Slope factor by common pitch
This calculator computes the geometric (theoretical) rafter length along the roof plane. Actual cut length in the field also depends on birdsmouth notches, ridge board thickness and the framing method used, which a carpenter accounts for at layout.
| Pitch (X:12) | Slope factor (rafter ÷ run) |
|---|---|
| 3:12 | 1.031 |
| 6:12 | 1.118 |
| 9:12 | 1.250 |
| 12:12 | 1.414 |
- The theoretical length calculated here does not include the deduction for ridge board thickness (typically half the ridge board's thickness, measured along the slope) or the layout of the birdsmouth seat cut at the wall plate — a carpenter applies these adjustments when marking the actual rafter for cutting.
- Structural sizing of the rafter itself (lumber species, grade, depth and spacing needed to carry roof loads including snow and wind) is a structural-engineering determination, governed by local building codes and span tables, and is outside the scope of this length calculation — it should be specified or reviewed by a qualified structural engineer or building inspector.
What does a rafter length calculator do?
A rafter length calculator finds the length of a common rafter — the sloped structural member running from the ridge to the wall plate — from the horizontal run it spans and either the roof pitch or the rise. It also accounts for the overhang (the horizontal projection of the eave beyond the wall), converting that horizontal measurement into its equivalent length along the slope.
Rafter length is a Pythagorean calculation: the rafter is the hypotenuse of a right triangle formed by the horizontal run and the vertical rise. Because the overhang is normally specified as a horizontal distance but is cut along the same sloped plane as the rafter, it must be stretched by the same rise/run ratio before being added to the rafter body length.
How to use this rafter length calculator
- Enter the horizontal run the rafter spans — the horizontal distance from the wall plate to the point directly under the ridge.
- Choose whether to enter the roof pitch (X:12) or the rise directly, then enter that value.
- Enter the horizontal overhang — the eave projection beyond the wall — measured horizontally, not along the slope.
- Read the total rafter length (body plus overhang along the slope), the body length alone, the overhang length along the slope, and the rise used in the calculation.
The formula behind rafter length
The rafter body length equals √(run² + rise²), where rise is either derived from the pitch (rise = run × pitch ÷ 12) or entered directly. The slope factor equals rafter body length ÷ run; multiplying the horizontal overhang by this same slope factor converts it into its along-the-slope length, which is then added to the body length for the total rafter length.
Worked example: a rafter spanning a 4 m run at a 6:12 pitch has a rise of 4 × 6 ÷ 12 = 2 m, giving a body length of √(4² + 2²) = √20 ≈ 4.472 m. A 0.3 m horizontal overhang, stretched by the slope factor of 4.472 ÷ 4 = 1.118, becomes about 0.335 m along the slope, giving a total rafter length of about 4.807 m.
Common mistakes
- Entering the overhang as a slope-length measurement instead of a horizontal projection, which double-applies the slope factor.
- Confusing 'run' (horizontal distance) with the sloped rafter length itself when measuring an existing roof.
- Forgetting to deduct for ridge board thickness when marking the actual cut length on site.
- Using the calculated theoretical length as the final structural rafter specification without confirming lumber size and span against local building code tables or an engineer's design.
Pertanyaan yang sering diajukan
How do I calculate rafter length from pitch and run?
Rafter length equals the square root of (run² + rise²), where rise is derived from the pitch as run × pitch ÷ 12. A 4 m run at a 6:12 pitch gives a rise of 2 m and a rafter body length of √(16 + 4) ≈ 4.47 m.
How does the overhang affect rafter length?
The overhang is normally measured horizontally, but because it is cut along the same sloped plane as the rafter, its length must be multiplied by the slope factor (rafter body length ÷ run) before being added to the total rafter length.
Does this calculator give the exact cut length for framing?
It gives the theoretical geometric length along the roof plane. The actual cut length used on site also accounts for ridge board thickness and the birdsmouth seat cut at the wall plate, which a carpenter applies during layout.
What's the difference between rafter length and run?
Run is the horizontal distance a rafter spans; rafter length is the actual sloped (hypotenuse) distance the rafter covers, which is always longer than the run for any pitched roof.
Who determines the structural size of a rafter?
This calculator's output is geometric only. The lumber size, species, grade and spacing needed to safely carry roof loads, including snow and wind loads, is a structural determination made using local building code span tables or a qualified structural engineer.
Referensi
- Standard Pythagorean/trigonometric relationships used throughout residential roof framing to convert run and pitch into rafter length.
- American Wood Council (AWC) — general framing and roof-slope terminology conventions for residential wood construction.
- International Code Council (ICC) — International Residential Code (IRC) rafter span tables set the structural (load-bearing) sizing requirements not covered by this geometric length calculation.