Inputs
ft
Horizontal distance from low plate to upper support.
in/12
Interpreted the same regardless of unit system.
ft
Set to 0 if no overhang.
ft
Used to estimate horizontal setback. Does not change slope length.
Results
| Parameter | Value |
|---|---|
| Roof angle (°) | — |
| Rise over run | — |
| Rise for given run | — |
| Rafter length (no overhang) | — |
| Overhang (along slope) | — |
| Total rafter length | — |
| Seat horizontal setback | — |
All outputs shown in the selected unit system.
Example Data
Sample scenarios to verify calculations. Imperial rows assume pitch as rise‑in‑12 with horizontal overhang unless noted.
| # | Run | Slope Input | Overhang | Angle (°) | Base Length | Total Length |
|---|---|---|---|---|---|---|
| 1 | 8 ft | 4 in / 12 | 1.0 ft (horizontal) | 18.435 | 8.433 ft | 9.487 ft |
| 2 | 10 ft | 3 in / 12 | 1.0 ft (horizontal) | 14.036 | 10.308 ft | 11.339 ft |
| 3 | 12 ft | 6 in / 12 | 0.8 ft (horizontal) | 26.565 | 13.416 ft | 14.311 ft |
| 4 | 3.0 m | Angle 20° | 0.25 m (slope) | 20.000 | 3.191 m | 3.441 m |
| 5 | 4.0 m | Angle 30° | 0.30 m (horizontal) | 30.000 | 4.619 m | 4.966 m |
Formulas Used
- Angle from pitch:
θ = arctan(pitch / 12), where pitch is rise‑in‑12. - Angle direct:
θ = angle_in_degrees × π / 180. - Rise for given run:
rise = run × tan(θ). - Rafter length excluding overhang (shed roof):
L = √(run² + rise²) = run × sec(θ). - Overhang along slope from horizontal projection
e:eslope = e / cos(θ). - Total rafter length:
Ltotal = L + eslope. - Birdsmouth seat horizontal setback (along run):
setback = seat_depth / tan(θ).
These equations assume measurements are taken to the outside faces of supports. Always verify local codes and detailing requirements.
How to Use This Calculator
- Select your preferred unit system.
- Enter the horizontal run from the low plate to upper support.
- Choose slope input: either rise‑in‑12 or angle in degrees.
- Provide overhang and select whether it is horizontal or along the slope.
- (Optional) Enter birdsmouth seat depth to estimate horizontal setback.
- Click Calculate to see angle, rise, base length, and total length.
- Use Download CSV or Download PDF to save your results.
Notes: Birdsmouth depth affects setback but not the sloped length. For framing layout, confirm cut lines and material allowances onsite.
FAQs
Span is full width between supports. For a shed roof, the run is the horizontal distance from the low plate to the upper support. This calculator uses the run.
No. Birdsmouth depth affects the horizontal setback on the plate but does not change the sloped length. The calculator reports the setback for layout convenience.
Many carpenters specify overhang as a horizontal projection. If you measure along the rafter, choose “Along slope.” The calculator converts between the two consistently.
Use whatever units your project follows. The calculator supports metric and imperial systems and reports results in your chosen unit for clarity.
This tool assumes clear run between outer faces of supports. Depending on your detail, you may adjust cut lengths to account for specific material thicknesses at bearing points.
Results are precise for layout, but always confirm onsite with a test piece, check local codes, and allow for saw‑kerf and fitting tolerances.
Typical Slope, Angle, and Length Factor
Multiply the length factor by the horizontal run to get rafter length without overhang.
| Pitch (rise / 12) | Angle (°) | Length factor sec(θ) | Rise per 1 run tan(θ) |
|---|---|---|---|
| 2 / 12 | 9.462 | 1.014 | 0.167 |
| 3 / 12 | 14.036 | 1.031 | 0.250 |
| 4 / 12 | 18.435 | 1.054 | 0.333 |
| 6 / 12 | 26.565 | 1.118 | 0.500 |
| 8 / 12 | 33.690 | 1.202 | 0.667 |
| 12 / 12 | 45.000 | 1.414 | 1.000 |
Common Rafter Spacing and Use Notes (Reference)
General practices only—confirm loads, spans, and sheathing with local codes and engineering tables.
| Rafter spacing (o.c.) | Typical applications | Notes |
|---|---|---|
| 12 in | High loads, heavy roofing, short spans | Stiffer roof; more material; tighter sheathing fastener schedule. |
| 16 in | Standard sheds, moderate spans | Common residential spacing; balances stiffness and material usage. |
| 24 in | Light roofs, engineered sheathing | Check span tables carefully; may require thicker sheathing or blocking. |