From one rafter to a roof
The geometry of a single common rafter is simple and it is worked in detail on the rafter length calculator: the run times the slope factor, minus half the ridge thickness measured along the slope, plus the tail. For a 6 in 12 roof the slope factor is the square root of 1 plus 0.25, which is 1.118034, so a 12 foot run gives 13.42 feet of rafter body before anything is added or taken off. That is 13 feet 5 inches, and the extra 17 inches over the run is the whole reason nobody estimates roof lumber by pacing the building.
Turning that into a roof is a different job. The rafter count comes from the ridge direction, not the span direction, and every position on layout carries two rafters because there is one on each slope. A 32 foot building at 16 inch centers has 25 pairs, which is 50 rafters. The ridge runs the length of the building plus both gable overhangs. The ceiling joists or collar ties come one per pair or one per two pairs depending on which you are using. And the sheathing is measured up the slope, which is always more area than the footprint suggests.
The three things people leave out
| Left out | Why it happens | Size of the error |
|---|---|---|
| The second slope | Counting layout positions instead of pieces | Half the rafters |
| Slope on the sheathing | Taking area off the plan footprint | 12% at 6/12, 25% at 9/12, 41% at 12/12 |
| Gable overhang on the ridge | Ordering ridge stock to the building length | One or two feet, which is a whole extra stick |
The sheathing error is the interesting one because it grows with pitch. On a 4 in 12 roof the slope factor is 1.054 and the difference between plan area and roof area is small enough to hide inside a waste allowance. On a 12 in 12 roof the factor is 1.414 and the roof is 41 percent bigger than the building it covers. If you have ever been told that steep roofs cost more per square foot of house, that number is most of the reason.
Ties, thrust and the ridge that is not a beam
A pair of rafters leaning against each other pushes outward at the bottom. In conventional gable framing that thrust is resisted by ceiling joists running the full width and nailed to the rafter feet, which turn the assembly into a triangle. The ridge in that arrangement is a ridge board: it aligns the rafters and gives them something to nail to, and it carries very little.
Take the ceiling joists away, as happens in a vaulted or cathedral ceiling, and the geometry changes completely. Now the ridge has to carry the rafters, which makes it a structural ridge beam with real reactions at each end that go down through posts to footings. Those two members look identical on a drawing and they are not the same thing at all. Collar ties in the upper third are not a substitute for ceiling joists either — they resist the rafters separating at the ridge under uplift, not the outward thrust at the plate.
If your roof has no ties, work the ridge load out on the header and beam load calculator and take the result to a span table or an engineer. Roof loads are taken on the horizontal projection, so the run is what feeds the tributary width, not the slope length.
Cutting and buying
Rafters are not spliced. If the cut length exceeds what you can buy, the roof has to change or the material has to come from somewhere else, and finding that out at the lumberyard is better than finding it out on the wall plates. Work out how many rafters come out of a stick before ordering, and add for crowning: every rafter goes crown up, and a few sticks in any bundle will be too bad to use.
Cut one rafter, check it in place on both ends, and only then use it as the pattern for the rest. The birdsmouth seat depth and the plumb cut at the ridge both want verifying against the actual wall plates rather than against the drawing, because walls are never quite where the plan says. Once the pattern is proven, mark every rafter from it rather than from the last one you cut, or the error accumulates down the roof.
For what goes on top of the sheathing, the roofing squares calculator converts roof area into bundles, and the roof pitch calculator is the quicker way to read a pitch off an existing roof.
Permits
Roof framing is structural and is inspected before it is covered. The items that get flagged most often are the connection at the rafter feet, missing or undersized ties, and rafters notched too deeply at the birdsmouth so that not enough of the depth is left bearing on the plate. Uplift connections at the plate are a significant issue in high wind regions and are checked. None of that is expensive to do right while the roof is open.
Questions people ask
How many rafters does a 32 foot long roof need at 16 inches on center?
Fifty. The layout runs along the ridge direction: 32 feet is 384 inches, divided by 16 gives 24 spaces, and 24 spaces need 25 positions because there is a rafter at each end. Each of those positions carries a rafter on both slopes, so 25 pairs is 50 pieces. The most common error here is stopping at 25. The gable end walls are not rafters — they are framed as walls with studs running up to the rake, and that is a separate takeoff.
Why is the roof area bigger than the building footprint?
Because the roof is sloped and the footprint is flat. Multiply the plan area by the slope factor, which is the square root of one plus the pitch over twelve squared. A 4 in 12 roof is 5.4 percent bigger than its footprint, 6 in 12 is 11.8 percent, 9 in 12 is 25 percent and 12 in 12 is 41.4 percent. Overhangs add further, since they extend the roof beyond the walls in both directions. Estimating sheathing or shingles off the house footprint is the reason people come up a bundle or two short on steep roofs.
What is the ridge deduction and how big is it?
The run of a common rafter is measured to the centreline of the ridge, because that is where the two slopes meet geometrically. The ridge board occupies real thickness there, so half of it has to come off each rafter. The subtlety is that the deduction is taken along the slope, not level: half the ridge thickness times the slope factor. For a 1-1/2 inch ridge on a 6 in 12 roof that is 0.75 times 1.118, which is about 27/32 of an inch. Small, but it is the difference between rafters that close on the ridge and rafters that hold it apart.
Do I need ceiling joists or will collar ties do?
They do different jobs. Ceiling joists run the full width of the building, tie the rafter feet together and resist the outward thrust that the rafters exert on the wall plates. Collar ties sit up in the top third and resist the rafters pulling apart at the ridge under wind uplift. A collar tie does not stop the walls being pushed out, so it is not a replacement for a ceiling joist. If you want a vaulted ceiling with no full-width ties, the ridge has to become a structural beam carrying the rafters, sized by a table or an engineer, with posts and footings under both ends.
Does this handle hip roofs, valleys or dormers?
No. It counts a plain gable with two equal slopes. Hips, valleys and dormers change both the count and the cutting substantially: hip and valley rafters run at a compound angle and are longer than commons, the jacks that die into them are all different lengths, and every valley is a line of extra cutting and extra sheathing waste. If your roof has any of those, use this to get the common rafter field and the sheathing baseline, then take the irregular areas off separately and push the sheathing waste allowance well above the 10 percent default.