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°

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
 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
 Rise/Run Degrees 5 Decimals 2 Decimals 3 Decimals 4 Decimals 6 Decimals 7 Decimals 8 Decimals 9 Decimals
 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

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
 Rise/Run Degrees 5 Decimals 2 Decimals 3 Decimals 4 Decimals 6 Decimals 7 Decimals 8 Decimals 9 Decimals
 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.