Roof Pitch, Rafter and Birdsmouth Layout Calculator
Convert roof pitch and angles, calculate common and hip or valley rafter lengths, and lay out ridge, tail and birdsmouth cuts with a drawn cut sheet and animated assembly.
Use this roof pitch calculator to turn a roof slope and building span into a common rafter layout. It is intended for engineers checking geometry, students learning roof framing, and people preparing dimensions for an approved framing detail. Enter either rise per 12 units of horizontal run or an angle above horizontal. A 6:12 roof rises six units for every twelve units of run; the same ratio works in inches or millimetres.
Measure the span between the outside faces of the opposing walls. The calculator assumes a centered ridge and equal slopes, so the theoretical common run is half that span. Enter the actual ridge board thickness to shorten the common rafter to its near face. Enter overhang as a horizontal projection from the outside wall to the tail plumb cut, excluding fascia. Use the viewer’s metric/US unit switch for dimensional inputs and results.
The rafter length calculator reports three top-edge measurements. A runs from the ridge plumb cut to the outside-wall plumb mark. B continues from that mark to the tail plumb cut. C is their sum. The conservative square-ended blank allowance includes the offset between the top and bottom intersections of the parallel end cuts. At zero overhang it exceeds the geometric minimum because the birdsmouth removes the lower tail corner. Add your own allowance for saw kerf, defects, end trimming, and site fitting before ordering stock.
For a birdsmouth cut, enter the actual timber depth, available wall plate width, and the horizontal seat length specified by the framing detail. The seat starts at the outside wall and extends inward. The enlarged drawing distinguishes vertical heel height V, perpendicular notch depth N, and height above plate H. These are different measurements. The seat and plumb angles are angles of pencil lines relative to the timber’s top edge; they are not universal saw dial settings.
Hip and valley results use equal slopes meeting at a square plan corner. Their diagonal plan run is longer than the common run, so their inclination is lower. The displayed lengths extend to theoretical intersections and include an optional theoretical tail. Connection-specific shortening, cheek cuts, hip backing or dropping, and valley joinery need separate detailing.
The assembly control illustrates how the cut common rafters meet their plates and ridge. The drawings are dimension guides, not printable full-size templates. Verify one trial rafter against the actual building before repeating cuts. This tool does not select member sizes, apply IRC span tables, or check strength, bearing capacity, uplift connections, roof covering requirements, or local code compliance. Construction and installation work belongs to a qualified person using the approved design.
How it is calculated
For a centered ridge, let S be outside-wall span, R = S/2, t ridge thickness, O horizontal overhang, d actual timber depth and s horizontal seat. Let q = p/12 = tan(θ). The calculation uses exact right-triangle geometry, without rounding intermediate dimensions.
Common top-edge measurements are A = (R − t/2)√(1+q²), B = O√(1+q²), and C = A+B. The ridge deduction is (t/2)√(1+q²), measured on the slope, rather than t/2. The reported square-ended blank allowance is C+dq before kerf and trimming. This is conservative rather than a guaranteed minimum: with zero overhang the birdsmouth removes the lower tail corner, and the finished outline instead needs C+(d−N)q. The reported allowance retains the unnotched end-cut envelope.
In the installed section, the seat runs inward from the outside wall. Its inner end meets the original bottom edge. Therefore V=sq, N=s sin(θ), remaining perpendicular depth=d−N, and H=d/cos(θ)−V at the outside-wall plumb plane. The plumb pencil line makes 90°−θ with the top edge; the horizontal seat line makes θ. A conventional square uses p on the rise leg and 12 on the run leg.
For equal slopes at a 90° plan corner, diagonal run=R√2, hip/valley inclination=atan(q/√2), and theoretical slope length=R√(2+q²). Add O√(2+q²) for the theoretical diagonal tail. Use 12√2 (about 16.971), rather than rounded 17, as the square run for that same rise.
The Johnson manual is used for independent length examples (attached pages 9–12 and 16–17); Swanson is used for the pitch conversion check. These checks do not establish structural adequacy.
Assumptions
- Straight, uniform timber with parallel edges and depth measured perpendicular to those edges.
- Centered vertical ridge board; equal pitch and equal plate elevation on both sides.
- Common birdsmouth: outside heel at the outside wall, seat extending inward, and vertical tail cut.
- Hip and valley lengths apply only to equal-pitch 90° intersections; they are theoretical line lengths, without connection deductions.
- The available plate width is an input for geometric fit, not a determination of required bearing.
- Assembly animation shows an illustrative placement sequence with exact common-rafter outline geometry; it does not model erection forces.
- The enlarged birdsmouth section preserves the roof angle and relative timber, seat and plate widths. Wall and plate heights are schematic. The dashed diagonal is the original underside before removing the notch.
Where it applies
Slope entry covers 0.5:12 to 24:12 (approximately 2.386° to 63.435°). The seat must fit the available plate, end before the ridge, and leave positive timber depth. Horizontal overhang is limited to the common half-span. A notch above 25% of timber depth produces a geometric review advisory; this threshold is not a claim about the code permitted for your project.
No member sizing, IRC span tables, allowable notch design, bearing resistance, connection design, bracing, load analysis, or jurisdiction-specific compliance is implemented. Follow the approved framing detail and check against the standard and code in force. Actual work requires a qualified construction or installation professional. Use a trial piece and verify site dimensions. Blank length excludes kerf, stock tolerances, defects and waste. Drawings are schematics, not scale templates.
References
- Johnson Level & Tool, The Johnson Rafter Angle Square manual, pp. 9–12, 16–17. https://www.johnsonlevel.com/Content/files/manuals/1904-0700_1904-1200_1959-0700%20manual.pdf
- Swanson Tool Co., Roof pitch reference, 6/12 entry (accessed 26 October 2026). https://swansontoolco.com/learn/pitch
Inputs
| Input | Symbol | Unit | Default |
|---|---|---|---|
| Enter roof slope as | pitch_mode | Rise per 12 run | |
| Rise per 12 run 6 means a 6:12 slope. A dimensionless rise/run ratio, not rise divided by full span. | p_in | 6 | |
| Roof angle | a_in | deg | 26.5650511771 |
| Span across outside wall faces | span | mm | 6000 |
| Actual ridge board thickness Measured across the span; zero returns theoretical centerline lengths. | ridge | mm | 38 |
| Horizontal overhang beyond outside wall To the tail plumb cut; excludes fascia thickness. | overhang | mm | 450 |
| Actual common rafter depth Measured perpendicular to the timber edges. Enter an already selected member; this tool does not size it. | depth | mm | 184 |
| Available wall plate bearing width | plate | mm | 140 |
| Horizontal birdsmouth seat length Starts at the outside wall face and extends inward. Specify from your approved framing detail. | seat | mm | 75 |
| Roof assembly progress â–¶ Play to lower the two cut common rafters onto the wall plates. Illustrative sequence only. | assembly | 1 |
Results
With the default inputs above, the calc gives:
| Result | Value |
|---|---|
| Roof angle | 26.57 deg |
| Rise per 12 run | 6 |
| A · Ridge face to outside-wall mark | 3,332.9 mm |
| B · Tail along top edge | 503.1 mm |
| C · Finished top-edge length | 3,836 mm |
| Conservative square-ended blank, before waste | 3,928 mm |
| N · Perpendicular notch depth | 33.5 mm |
| V · Vertical heel cut | 37.5 mm |
| H · Height above plate | 168.2 mm |
| Notch / actual timber depth | 0.182 |
| Plumb line to timber edge | 63.43 deg |
| Seat line to timber edge | 26.57 deg |
| Hip / valley inclination | 19.47 deg |
| Hip / valley to theoretical intersection | 4,500 mm |
| Hip / valley with theoretical tail | 5,175 mm |
Checked against sources
Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).
Johnson: 13 ft run, 8:12 common rafter
Source: Johnson Rafter Angle Square manual, pp. 9–12: 13 ft run at 8:12 (the example rounds its original rise to 8:12); common 15 ft 7½ in, tail 2 ft 1⅜ in, stock 18 ft 0 9/16 in. Published table sums round intermediate values; tolerances cover their cumulative rounding. No ridge deduction in this example. Exact tail is 25.2389 in, 0.1361 in below the published sum of rounded sublengths; exact blank is about 0.1684 in below the printed total. Tolerances 3.6 and 4.5 mm cover those explicitly identified accumulated rounding discrepancies; formulas retain exact trigonometry.
Inputs: Rise per 12 run = 8; Span across outside wall faces = 7,925 mm; Actual ridge board thickness = 0 mm; Horizontal overhang beyond outside wall = 533.4 mm; Actual common rafter depth = 139.7 mm; the others as above.
| Result | Source | This calc |
|---|---|---|
| A · Ridge face to outside-wall mark | 4,763 mm | 4,762 mm |
| B · Tail along top edge | 644.5 ± 3.6 mm | 641.1 mm |
| Conservative square-ended blank, before waste | 5,501 mm | 5,496 mm |
Johnson: 13 ft common run, 8:12 hip/valley
Source: Johnson Rafter Angle Square manual, pp. 16–17: equal-pitch 90° corner, common run 13 ft, slope 8:12; theoretical hip/valley 20 ft 3⅞ in; tail for 1 ft 9 in common overhang 2 ft 8⅞ in. Values rounded to ⅛ in.
Inputs: Rise per 12 run = 8; Span across outside wall faces = 7,925 mm; Actual ridge board thickness = 0 mm; Horizontal overhang beyond outside wall = 533.4 mm; the others as above.
| Result | Source | This calc |
|---|---|---|
| Hip / valley to theoretical intersection | 6,194 mm | 6,195 mm |
| Hip / valley theoretical tail extension | 835 ± 1.6 mm | 834 mm |
Swanson: 6:12 pitch conversion
Source: Swanson Tool Co., Roof pitch reference, 6/12 entry: 26.57°, 50%, rafter multiplier ×1.118. https://swansontoolco.com/learn/pitch
Inputs: the default inputs above.
| Result | Source | This calc |
|---|---|---|
| Roof angle | 26.57 deg | 26.565 deg |
| Slope percent (numeric percent) | 50 | 50 |
| Common rafter slope multiplier | 1.118 | 1.118 |
Responses