Square Cut Fascia and Hip Rafter
Main Slope = 12/12 , Adjoining Slope = 8/12
Plan Angle measured between eaves = 165
Hip Rafter Pitch Angle = 23.56209


Plan Angles and section view of Hip Rafter backed both sides
Exploded View of Fascia and Hip Rafter backed 8/12 side
Views of Hip Rafter backed 8/12 side
Angles on Square Cut Fascia
Exploded View of Fascia and Hip Rafter backed both sides
Summary of Miter and Bevel Angles
R1 = 23.56209 ... Hip Rafter Pitch Angle
Main (12/12) Side:
DD = 25.85541 ... Plan Angle
90 P2m = 34.42462 ... Sheathing Angle
C5m = 39.51822 ... Backing Angle
R2m = 42.87582 ... Hip Saw Miter Angle
C1m = 39.51822 ... Hip Saw Bevel Angle
SFMm = 39.26913 ... Fascia Saw Miter Angle
90 + SFMm = 129.26913 ... Angle on the Fascia
SFBm = 48.48307 ... Fascia Saw Bevel Angle
90 R3m = 41.61847 ... Hip Side Cut Angle
C2m = 31.66048 ... Saw Bevel along Hip Side Cut Angle
P3m = 25.00045
P1m = 55.57538 ... Purlin Saw Miter Angle
Adjoining (8/12) Side:
D = 139.14459 ... Plan Angle
180 P2a = 133.89213 ... Sheathing Angle
C5a = 24.80647 ... Backing Angle
R2a = 21.98075 ... Hip Saw Miter Angle
C1a = 39.00085 ... Hip Saw Bevel Angle
SFMa = 48.85799 ... Fascia Saw Miter Angle
90 SFMa = 41.14201 ... Angle on the Fascia
SFBa = 32.33233 ... Fascia Saw Bevel Angle
90 + R3a = 131.13033 ... Hip Side Cut Angle
C2a = 16.91055 ... Saw Bevel along Hip Side Cut Angle
P3a = 18.42210
P1a = 32.67495 ... Purlin Saw Miter Angle

Checking the Dihedral Angle at
the foot of the Hip Rafter

Framing Angle Calculator Entries
Main Rise =
Main Run =
Adjoining Rise =
Adjoining Run =
Total Deck Angle =


Main Pitch Angle = 90 C2m = 90 31.66048 = 58.33952
Adjoining Pitch Angle = 90 C2a = 90 16.91055 = 73.08945
Total Deck Angle = 90 R3m + 90 + R3a = 172.74880
  returns ... C5m = 55.60704
* Note that DD = 165.80462 ... the backing angle is negative and oriented as per a Valley
  returns ... C5a = 71.75778
The Dihedral Angle measured between the
fascia equals 90 SFBm + 90 + SFBa
= 90 48.48307 + 90 + 32.33233 = 163.84926

The Dihedral Angle measured between the planes
about the skewed line at the Hip Rafter foot
equals 90 + C5m + 90 C5a
= 90 + 55.60704 + 90 71.75778 = 163.84926
Both methods of calculating the Dihedral Angle produce equal results.
Dihedral Angle between Fascia = Dihedral Angle at Hip Rafter Foot

Angles about the skewed line
at the foot of the Hip Rafter
  returns ... 180 P2m = 154.26958
154.26958 P3m = 154.26958 25.00045
= 129.26913 ... the Angle on the Main Side Fascia
  returns ... 90 P2a = 22.71991
22.71991 + P3a = 22.71991 + 18.42210

= 41.14201 ... the Angle on the Adjoining Side Fascia

Checking the Dihedral Angle at
the foot of the Hip Rafter

Framing Angle Calculator Entries
Main Rise =
Main Run =
Adjoining Rise =
Adjoining Run =
Total Deck Angle =


Main Pitch Angle = 90 C1m = 90 39.51822 = 50.48178
Adjoining Pitch Angle = 90 C1a = 90 39.00085 = 50.99915
Total Deck Angle = 90 R2m + 90 + R2a = 159.10493
  returns ... C5m = 5.84571
  returns ... C5a = 10.30503
The Dihedral Angle measured between the planes
about the skewed line at the Hip Rafter foot
equals 90 C5m + 90 C5a
= 90 5.84571 + 90 10.30503 = 163.84926
Equal to the result of the previous Dihedral Angle calculation.

Angles about the skewed line
at the foot of the Hip Rafter
  returns ... 90 P2m = 85.15547
  returns ... 90 P2a = 81.53295
180 (Angle on the Adjoining Side Fascia + 90 P1a)
= SFMa + P1a = 48.85799 + 57.32505 = 81.53294
Angles about skewed line at foot of Hip Rafter backed both sides
Dihedral Angles at foot of Hip Rafter backed both sides
Development of Hip Rafter Foot
3D Models of Hip Rafter Foot
Joe Bartok
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