Hip / Valley / Jack Rafter Schedule

Common-rafter and hip multipliers, jack-rafter shortening per OC, irregular-hip second pitch handling.

Run the calculator

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

Details, formula, and sources

Framing-square method.

Common-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). Jack-rafter shortening per OC: dx_oc = oc × m_common; jack length at distance n × dx_oc = (run − n × dx_oc) × m_common.

Carpentry 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.

Older Steel Square Pocket Book editions free at archive.org.

Estimate. AHJ and licensed structural engineer govern.

Field names used by the API: run_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