1. Pattern Rafters & Calculations
Gable & Hipped Roof
M.S.Martin
Nov. 2005, Revised Feb. 2006
Reviewed March 2010

2. Explanatory Note
The Rafters (Timber sections) shown in this slide show will not appear full size in relation to the dimensions given, however
The overall principle and methods used are precise and have been purposely made larger in scale to aid explanation.

3. First some simple Terms
SPAN
½ SPAN

4. Now lets look at some simple Math's
Lets use 28° as an example for the pitch of our roof.
Find the tan button on your calculator.
Now press tan, 28, = and your answer should be .532mm
You have just given yourself the rise per metre run for the common rafter.
Lets relate this to a square on the next slide.

5. Rise per metre run of rafter
This means for every 1.0m you go along the bottom or span of the roof, you rise up 532mm. (for our example of 28º)
If you simulate a steel square as the triangle of a roof, you can divide these measurements by two to use on here.
See opposite
1.0m = 500mm (goes on the
blade of the square)
532 = 266mm (goes on the
tongue of the square)
266mm
500mm

6. You have also now created the two bevels you need
Plumb bevel common rafter.
Level bevel common rafter.
We can use the square set up like this to set out our pattern rafter.
266mm
500mm

7. True length per/m and Centre Line Length
Use your rise per /m run measurements for this and square root them.
√ .532² + 1.0²
= √ 1.283
= 1.133mm
Centre line length
Use the true length per/m and half span for this.
T/L per/m x ½ span of roof
As an example we will use 3.6m for the ½ span of our roof.
1.133 x 3.6
= 4.079m
This is the measurement from the centre line of the ridge, to the back of the birdsmouth, measured along the top of the rafter.

8. The Gable Roof

9. Start with a simple Plumb Bevel
Use your steel square for this bevel, or other means if you prefer.
This is the centre line for the top of the rafter (centre of ridge position)

10. Measure the centre line length of rafter and place another plumb bevel
This line is the back of the birdsmouth position

11. Alternatively, step out your length with a steel square
This line is still the same position (back of birdsmouth)

12. Now we mark the level cut on the birdsmouth (Max. 1/3 Rafter depth)
Maximum 1/3
This is easiest with a builders square, or you can simply mark square off the plumb cut.

13. Two more things left, 1. Reduction at the ridge, 2. Eaves overhang
Now measure eaves overhang square off bottom plumb cut
Measure half ridge thickness square off plumb cut and place another plumb cut
This pattern is now ready to cut, so other rafters can be marked off it.The lines shown blue are where you cut the rafter.

14. Your pattern rafter and the Gable Roof.
Now look at the roof and your pattern above, any questions?

15. The Hipped Roof

16. Lets first look at the pattern we know, then add to it.

17. For the hip lets look at it in solid form, for there is marks we need to place on the edge as well
Cut for eaves overhang
Cut for top end of rafter
Centre line
Birdsmouth

18. With a hipped roof, we need to add creeper cuts to this patternL
Now this becomes the centre line of first creeper C
We can do this with your square or by measurement
The two distances you need are either (1) rafter spacings at base of square, or (2) true length at the top.

19. Measurements and calculations
Before we go any further, lets note down some more figures.
(1) Rafter spacings, for our exercise, lets say they are at 450mm centres. This means your centre to centre measurement on base of square would be 450mm.
(2) Now for the true measurement at top, if you choose to do it this way, we need to do a simple calculation. Remember our ‘True length per / m’?
True length per / m x rafter centres gives you measurement (2) above.
1.133 x .450 = .509mm
Lets look at the rafter again

20. Steel Square centre to centre measurement
450mm measured at base of square

21. True length centre to centre measurement
True length of 509mm is measured at top of rafter.

22. 1st Creeper adjustment Centre line of first creeper C
From this centre line point we need to mark the ‘long point for the first creeper' and we can do this with two simple measurements.
1) half mitre thickness of the hip
2) Half the thickness of a rafter. First lets look at what this means

23. Adjustment measurements
Half the mitre thickness of a hip
Half the thickness of a rafter

24. Adjustments on the rafter
Forward half thickness of rafter
Centre line of first creeper C
Gives you long point of first creeper
Back half mitre thickness of hip

25. The Geometry as to Why
Now lets look at the rafter again

26. Pattern Rafter with first Creeper
Centre line of first creeper C
Long point of first creeper
The last step is to mark remaining creepers, which you do with centre to centre measurement, either by square or by measurement of true length.

27. Marking remaining creepers Note: this will be there long point
Long point of next creeper, and continue down the length of the rafter for longer lengths C
Start from long point of first creeper
Simply mark remaining long points from here, the simplest way is with a steel square

28. One more item – the Crown end cut
Simply measure ½ the thickness of a rafter from original centre mark, this is your crown end cut.

29. Your finished Pattern for a hipped roof
Second creeper long point
Crown end cut C
Common Rafter cut
Birdsmouth
First creeper long point
Centre line of ridge
Remember: longer rafter, more creepers marked
Plumb cut for eave overhang

30. Have another look at the Hipped Roof