Rafter & Roof Pitch Calculator
Common, hip, valley and jack rafter lengths from a pitch — plus why a hip sits at a shallower angle than the common on the same roof.
Bird's mouth and roof area
Framing square reference
These are the rows printed on the blade of a framing square. The hip column uses a 17″ unit of run rather than 12″, because a hip crosses the diagonal of the square that the common rafter crosses the side of.
The two things that catch people out
A hip rafter sits at a shallower angle than the common rafter on the same roof. Both land on the same ridge at the same height, so the instinct is that both are at the roof's pitch. They are not. The hip runs diagonally across the corner, so it travels 1.414 times as far horizontally to gain the same rise. On a 6/12 roof the common rafter is at 26.57° and the hip is at 19.47° — and the gap widens as the roof gets steeper. At 12/12 the common is exactly 45° and the hip is 35.26°.
That is the whole reason there is a 17 on a framing square. A common rafter advances 12″ of run per unit. A hip crosses the diagonal of that same 12″ square, which is 12 × √2 = 16.97″, called 17 in the trade and near enough for layout. So every hip figure uses 17 where the common figure uses 12. Cut a 6/12 hip off the common table and it comes out 25% short, with the plumb and seat cuts both at the wrong angle — an error large enough that it usually gets discovered only after the stock is cut.
And pitch is measured on the run, not along the rafter. "6/12" means six inches of rise per twelve inches of horizontal travel. Hold a level twelve inches up the slope instead and you read 5.37/12 — about 11% shallow. The error grows with the pitch: on a 12/12 roof the same mistake reads 8.49/12, nearly 30% out. If you are measuring an existing roof, level first, then measure down.
- The run stops at the face of the ridge. Half the span, less half the ridge thickness. Forgetting the deduction leaves every rafter ¾″ long on a 2× ridge, which shows up as a ridge that will not close.
- Overhang is a horizontal distance too. An 18″ overhang on a 6/12 roof adds 20⅛″ of rafter, not 18″. It is the same multiplier as everything else on the slope.
- Roof area uses the same multiplier as rafter length. The slope stretches the plan in one direction only, so a 6/12 roof has 11.8% more surface than its footprint. That is the number that decides how much covering to buy — and 12/12 is 41% more, not double.
- Jacks shorten by a constant. Every jack rafter loses one spacing worth of run to the hip, so it loses that spacing × the common multiplier in length — 17⅞″ at 16″ centres on a 6/12 roof. One measurement and repeated subtraction gives the whole hip end.
- The bird's mouth is the one structural cut on a rafter. It is an end notch, and end notches in sawn lumber are generally limited to a quarter of the depth. Deepening the seat to gain bearing removes material exactly where the rafter delivers its load to the wall.
How to use
- Enter the pitch as rise per 12 inches of run, or switch to degrees if you measured an existing roof.
- Give the span outside to outside — the ridge thickness is deducted for you.
- Read the common rafter length, then the hip figures below it.
- Use the framing square table to check your layout against the printed rows.
Frequently asked questions
Is a hip rafter at the same pitch as the common rafter?
No, and this is the single most common misconception in roof framing. A hip rafter reaches the same ridge at the same height, so the instinct is that it must be at the roof pitch — but it runs diagonally across the corner, travelling 1.414 times as far horizontally to gain that same rise. On a 6/12 roof the common rafter sits at 26.57 degrees and the hip at 19.47. The gap widens as the roof steepens: at 12/12 the common is exactly 45 degrees and the hip is 35.26.
Why is there a 17 on a framing square?
Because it is the diagonal of the 12 inch square a common rafter crosses the side of. Twelve times the square root of two is 16.97 inches, which the trade rounds to 17 for layout. Every hip and valley figure uses that 17 inch unit of run where the common figures use 12. If you cut a 6/12 hip from the common rafter table it comes out about 25 per cent short, with the plumb and seat cuts at the wrong angle at both ends — an error usually discovered after the stock is cut.
How do I measure the pitch of an existing roof?
Hold a level horizontally, mark twelve inches along it, and measure straight down from that mark to the roof surface. That drop is the rise. The mistake to avoid is measuring twelve inches along the slope instead of horizontally, which always reads shallow — on a 6/12 roof it gives 5.37/12, about eleven per cent out, and on a 12/12 roof it gives 8.49/12, nearly thirty per cent out. Level first, then measure down.
Do I subtract the ridge board from the rafter run?
Yes. The run is half the span less half the ridge thickness, because the rafter stops at the face of the ridge rather than its centreline. On a standard inch and a half ridge that is three quarters of an inch off every rafter. Skip it and the rafters are all long by the same amount, which shows up as a ridge that will not pull together at the top.
How much longer does an overhang make the rafter?
More than the overhang itself, because an overhang is specified as a horizontal distance and the rafter runs on the slope. It gets the same multiplier as everything else: an eighteen inch overhang on a 6/12 roof adds twenty and an eighth inches of rafter, and on a 12/12 roof it adds nearly twenty-five and a half. Cutting stock to the nominal overhang is a reliable way to end up short at the tail.
How do I work out jack rafter lengths?
They shorten by a constant, so one measurement and repeated subtraction gives the whole hip end. Each jack loses one rafter spacing worth of run to the hip, so it loses that spacing multiplied by the rafter length per unit of run. At sixteen inch centres on a 6/12 roof that is seventeen and seven eighths inches per jack. It is printed on the framing square as the difference in length of jacks, and there are separate rows for sixteen and twenty-four inch centres.
How much roof area does a pitch add?
The same multiplier that gives the rafter length gives the surface area, because the slope stretches the plan in one direction only and leaves the other untouched. A 6/12 roof has 11.8 per cent more surface than its footprint, so a 1,200 square foot plan carries about 1,342 square feet of covering. A common wrong guess is that a 12/12 roof has twice the area of its footprint — it has the square root of two times, which is 41 per cent more.
How deep can the bird’s mouth be?
It is an end notch, and end notches in sawn lumber are generally limited to a quarter of the member depth — so about one and thirteen sixteenths inches on a 2x8. It matters more than the other cuts on a rafter because it sits exactly where the rafter delivers its load into the wall. The usual way the limit gets broken is deepening the seat to gain bearing on a wide plate; a raised heel detail or an engineered connection is the answer there, not a bigger notch. Check your local code, since jurisdictions vary.
Can I use asphalt shingles on a low-slope roof?
Down to 2/12, and only with doubled underlayment; below that they are not permitted at all and manufacturers will decline a warranty claim. The reason is not conservatism. A lapped covering works because gravity carries water over the lap faster than wind can drive it back under, and below the minimum pitch that stops being true. Standing seam metal goes lower because its seams are raised above the water line, and membrane is the practical choice on anything near flat.
Does this size the rafters as well?
No — these are layout figures, not a structural design. How big a rafter needs to be depends on span, spacing, species, grade and the loads your area actually sees, and a roof carrying snow, tile or solar panels is a different calculation from one carrying asphalt shingles. Span tables cover the ordinary cases and an engineer covers the rest. Use these numbers to cut to, once the size is settled.
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