This page explains how to calculate, set-out and cut common rafter lengths used in a gable roof. A hipped roof unless small and completely square would also have common rafters in between the hipped ends.
Unless you want to just leave the rafters long and pull a string line through and cut the tails off later there are two quick calculations to do for the roof rafter lengths as shown in the picture above. One for the actual length from plate to ridge, the other for the added overhang that will take the fascia and soffit boards. You can see in the picture below where the two right angle triangles are that we use to make the calculations.
The difference between the green span and the purple span below is the addition of the horizontal overhang shown above to allow a fixing for the fascia and soffit boards.
We'll cover the purple overhang seperately and deal with the green triangle in the picture first that takes the rafter to the wall plate.
The first thing to do when working out the actual length of a common rafter is determine the horizontal span of the rafter as discussed in the previous page.
Each common rafter span is calculated by subtracting the thickness of the ridge from the total span, then dividing the answer by two. You might need a long tape measure to get the span, then;
(Total span - ridge) / 2 = rafter span
The other thing you'll need is the roof pitch/angle. The roof pitch should be specified on your technical drawings for the job, along with the sizes of the roof timbers. If you are deciding yourself on the pitch make sure it is suitable for your roof covering. There are minimum roof pitches many tiles like slates for example must be laid on to work and not leak.
Once we have the information found above, to calculate the length of a rafter you need to choose from a couple of options.
Depending on the method you choose you can either use a scientific calculator and trigonometry (complicated).
Or, when I pitched my shed roof and when i'm setting out small dormer roofs I often just draw and set the rafter lengths out on a sheet of ply - no need for complicated calculations, just a straight edge and a bevel.
For larger roofs though, you need to use a roofing ready reckoner. A ready reckoner is pretty much a 'rafter calculator' - a book full of rafter lengths tables. Each page has a different table depending on the pitch (angle) of your roof.
There are a few available, I bought a copy of Goss's Roofing Ready Reckoner that a friend recommended for around £15. No sh#t, it's probably paid for itself a hundred times over!
All the complicated trigonometry calculations are done for you, and there's loads more in there too, like diminishing jack measurements and hip rafter lengths and angles as well. I use it with an adjustable stanley quick square.
Once you've measured the run of a rafter, simply look up the right table in the ready reckoner for your roof pitch angle and using the measurements relevant to the span of the wall plates it tells you everything from all the common rafter lengths, plumb and seat angles to the length of the hips, the jack rafter cuts and several others are covered too!
It is also handy when quoting a price for a roof that you haven't been supplied a technical drawing for. You don't need a framing square or rafters to calculate the rafter lengths, you can do it all on paper allowing you to calculate all the materials needed to price the job accurately just by knowing the size of the roof and the centres for the rafters.
So let's imagine the roof has a 3265mm span, the ridge is 45mm thick and the pitch is 30°.
First we need to subtract the thickness of the ridge so that it will fit between the rafters, then divide the measurement by two to get the rafter span:3265 - 45 = 3220
Now, when we turn to the 30° page in the rafter ready reckoner and look up the rafter lengths one of the things it tells us is;
The length of rafter per meter of run is 1.1543.
All we do now is multiply 1.610 by the measurement in the book:
1.1543 x 1.610 = 1.858m
So, the rafter lengths 1.858m long. Easy!
To work out the second length of the rafter we need to work out the overhang measurement. This will ultimately define the width of the eaves soffit board, so it's important to know what you are going to use for that.
In some instances I will work out the exact overhang needed for the fascia and soffit boards and add that to the rafter lengths already calculated. That way you can completely finish the cutting on the bench before taking them up and installing them. Instances like that include things like sheds, dormers, timber framed and other structures where there's little chance of getting it wrong.
If I'm cutting a roof where the wall plate or brickwork aren't perfectly straight/parallel it's better to leave the rafter lengths too long and then cut them off after the roof is installed. You can do this by using a string or chalk line to mark them. So in that instance, I work out roughly what the overhang will be at each end of the roof and make sure the rafter tails are long enough to allow for that when setting out the rafter lengths.
If you are building an extension you will probably need to match it with the existing soffit size of the main building. Otherwise, if you are building new and will be using UPVC fascia and soffit you'll want to know the sizes that it's available in. For this example we'll assume the soffit will be 250mm deep.
That measurement though is horizontal from the end of the rafter to the brickwork (shown in green). We need to hold a spirit level up vertically against the brickwork and measure from the wall plate to the brickwork as well (purple).
Adding these two measurements to the original span (blue) will arrive at the total span for the second rafter length we need. Lets assume for this example from the wall plate to the outside of the brickwork measures 300mm and the soffit size we want is 200mm. Add these to the span we calculated before;
1610 + 300 + 200 = 2110
Now we need to multiply that by the length in the ready reckoner which was 1.543.2.110 x 1.543 = 3256mm
So the second rafter length we need is 3.256 metres.
If you prefer to use the mathematical trigonometry method the calculation for the hypotenuse/rafter size using the pitch and run of rafter can be found here.
Before you can start cutting to length and assembling the roof rafters the first thing to familiarise yourself with is the various terms and cuts that are used on a roof rafter;
A Plumb cut is a vertically 'plumb' angle.
A Seat cut is a horizontally level angle.
A Birdsmouth is a combination of the two cuts made so the roof rafter sits tightly onto the wall plate.
It's also worth noting that the seat cut and plumb cut are always 90° from each other. So if you know one, you can put a square on it to find the other. Also, they will both add up to 90. So if the plumb cut is 45, so is the seat cut. If the plumb cut is 30°, the seat cut must be 60° and so on.
When constructing roof rafters, always cut a pair first and try them to check they fit. Once happy, use one of those as a pattern to cut the rest with. Always use the same rafter as the pattern to ensure accuracy.
Cutting roof rafters can be done as simply as with just a sharp hand saw and a bevel (or two to save setting them up twice) if that's all you have but it is both labour intensive and time consuming. The problem with two bevels though is they are easy to mix up and therefore make a mistake with and they can also move if knocked. It's better to make a ply jig (cut a plumb cut on an offcut of ply or timber around 500mm long and a birdsmouth, this can be used to quickly mark rafters once measurements have been applied) or use a roofing or framing square. For speed when cutting lots of rafters use a circular saw.
Before you can mark the rafter lengths and layout, check the camber of the timber. Lengths of roofing timber almost always bow slightly. Look down the length of the timber to see which way it 'bows'. The Bow should always be on the upside of the rafter so when the weight of the tiles goes on it will more likely straighten the rafters out than bow them down even more.
Set a square or bevel to the plumb cut and mark the angle on the end of the timber. The picture above shows the first rafter lengths in green which is from the ridge to the wall plate. The purple length is the second length to carry the fascia. The lengths are the same from long point to long point, or back point to back point.
When cutting the birdsmouth it should only be cut into the roof rafter up to 1/4 of the width. Sometimes its easy to measure the width and divide it by 4. The fastest way i've found to mark 1/4 of the width when it's not straight forward?
Take for example, a rafter with a width of 175mm, or 7 inches. Hold the tape measure across the width of the timber and keeping the 'zero' end in place, pivot the other end of the tape round until the 8 inch mark meets the timber. Now mark 2 inches onto the timber, which is a 1/4 of 8 (alternatively if metric, hold 200mm across and mark where 50mm falls).
Cut the birdsmouth with a circular saw and finish off with a handsaw if needed.
Mark a plumb and seat cut at the bottom of the rafter where you want the fascia and soffit to be.
Have a question or comment about rafter lengths?