Hip / Valley / Jack Rafter Schedule
Common-rafter and hip multipliers, jack-rafter shortening per OC, irregular-hip second pitch handling.
Example
You enter
- Building run (ft, half-width) 14
- Pitch (rise per 12 in) 6
- Overhang (in) 12
- Jack OC (in) 16
You get
- Common multiplier 1.118
- Hip multiplier 1.5
- Common length 15.65 ft
- With overhang 16.77 ft
- Hip rafter length 21 ft
- Pitch diagonal factor for 12 16.97
Checked against published worked examples from: Naval Education and Training Professional Development and Technology Center (US Navy).
Details, formula, and sources
ScopeFraming-square method.
Formula or tableCommon-rafter run multiplier m = sqrt(P² + 144) / 12 (P = pitch, rise per 12 in run). Hip / valley multiplier m_hip = sqrt(P² + 288) / 12 (square 12 × 12 diagonal = 16.97). Hip jacks: the n-th jack sits n × oc along the plate from the corner and runs that far to the hip, so its length is n × oc × m_common, each jack longer by the common difference oc × m_common (NAVEDTRA 14044: 19.23 in at 16 in o.c. and 8 in rise).
Source and editionCarpentry framing-square method by name. Public layout taught in any framing-square reference (Steel Square Pocket Book, Audel's Carpenters and Builders Library) by name.
Free accessOlder Steel Square Pocket Book editions free at archive.org.
What governsEstimate. AHJ and licensed structural engineer govern.
API field namesrun_ft, pitch, overhang_in, jack_oc_in, common_run_multiplier, hip_run_multiplier, common_length_ft, common_with_overhang_ft, hip_length_ft, pitch_diagonal_factor_for_12
- Diagonal of 12-by-12 square 16.97 in (sqrt(2 × 12²))geometry
- Default jack OC 16 in unless user suppliescarpentry convention