Roof pitch from any measurement
Enter a rise and a span, a rise and a run, an x/12 pitch or an angle, and get all the others back: the pitch, the angle, the slope multiplier, the framing-square figure, and the plumb and seat cuts — with the plumb line printed at true size to set a bevel gauge from.
Plate to ridge, plumb
Outside of wall to wall
26.6° from level
6:12pitch
Angle
26.6°
Slope multiplier
1.1180
Grade
50.0%
The same roof, every other way
- Rafter per foot of runThe framing square's common-rafter figure
- 13.42"
- Plumb cutSaw setting off square, for the ridge cut and the heel
- 26.6°
- Seat cutSaw setting off square, for the birdsmouth seat
- 63.4°
- Bevel gaugeBetween the rafter's edge and a plumb line — the template below
- 63.4°
- Rafter line, plate to ridge168" of run — before the ridge board and the tail; the rafter calculator takes both off
- 187 13/16"
What can go on it
All 2 checks passShow the numbers
- At least 2:12 for asphalt shingles — passesAt 6:12, shingles take a single layer of underlayment.
- At least 3:12 for exposed-fastener metal — passesAt 6:12, lapped exposed-fastener panels need no lap sealant (R905.10.2).
- At least 2:12 for asphalt shingles — passesAt 6:12, shingles take a single layer of underlayment.
- At least 3:12 for exposed-fastener metal — passesAt 6:12, lapped exposed-fastener panels need no lap sealant (R905.10.2).
The slope limits are the 2021 IRC's, and they are defaults rather than law where you are building. The roofing maker's own minimum is often stricter. Ring your building department.
Plumb cut, at true size
Print at 100%, check the ruler, then lay a sliding bevel's stock on the baseline and its blade on the second line. Locked there, it marks every plumb cut on the rafters.
Put a tape on the printed ruler. If it does not read exactly 6 inches, the print was scaled — set the print dialog to 100% or “Actual size” and print it again. Do not cut wood from a template that failed this.
The baseline is the rafter's top edge; the second line is plumb. The seat cut is square to it.
Printing this properly
In the print dialog, set the scale to 100% or “Actual size” and turn off “Fit to page”. Measure the printed ruler with a tape before you trust the angle.
Worked example: a 7 ft rise over a 28 ft span
A ridge 84" above the plates of a building 28 ft wide rises that far in half the span, 168" of run — a 6:12 roof, 26.6° from level and a 50% grade.
Its slope multiplier is 1.1180, the framing square's 13.42" of rafter per foot of run, so the rafter line from plate to ridge is 187 13/16" before the ridge board and the tail.
Plumb cuts go 26.6° off square and the seat cut 63.4°; a bevel gauge set to 63.4° from the rafter's edge marks the plumb line.
- Pitch
- 6:12
- Angle
- 26.6°
- Slope multiplier
- 1.1180
- Plumb cut
- 26.6°
- Seat cut
- 63.4°
These are the figures the calculator above opens on. Change any field and it works the same problem for your numbers.
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About roof pitch
- How do I convert roof pitch to degrees?
- Take the arctangent of the rise over 12. A 4/12 roof is 18.4°, a 6/12 is 26.6° and a 12/12 is exactly 45.0° — the one pitch where the rise and the run are equal. Going the other way, the rise per foot is 12 times the tangent of the angle.
- How do I find the pitch of a roof I can't get on?
- Measure it from the attic or the gable end: the height of the ridge above the top of the wall plates, and the width of the building. The run is half the width, because the roof rises from both walls to one ridge — so a ridge 7' above the plates on a 28' wide building is 6:12, not half that. A level and a tape held against a rafter, reading the rise in 12" of run, gives the same answer directly.
- What is a roof pitch multiplier?
- How much longer the roof is along its slope than across its plan. At 6/12 it is 1.1180: multiply a footprint by it for the roof area, or a run by it for the rafter length. It is the same figure as the framing square's 13.42" of common rafter per foot of run, divided by twelve.
- What is the lowest pitch for shingles or metal roofing?
- Under the 2021 IRC, asphalt shingles need at least 2/12, with a doubled underlayment below 4/12 (R905.2.2). Lapped exposed-fastener metal panels need 3:12 without lap sealant, 1/2:12 with it, and standing seam 1/4:12 (R905.10.2). Those are defaults rather than law, and the roofing maker's own minimum is often stricter.
- What angle do I set the saw to for a plumb cut?
- The pitch angle, off square: 26.6° at 6/12, for the ridge cut and the heel. The seat cut is its complement, 63.4°. If you are marking with a bevel gauge against the rafter's edge instead, the plumb line sits at 63.4° to the edge, and the calculator prints that angle at true size to set the gauge from.
You might also need
- RaftersCommon, hip and jack rafters for any pitch, with the birdsmouth laid out and the cut angles alongside.
- Roofing calculatorSquares, bundles, starter strip, ridge cap and underlayment from a building footprint and a pitch.
- Metal roofing calculatorPanels and their cut length from a footprint and a pitch, with ridge cap, eave and rake trim, purlin rows and screws.
- Roof truss calculatorTop chord, bottom chord and web lengths and angles for a king post, queen post or Fink truss — the geometry, not the engineering.