Regular Jack Rafter Dimensions
Equal Common Pitches create 45° Plan Angles
All stock is assumed to be 1½" wide

Hip Roof: Plan and Section Views of Jack Rafter Dimensions

GIVEN: Common Rafter Run Reference Line (Soffit Line) to Ridge Board = 131.25"
Distance in plan from Reference Line to Framing Point = 131.25" + .75" = 132"
Projecting the 132" run to the slope of the roof (Section C - C)
132" ÷ cos Common Pitch Angle = 132" ÷ cos 45.00000° = 186.67619"

The next calculation is carried out on the slope of the roof by employing the Sheathing Angle.
Center to Center Distance along Reference Line = 16"
Distance to long side of Jack Rafter along Reference Line = 16" - .75" = 15.25"
Sheathing Angle = arctan(tan Plan Angle cos Common Pitch Angle)
= arctan(tan 45.00000° cos 45.00000°) = 54.73561°
Distance along roof slope between Framing Points = 15.25" × tan 54.73561° = 21.56676"
Length on the slope of the roof, longest side of Jack Rafter
Reference Line to Framing Point = 186.67619" - 21.56676" = 165.10943"

The Framing Point lies above the Hip Rafter (refer to Side View J - J) and must be adjusted to reflect the point of intercept of the Jack Rafter and the shoulder of the Hip Rafter.
Half of Hip Rafter width = .75"
Converting .75" to a plan dimension parallel to the Jack Rafter run
= .75" ÷ cos Plan Angle = .75" ÷ cos 45.00000° = 1.06066"
Projecting the 1.06066" plan dimension to the slope of the roof
= 1.06066" ÷ cos Common Pitch Angle = 1.06066" ÷ cos 45.00000° = 1.50000"
Length on the slope of the roof, longest side of Jack Rafter
Reference Line to shoulder of Hip Rafter = 165.10943" - 1.50000" = 163.60943"
Expressing the measurement in feet-inches: 13' - 7 5/8"
Expressing the measurement in millimeters: 4156 mm

Wireframe sketch of Hip Roof detailing Jack Rafter dimensions on the slope of the roof

Joe Bartok
1