Free · Roofing calculators 🏠

Rafter Run and Birdsmouth Geometry

Calculate rafter slope geometry and a birdsmouth cut using an explicit four-times-cut depth convention.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

In initial displayed units, Building width (W) 4, Ridge board thickness (tridge board) 0, Roof pitch (x:12) 12, Heel cut depth (ch) 2, Overhang distance (O) 0 gives Rafter segment run (X) 2, Rafter segment rise (Y) 2, Seat cut length (cs) 2, Minimum ridge board depth (dmin ridge board) 8, Height above plate (y) 6.

Half run = (building width−ridge thickness)/2; rafter length = (half run+overhang)/cos(pitch); seat = heel/tan(pitch).

Worked example

Enter these known values and leave the other values blank.

Building width (W): 4 m
Ridge board thickness (tridge board): 0 cm
Roof pitch (x:12): 12 :12
Heel cut depth (ch): 2 cm
Overhang distance (O): 0 m

Roof pitch angle (θ): 45 deg
Roof pitch (%): 100 %
Seat cut length (cs): 2 cm
Rafter segment run (X): 2 m
Rafter segment rise (Y): 2 m
Rafter segment (Lsegment): 2.8284 m
Total rafter length (Lrafter): 2.8284 m
Rafter depth at four-times-cut convention: 5.657 cm
Ridge-depth geometric convention: 8 cm
Height above plate (y): 6 cm

Assumptions and limitations

The depth fields apply the retained four-times-heel-cut geometric convention. They do not select a structural member or establish code compliance. Overhang is horizontal; building width must exceed ridge thickness.
Use compatible measurement units. Clear an unknown before solving for it, and lock independent known values when comparing changes. Currency choices label amounts without exchange-rate conversion.

Common questions

Can I solve backward from the result?

Clear the unknown and enter independent known values. A rounded whole count cannot uniquely recover a continuous dimension; keep the original measured dimensions for procurement planning.

References

Enforce the stated physical geometry and whole-count domains.

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