Define the roof run and pitch
The run is the horizontal distance from the rafter's ridge reference to the outside wall bearing line. The rise is the vertical change over that run. In the common U.S. notation, a 6/12 roof rises 6 inches for each 12 inches of horizontal run. Its slope is 50%, and its angle above level is about 26.565°.
For a roof pitch written as rise per 12 inches of run:
θ = arctan(pitch ÷ 12)
Angle and slope are two ways to describe the same roof geometry. In other regions, plans may specify degrees or a percentage slope, so confirm which convention the drawing uses.
Calculate common-rafter length
Once the horizontal run and roof angle are known, the roof section forms a right triangle. Calculate the rise and the sloping rafter line with:
rise = run × tan(θ)rafter line length = √(run² + rise²) = run ÷ cos(θ)
Use one consistent unit for run, rise and length. The result is a straight geometric line along the common rafter; it is not a complete cut list for every ridge, fascia, seat or trim detail.
When starting from the building span
For a symmetrical gable with equal bearing lines, each side starts with half the horizontal span. If the ridge board occupies space between the rafter reference points, account for half its thickness on that side:
effective run = (bearing-line span − ridge-board thickness) ÷ 2
This assumes a centered ridge and matching roof slopes. If the roof is asymmetrical, the ridge is offset, or the measured dimensions use different reference faces, enter the actual horizontal run for that side instead of inferring it from the full span.
Include a horizontal overhang
An overhang measured level from the outside wall bearing line to the tail's plumb line is a horizontal distance. Convert it to distance along the sloping rafter:
sloped tail length = horizontal overhang ÷ cos(θ)
With a horizontal overhang, the total ridge-reference-to-tail-plumb-line geometry is (effective run + horizontal overhang) ÷ cos(θ). Check whether a plan measures from the ridge centerline, ridge face or another cut face; those reference choices affect the cut length.
Worked example: 12 ft run at 6/12
For a 12 ft horizontal run, 6/12 pitch and 18 in horizontal overhang:
- Roof angle: 26.565° above level.
- Rise over the run: 6 ft.
- Rafter line over the run: 13.416 ft, approximately 13 ft 5 in.
- Sloped tail for the 18 in horizontal overhang: 1.677 ft, approximately 1 ft 8 1/8 in.
- Total from the selected ridge reference to the tail plumb line: 15.093 ft, approximately 15 ft 1 1/8 in.
These are unrounded geometry values followed by practical inch approximations. Actual layout should follow the construction drawing and the chosen cut-face references.
Understand birdsmouth and HAP measurements
A birdsmouth is the notch layout where a rafter bears at a wall or plate. This calculator separates the entered horizontal seat length from the resulting dimensions, since measurements in different directions are not interchangeable:
- Seat length: the horizontal bearing-seat length entered for the layout.
- Heel rise: the vertical difference across that horizontal seat.
- Perpendicular notch depth: material removed measured perpendicular to the rafter faces.
- Remaining depth: the entered actual rafter depth minus that perpendicular notch depth.
- Height Above Plate (HAP): vertical distance from the horizontal seat plane to the rafter's top edge at the heel/plumb line.
For roof angle θ, horizontal seat length s and actual rafter depth d, the geometry used here is:
heel rise = s × tan(θ)perpendicular notch depth = s × sin(θ)remaining depth = d − perpendicular notch depthHAP = d ÷ cos(θ) − heel rise
Birdsmouth example for the same 6/12 roof
Using a 3.5 in horizontal seat and a measured 7.25 in rafter depth, the geometry gives a 1.75 in heel rise, about 1.565 in perpendicular notch depth, about 5.685 in remaining depth and about 6.356 in HAP. The notch depth is about 21.59% of the entered depth. That percentage is only a geometric comparison; it is not a code limit or a recommendation for a cut.
Use the member's actual depth
Nominal lumber labels are not the same as the dressed dimensions of the member in hand. The dry minimum-dressed depth shown for nominal 2×8 dimension lumber in NIST Voluntary Product Standard PS 20-25 is 7.25 in. The standard also distinguishes dry and green lumber dimensions. Measure the actual member and use its perpendicular depth for geometry; do not assume every product, condition or country uses the same dimensions.
Check structural and code requirements separately
Geometric calculations cannot determine rafter capacity, species or grade suitability, required bearing, fasteners, uplift resistance, snow or wind design, or whether a notch is permitted. The 2021 International Residential Code roof-framing chapter addresses structural roof-member cuts and notches, but it is a model-code edition; local adoption, amendments and project conditions matter. Engineered members can also have product-specific cutting restrictions.
Use approved drawings, the applicable local code and the member manufacturer's instructions. Ask the project designer or a qualified building professional when the framing detail is uncertain. A geometry result is not structural approval.
Calculate your measurements
Use the Rafter & Birdsmouth Calculator to calculate common-rafter line length, overhang and birdsmouth geometry from a symmetrical span or a directly measured run. If you first need to convert pitch, use the Roof Pitch Calculator. For roof surface area, see the Roof Area Calculator; for shingles and other roofing quantities, use the Roofing Material Calculator. Browse the Roofing & Construction tools.
Sources: NIST, Voluntary Product Standard PS 20-25, Table 3, for nominal and minimum-dressed lumber sizes; and the International Code Council, 2021 IRC Chapter 8, for one model-code edition's roof-framing provisions. Equations and worked values above are calculated from the stated right-triangle geometry.
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