof pitches intersect, but if you'd like to use 17 on the body of the square, the setting on the tongue would be 8 9/16".

The reason that I like to use 22 rather than 17 or 12, is simply to get a longer plumb line on the tongue of the square.

Tom, could you be a little more specific about the vaulted area? Where does it end? and at what level? Thanks


(post #160554, reply #22 of 113)

The vaulted area is the 20x14 area directly below V1, H4 and H3. What you call vaulted - I really mean as cathedral. Plate height is 8 ft high. Ken I appreciate your help on this, and your spending a lot of time with me here, but don't go crazy on this (that is my job!) I'm just looking for general help and advice. But thanks for all you have to offer.

For the rafter settings, on the bastard hip/valley, how are you figuring your 11 1/16 or the 8 9/16 ?


(post #160554, reply #23 of 113)


I've posted information showing how to determine the pitch of an irregular hip/valley several times in the past. As a matter of fact, if you scroll down towards the bottom of "Construction Techniques" topics, you'll find the thread,

< Obsolete Link > Maurice Doyle "Roof framing - HIP joining two different pitch roofs" 2/26/01 3:02am

In that thread, I showed how to find the rafter square settings for 17 on the body of the square, but as I've mentioned, I usually use 22 on the body to get a longer plumb cut line.

Let me go over it once again for your situation where the 2 roof pitches are 7/12 and 12/12.

The two unit rises involved are 7 and 12.

Step 1) find the product of the unit rises...7x12=84

Step 2) find the square root of the sum of the squares of the unit rises,

square root(7²+12²)=square root(49+144)=square root(193)=13.8924

Step 3) divide the result of step 1 by step 2


This is the unit rise of the hip/val. In other words, the pitch of the hip/valley = 6.0465/12 or about 6 1/16/ 12

If you want to use 17 on the body instead of 12, just multiply 6.0465 by 17 then divide by 12

6.0465 x 17 = 102.7905

102.7905/12 = 8.56, or about 8 9/16". This would be the setting on the tongue for 17 on the body.

If you want to use 22 on the body, multiply 6.0465 by 22, then divide by 12.

6.0465 x 22 = 133.023

133.023/12 = 11.08 or about 11 1/16". This would be the setting on the tongue for 22" on the body of the framing square.

This method will work for ANY 2 roof pitches at a 90º corner.

I'm reposting the roof plan that I drew with the cathedral ceiling shown by the rectangle ABCD. Is this correct?

Apparently, the bottoms of the rafters will form the ceiling in this entire area, which I find unusual. Usually a vaulted or cathedral ceiling is more symmetrical in appearance, as viewed from below. But so be it.

Notice that a small part of ridge 2 (R2) extends into this area and will also have to be beveled to the plane of the ceiling.

A quick comment about your concern regarding the time that I put into these posts. Nobody is twisting my arm Tom. I enjoy what I am doing here, as long as I have the free time, which I usually do.

< Obsolete Link >

(post #160554, reply #24 of 113)


I didn't get around to answering one of your questions from a previous post.

As you suggested, you could either allow Hip 4 to run all the way to the plate, or, extend ridge 2 to butt to the king rafter as shown in the attached diagram.

My choice would be to extend the ridge, but you could do it either way.


(post #160554, reply #25 of 113)


Your sketch is right on as always. I agree with you that it is an unusual structure, to the point that I don't think that I can't make a fair $ on it. It is being built as an "Outbuilding" on an estate to be used as a clubhouse/boathouse/workshop/"stable" for the porshe.

Anyway, your post gives me a good formula for the hips/valleys that I was looking for. This looks just like what Allyson told me a few days ago but his base 12 was throwing me off. Your explanation brings it all together for me.
So, now I'm smart on hip and valley cuts. I'm pretty good on the jack cheek cuts. I found your archive seminar on backing bevels. I quess the only thing I don't know now is how to figure how much to drop the hip, and maybe the common difference on these bastard jacks. Also Ken do you ever need to drop a valley rafter as we would do on a hip? If you get some time can you spare me a few words about these?
Thanks again

(post #160554, reply #26 of 113)

Hey Joe,
How is it you have the energy and mind matter to do these graphics after working all day? Your website is fantastic and a good service for any body coming along in our footsteps that wants to learn. If only I had access to this stuff years ago, and to guys like you and Ken. Anyway, this building is not much more than a clubhouse for a rich kid. My last posts to Ken basically describes all there is to know about it, except the area above the long part will have a loft.
Thanks Joe,

(post #160554, reply #27 of 113)


I'll talk about dropping the hip in another post, if you don't mind. I don't have the time to go into it thoroughly tonight. But let me answer 2 of your other questions.

There never is a need to drop a valley rafter. When the valley rafter passes over the corner at the building line, it should have the same HAP as the common rafters at that point. ( the HAP is the plumb measurement that remains above the heel cut of the birdsmouth ) The reason that you never have to drop the valley rafter is that the jack rafters can always plane into the center of the valley. This isn't possible with the hip rafters, as the edges get in the way.

Here's how to find the common difference for the jack rafters. Let's do the 7/12 jacks first.

Take your On Center rafter spacing, which I believe you mentioned was 16", multiply it by the larger unit rise, which is 12, and then divide it by the smaller unit rise, which is 7.

16" x 12 = 192"

192"/7 = 27.4286"

Enter this as the RUN on your CM Calculator, then enter 7" as the pitch, and press diagonal to find the common difference for the 7/12 jacks. You should get 31 3/4"

To find the common difference for the 12/12 jacks, multiply 16" by the smaller unit rise and then divided it by the larger unit rise.

16" x 7= 112"

112"/12 = 9.3333"

Enter this as the RUN and then enter 12" as pitch and press diagonal. You should get 13.2", or about 13 3/16". That's the common difference for the 12/12 jacks.

Talk to you tomorrow


(post #160554, reply #28 of 113)


Arent these guys amazing ? Ken helped me sometime ago and these posts are just great for me to read as I wish to learn all I can about roof framing.....Thanks to all that are helping Tom, as many of us, as we peruse your posts, learn as well. Much appreciated. In Toronto, Ontario, Canada.

(post #160554, reply #29 of 113)

Joe and Ken-

If I think about this stuff too much I get confused all over again. You are you saying that if we cut the valley seat to have the same HAP as the commons, that any additional "dropping" is not required. If so, when the valley jacks are cut (starting with a common difference from the last common), where will the jacks attach to the valley rafter ? by this I mean will the top edge of the valley jack cheek cut align with the top edge of the valley rafter, or will the valley jacks stick up from the top edge of the valley rafter a little bit ?

Your attachment of the "Sunroom" is an interesting chronicle of all the calculations for a hip roof. However, your method of dropping the hip is a bit misleading and artificial, as it would only work if your hip was jacks were of the same 2x dimension. For a larger span roof you will likely have to work with 2x8 jacks and a 2x10 or larger hip. what would you really do in this case?

(post #160554, reply #30 of 113)


You have to hold the valley jacks up a little so that they can plane into the center of the valley rafter, unless you cut backing bevels on the top of the valley rafter, then they just plane right in with the edge of the bevels.

You'll have to hold them up higher on the 12/12 side than on the 7/12 side, as you might expect. In addition, if you double the valley rafter, you'll have to hold them up twice as much to plane in, unless you cut the backing bevels ( 14 3/4º on the 7/12 side, and 37 3/4º on the 12/12 side)

I'll explain how to handle the hip rafters over the weekend.

Two questions. 1) are the outside walls 2x4 or 2x6?
2) how much overhang, including the fascia, do the plans show?


(post #160554, reply #31 of 113)


In your last post, you mention that the amount to drop a hip is

"((rise) * (1/2 thickness of the hip)) / 16.97)"

That formula only works for regular hip rafters where a single pitch is involved. It wouldn't be of any use to Tom for his split pitch irregular roof.

I'll go over how to handle the hip rafters tomorrow.