Hip Roof Framing Calculator
15.62 ft common rafter
Slope factor 1.2; hip/valley members: 20.33 ft (factor 1.56, the larger of the two). 19 rafters along your wall at 16″ OC.
- Common rafter length = (run + overhang) × √(1+(rise/12)²) = × 1.2. Pure geometry (measured along the slope, ridge-to-tail).
- Hip/valley members use the larger factor √(2+(rise/12)²) = 1.56 per foot of common run; applying the field-area factor to hips instead understates them (JLC field-guide convention).
- Lengths are geometry; rafter sizing (depth, species, grade, spacing for your span and snow load) is structural, so use IRC R802-class span tables or an engineer. This calculator refuses to size members.
- Birdsmouth seat cuts and ridge deductions change the cut length slightly; this is the theoretical line length.
Why This One Is Different
Cut your hip rafters to the same length as the common rafters on that roof and every one of them will come up short, not from a measuring mistake but from real geometry a flat shortcut misses. A hip rafter runs diagonally across two roof planes at once instead of one, so it needs extra length per foot of run beyond what a common rafter needs at the same pitch (the hip factor is √(2 + (rise/12)²) versus the common rafter's √(1 + (rise/12)²)). That difference is the entire reason this calculator exists as its own page: enter your pitch and it hands back the correct hip length instead of a rough field-guide shortcut. It also accounts for jack rafters shortening progressively as they step in toward the hip, rather than assuming every jack matches the common rafter length.
Where the Numbers Come From
- Applying a common rafter's factor to a hip shortchanges the cut list every time: hip and valley rafters use the larger factor √(2 + (rise/12)²) per foot of run, versus a common rafter's √(1 + (rise/12)²). Source: Journal of Light Construction field-guide rafter-framing convention
- That gap shows up clearly on a common 8/12 pitch roof: the slope factor is 1.20 for a common rafter but 1.56 for a hip, nearly 30% more length per foot of run, exactly the shortfall a shortcut calculation misses on a hip. Source: worked example, closed-form arithmetic
- Hip jack rafters shorten by a consistent common difference as they step in from the hip toward the ridge (a standard framing-square layout method), not something this calculator's length-only output replaces. Source: traditional rafter-framing trade convention, labeled
- Hip member depth, grade, and spacing are structural questions answered by your adopted IRC edition and the AWC span tables behind it. This calculator computes length only and does not size the lumber. Source: AWC / ICC code-adoption documentation
More Questions
Do hip jack rafters all measure the same length?
No, jacks shorten progressively as they step in from the hip toward the ridge, following a fixed common-difference pattern from the framing-square method, not one repeated length.
Related Calculators
Formulas, waste factors, and cost models on this page follow the sourced conventions on our methodology page. Estimates only; verify with your supplier and local code.