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Available pitches 4/12 5/12 6/12 7/12 8/12 9/12 10/12 11/12 and 12/12
Use our Roof Building Guide below and train yourself on
How to build a Hip Roof and a Gable Roof
In this article I will try to show you how to build a simple
"Hip Roof Garage Building" and "Standard Gable Roof Garage Building
" and try to show the component parts that make up a "equal pitch hip
roof" structure using the "double cheek cut hip rafter method"
used by most framers today.
In this method of construction the center ridge board will grow by half the thickness
of the 1 1/2" ridge board material, usually 3/4" at each end of the structure.
Our example building for this Article:
In this example I will use a 4/12 pitch simple structure measuring 18' 4 3/8" wide and 12' 9 7/8" deep to show that fractional sizes does not present a problem in determining rafter lengths. Also I will be using a 2x10 rafter and a 2x12 ridge board and hip rafter. Rafter material sizes can be changed easily and the lengths will remain the same since I measure all diagonal lengths at the top of the rafter material from the seat cut plumb line to the longest point of the rafter. The HAP (height above plate) figure would be different for different size materials and can be changed for different size material. I will give you the HAP measurements for each rafter material size in figure #1.
This building example will represent a small garage or shed building and will not have interior walls to lap ceiling joist on, so your rafter layout will line up straight across front and back allowing your ceiling joist to tie the rafters together see figure #6. You can change material size to meet your specific requirements and of course comply with local state, city and county building codes.
Developing your building size:
Begin by taking your building depth or the lesser of the two dimensions which would be the "SPAN" and subtracting half the 1 1/2" ridge board which would be 3/4" giving you the "RUN" distance for a regular pitch hip roof see figure #1. This calculation will also give you the ridge board length by doubling the run measurement and subtracting it from the building width as shown below in our example building measurements and also in figure #1.
Building Width 18' 4 3/8" - Building Span 12' 9 7/8" RUN = 6' 4 15/16" Less 3/4"
or half of 1 1 /2" Ridge Board = 6' 4 3/16" Ridge Length = 5' 8"
Figure Your Building now:
Building Width __' ______" - Building Span __' ______" RUN = __' ______" Less __' ______"
or half of __' ______" Ridge Board = __' ______" Ridge Length = __' ______"
How to convert the fraction 3/16" to a decimal:
In the Example building and shown in figure #1 this would be 6' 4 3/16" of run. Since you can't multiply fractions and decimals you can convert the fraction 3/16' using figure #13 "Fraction to Decimal Table" to 0.1875 or you can divide 16 into 3 and carry it out four places to get 0.1875.
You would divide 3 by 16
Now add 6' or 72" plus the 4"
= 76.1875" Total inches of "RUN"
On the face side of your framing square body you will find on the first line the words "LENGTH COMMON RAFTERS PER FOOT RUN". Both common rafter and hip/valley rafter figures are based on your buildings run figure. Some very smart people figured all this out many years ago and it still holds true today.
Now for your building follow that line over toward the right to the tongue or short limb of the framing square until you see above it the pitch you are using on your building. In my example building it would be 4" and under it you find the number 12 65 or 12.65" this would be the multiplier for the example building.
Calculating the Common Rafters:
Common Rafters in my example building would look like this:
- 72" or 6'
6' 8 5/16" the diagonal length of the common rafters.
Using the figure #13 table you will see that .31432 is equal to 5/16" or you can convert the decimal back to fractions by multiplying.
5.02912 or simply 5/16"
As you can see roof builders have been using the framing square and its figures for a long time and they still work fine. Any math calculator will work fine for this math also.
Calculating the Hip/Valley Rafters:
Using your "RUN" figure again multiply it by the number on line 2 under your particular roof pitch desired as follows.
My example building would look like this:
- 108" or 9'
9' 2 3/4" the diagonal length of the Hip/Valley rafters.
Again using the figure #13 table you will see that .7258 is equal to 11/16" or you can convert the decimal back to fractions by multiplying.
= 11.6128 or rounding up 3/4"
Marking your Hip rafters is the same as marking common or jack rafters except you would use 4x17 instead of 4x12 for top and bottom cuts as well as overhang and seat plumb lines. see figure #1f Side cuts are figure #14 to figure #14i
Calculating the Ridge Board:
To calculate the exact length take you total width of your building including the sheathing that the rafters will set against and deduct the calculated "RUN" distance two times leaving you the Ridge Board Length.
In my example it would look like this:
18' 4 3/8"
- 6' 4 3/16"
- 6' 4 3/16"
= 5' 8"
Figure you own buildings common rafter length:
All you need to do is multiply your "RUN" distance you have figured to be _____' __" by the number on your framing square representing your "LENGTH COMMON RAFTERS PER FOOT RUN" and then divide by 12 to giving you the total diagonal length of your rafter. You can do this in the field using a pencil and paper or any normal calculator. You can figure the fractional number or just use the table figure #13 I have provided for you.
If you are building a standard gable roof you can using the method above determine
the diagonal length of the rafter itself and the overhang. This length will also work
for the hanging rafter or "Barge rafter". Figuring the ridge board you would want to
add to the length of the building including the sheathing thickness and the amount of
overhang you want to have. You can rip this overhang portion so as not to protrude
below the hanging rafter for boxing purposes see
and figure #10b.
Laying our your GABLE ROOF system you would measure from the outside of the wall top plate (excluding) the exterior sheathing and mark 15 1/4" and set ahead 1 1/2". Then start your 16" layout from the right side of this mark and set ahead for each rafter. You do not include your exterior sheathing so you can sheet the gable ends with the same material and remain flush with the side wall for siding installation later on. See figure #10c and figure #10d.
Now that you have the common rafter length and run measurements you can layout the
building for all common rafters and jack rafters. Lets start with the rear wall in the
right corner as we are facing it. We now know the run is 6' 4 3/16" "Or Your personal
run _______ " so hooking your tape on the right wall "including the sheathing material"
measure along the rear wall top plate inward or to your left that distance for your
first common rafter and make a mark, now you can square all the way across the top plate
and set ahead 1 1/2" making an X between the two marks so you know exactly where to set
your first common rafter see
figure #5. Now go to the front wall and do the same. Once you have finished this you can then find the exact center of the right hip end wall "including the sheathing material" and layout for the only common rafter that will be on the hip end of the building.
This common rafter will set against and directly in line with the ridge board and be
flush with the top edge of the ridge board just like the first common rafter front and
rear again see
figure #5. From that center mark be sure to offset 3/4" each way to keep the rafter exactly centered. You can now go to the other end and lay it out the same way. Laying out the hip rafter is as simple as marking the center of the corner and off setting 3/4" each way on both corners. You will want to make sure your sheathing forms a correct square corner because you rafter must be set against it or the length will be changed from what it should be.
Once you have completed this, your layout would look like figure #5. There will be only two "first common rafters" that will set at the ends of the ridge board. The rest are the same but only called common rafters.
Working on the rear wall top plate you can now layout all of the common rafters in between the two by hooking your tape to the right side of the first common rafter and proceed to mark each rafter on 16" or 24" centers on both the rear and the front walls as the rafters will line up exactly against each other in this example drawn with 16" on center rafters. It will work the same if you are setting your rafters on 24" center. See figure #5c.
Now still on the rear wall hook on the left side of your mark for the first common
rafter and layout your jack rafters to the right or corner. And again the front corner
jack rafter section will layout the same on any open building allowing a single ceiling
joist to lap and tie the rafters together. The 16" or 24" on center layout will be
maintained until you reach the other end of the hipped building as shown in
and figure #6.
At this point you would simply have to cut a few pierces of roof sheathing to land on
a jack rafter. But this method would allow you to cut all four corners exactly the same
saving you time and money.
If you like you can figure the 16" on center position of the first jack rafter and calculate the remaining jacks like the first section by deducting the difference in Jacks given on the 3ed. and 4th. lines of your framing square.
If you do elect to maintain 16" center on the left side of the building you can calculate the jack rafter diagonal lengths you need to make sure that the jack rafters on the left end of the building at the point they touch the same hip rafter does not differ more than 4" to meet code see figure #7. That's why I say its just easier and more economical to just cut all four corner jacks the same and simply cut a few pieces of sheathing to hit on the center of a jack rafter and continue on in the sheathing process. You likely wouldn't have to cut more than two pieces anyway on each side. see figure #8 and figure #9
If your project happens to be a residence you will need to offset the front rafters
from the rear ones 1 1/2" to work with your ceiling joist which will have to lap over
an interior supporting wall. See figure #11
figure #11 is given to show a typical house rafter layout where the rafters and ceiling. Joist on the front are offset 1 1/2" allowing two piece ceiling joist to lap on an interior wall and tie everything together. In that scenario jack rafters for corner sections 1, 2 and 3 will have to be special cut. If you look at the left end rear wall in figure #11 the first jack rafter would have 4 1/2" between it and the first common rafter. In order to maintain the 16" on center spacing and due to the offset the front jack rafter would have 3". You can simply measure over from the first common rafter with your framing square and mark the top of the first common rafter to get the diagonal length of the first jack rafter. From there you would just deduct the difference in length on lines 3 or 4 to get the rest. The opposite side of that particular hip rafter in that corner section would be the same length.
You would need to do the same thing on the front left corner section (section 2 as indicated on the plan image). And again on the front half of (section 3 as indicated on the plan image) in figure #11.
You can do this two ways, method A starts at the corner and comes inward toward the
first common rafter. It does require you to square the rafter up with the rear wall
which is not always the easiest thing. Or you can us method 8 as shown in
A. You can use the "DIFF IN LENGTH OF JACKS 16" OR 24" CENTERS" given on your framing square line 3 and 4. As in our example building with 4X12 pitch under the number 4 you would find 16 7/8" for 16" layout or 25 5/16" for 24" layout as your long point for the diagonal length of the first jack starting from the corner and coming inward toward the first common rafter.
To gain the other jack rafter lengths you would just add that figure to the diagonal length of the first and so on until you have all the jack rafters you need for your particular building and they would work for all four corners as long, point diagonal lengths. The same will hold true if your building would have any other rafter pitch, just use the lengths given under that number representing your pitch on either line 3 or 4.
B. To maintain your 16" or 24" on center you can use your framing square as shown in figure #8 or figure #9 and mark the top of the first common rafter. You will need to transfer the plumb line at the seat cut to the top of the rafter and then measure that length giving you the long point of the first jack rafter. From that length deduct "DIFF IN LENGTH OF JACKS 16" OR 24" CENTERS" on lines 3 or 4 depending upon which you are using to give you the second jack rafter and so on to the. corner. Its really that easy but you will have to do a little math.
When you start cutting your jack rafters the top or long point will cut on the same angle as your roof system see figure #1d. On your framing square line 5 you will find the side cut for your particular pitch. Our example pitch 4x12 is shown in figure #7 for it to fit properly against the hip rafter. For your particular pitch you can mark it on top of your first jack rafter and then use a small speed square to determine the saw angle to use.
I have included the side cut angles from 4x12 pitch to 12x12 pitch figure #7b / 4x12 - figure #7c / 5x12 - figure #7d / 6x12 - figure #7e / 7x12 - figure #7f / 8x12 - figure #7g / 9x12 - figure #7h / 10x12 - figure #7i / 11x12 - figure #7j / 12x12.
Always sight your rafter material and lay it on your saw horses with the crown or bow
away from you and work from the top of the material if you can as in
figure #1b. If
your material is close to the length you actually need work from the bottom for the top
cut as in
In a perfect world the material would be straight, but that's now
normally the case. I wouldn't recommend using a crown with more than 1/4". You can always
use a straight edge and rip the excess crown off.
What we will layout first is your "Rafter Pattern" that you will use to mark all the other common rafters needed and use the very best material you have.
Start at the bottom of your rafter material with your framing square set on the pitch you want to use and leave enough room for your overhang, see figure #1c. Our rafter material in this example is 2x10. So looking at figure #1 we know that the HAP height or plumb line is 7 5/16". With your square in place mark the plumb line all the way through the material. Since your framing square is set on 4x12 you can just add 4" and 7 5/16" giving you 11 5/16" and make a mark there.
Now with your framing square still set, slide it to the left until you see your mark and mark the seat cut line to your right and to the end of the material. Now you have the birds mouth marked and ready to cut out. While you are there square the plumb line across the top edge of the rafter and you will have it available to measure your first jack rafter if you choose to use that method.
When you start cutting mark at least six on top in the same manner and label them for the four "first common rafters" and two for the two hip ends. You will want to cut this pattern as accurately as possible because all the others would be cut the same way. With this size rafter you can cut through the opposite lines just enough so the birds mouth material can fallout on its own. If your using smaller materials you might want to cut to the lines and finish with a hand saw so not to weaken the overhang. I would say this holds true for material as small as 2x6 and that depending on not more than 24" overhang or you might be subject to overhang failure or sagging.
Now you can turn your framing square over and mark the top of the common rafter as shown in figure #1d. Since you have selected the very straightest material for your pattern it won't hurt a thing working from the bottom.
OK, we now have a common rafter pattern and we re ready to get to some real work
and see some progress. But I have one more piece of advice. Using a scrap piece of 1 x4
cut two pieces about four inches long and nail it to the top of the pattern as shown in
letting it hang below the pattern to create a positive stop and use this as a guide to
keep the top of the pattern flush with the top of the rafter to be marked.
You want to flush the material at the top and at the bottom over the HAP or plumb line so all the rafters set on the outside wall the same. If you try to flush it at the end of the overhang it will cause humps at the outside wall line due to some bowing in the lumber material.
"So don't do that"
Just a couple of special notes here that will help and make your process work better
for you. You already have the length so site you material putting the crown up and go
ahead and mark the length. Don't cut it yet though. You may have a wide structure and
need to have multiple ridge boards as you can only find lumber so long. If that is the
case lay your ridge board out as far as you can go and when you get to the left end cut
the board in the center of the last rafter layout so you can start a new board and keep
going to the other end. I said don't cut it yet and here is why. If your outside walls
differ in length any at all or the hip end walls are not straight you could come up short
on you ridge board.
I recommend adding an additional 3" to it for safety. You can always cut it in the air once you have set the four first common rafters. See figure #5b
Hip rafters are always marked out using 16.97 or 17" on the body and your pitch on
the young of your framing square. see
Side cuts for your hip rafter is found on line 6 of your framing square and must be used for a proper fit. This angle is not a normal 45 degree but will be less. I have drawn them out for you in figure #14 / 4x12 - figure #14b / 5x12 - figure #14c / 6x12 - figure #14d / 7x12 - figure #14e / 8x12 - figure #14f / 9x12 - figure #14g / 10x12 - figure #14h / 11x12 - figure #14i / 12x12 ranging from 4x12 to 12x12 pitch angle.
Cutting the jack rafter is the same as common rafters, using your framing square on 4x12 pitch or what ever your roof angle need to be. see figure #1b, figure #1c, and figure #1d Again you would want to us the side cut angle and not a 45 degree as you might think. I have supplied these roof pitch angles in figure #7b / 4x12 - figure #7c / 5x12 - figure #7d / 6x12 - figure #7e / 7x12 - figure #7f / 8x12 - figure #7g / 9x12 - figure #7h / 10x12 - figure #7i / 11x12 - figure #7j / 12x12.
At this point in the project I would recommend installing all of the ceiling joist. see figure #12 or figure #12c. You can set them on the right or left side of all of your rafters you have already laid out making sure not to set one in the place of a rafter. Once they are up you can install what the old timers used to call a rat run down the center to straighten the joist as you nail the 2x4 down flat and tight to the ceiling joist. Then apply a 2x6 up right beside it see figure #12b. You can and should install this rat run so it will tie with the center common rafter on each hip end of your building see figure #12b. This up right member will keep your ceiling nice and flat and also provide you a walking platform for setting your rafters. You can even lay some of your roof sheathing down giving you a safe platform on which to work. You can use it on the roof when your ready for it.
With your six first common rafters cut you can start setting them in order as I have shown in figure #5b. Let them rest against each other until you have rafters 1-4 set. Now slide your ridge board up between them at the same time on each end. Don't lift either one up as you go. Their own weight will hold them tight against the ridge. Nail rafters 1-3 first and wait on number 4. Slide it inward about three inches and tack it to hold it in place. Now go back to the right hip common rafter and nail it in place flushing it with the top of the ridge board. With that completed go to the left end and set your common rafter in place. If everything is perfect it should be flush with the top and align with your mark. But it probably will not be exactly right for a number of good reasons. So raising it flush with the top just make a new mark and cut the ridge to proper length and finish nailing that end together.
Now you can install the remaining common rafters being sure to pull them tight against the outside walls. I would recommend holding the top of the rafter a little high not touching the ridge board until the seat of the rafter has been nailed completely so as not to push the side walls out. Now your hip roof should look like figure #5.
With your hip rafters cut you can install them now. You have already cut the drop portion off so the top edges should be flush with the side edges of the two common rafters. This will make the long point of the hip appear to be too low but it has to be that way in order to keep the roof sheathing on the same plane coming across the roof. After installing it you can use a piece of scrap and secure it in a straight position.
Installing the jack rafters is not hard at all though I would recommend setting the middle ones first on each side so as not to push a bow in the hip rafter which will cause problems . with the sheathing not resting squarely on each rafter. Again I would recommend holding the top loose until the seat has been nailed completely and then nail the tops of two joining rafters together. see figure #5
For your convenience I have included the plywood cut angles and measurements for hip roofs of 4x12 to 12x12 pitch in figure #12d - 4x12 - figure #12e - 5x12 - figure #12f - 6x12 - figure #12g - 7x12 - figure #12h - 8x12 - figure #12i - 9x12 - figure #12j - 10x12 - figure #12k - 11x12 - figure #12L - 12x12.
All images and designs are owned by Vance Hester Designs and copyrighted 2008-20011. No material may be reproduced or republished for any reason anywhere without written permission.