SQUARE CUT FASCIA: Sample Calculations
Main Pitch = 7 ÷ 12         Adjacent Pitch = 9 ÷ 12
Total Deck Angle or Angle in Plan between Hip Roof Eaves = 135°
Main Common Pitch Angle = SS = 30.25644°
Main Deck Angle or Main Plan Angle = DD = 84.29259°

Adjacent Common Pitch Angle = S = 36.86990°
Adjacent Deck Angle or Adjacent Plan Angle = D = 50.70741°

Main Span Angles

MAIN SPAN COMPLEMENT of ANGLE between HIP RIDGE and EAVE
arctan (cos Main Common Pitch Angle ÷ tan Main Deck Angle)
P2m = arctan (cos SS ÷ tan DD)
P2m = arctan (cos 30.25644° ÷ tan 84.29259°) = 4.93408°


MAIN SPAN FASCIA MITER ANGLE
arctan (sin Main Common Pitch Angle ÷ tan Adjacent Deck Angle)
SFMm = arctan (sin SS ÷ tan D)
SFMm = arctan (sin 30.25644° ÷ tan 50.70741°) = 22.40659°


MAIN SPAN HIP RAFTER MITER ANGLE
arctan (cos Main Common Pitch Angle sin Main Common Pitch Angle cos Main Deck Angle ÷ tan Main Deck Angle)
R2m = arctan (cos SS sin SS cos DD ÷ tan DD)
R2m = arctan (cos 30.25644° sin 30.25644° cos 84.29259° ÷ tan 84.29259°) = .24785°


MAIN SPAN FASCIA BEVEL ANGLE
arcsin (cos Adjacent Common Pitch Angle cos Main Deck Angle)
SFBm = arcsin (cos S cos DD)
SFBm = arcsin (cos 36.86990° cos 84.29259°) = 4.56320°

Check :
arctan (cos Main Span Fascia Miter Angle tan Main Span Complement of Angle between Hip Ridge and Eave)
SFBm = arctan (cos SFMm tan P2m)
SFBm = arctan (cos 22.40659° tan 4.93408°) = 4.56320°


MAIN SPAN HIP RAFTER BEVEL ANGLE
arcsin (cos Main Common Pitch Angle cos Main Deck Angle)
C1m = arcsin (cos SS cos DD)
C1m = arcsin (cos 30.25644° cos 84.29259°) = 4.92786°


MAIN SPAN ANGLE between MATCHING FACES of FASCIA
arccos (sin Main Span Complement of Angle between Hip Ridge and Eave sin Main Span Fascia Miter Angle)
SFCm = arccos (sin P2m sin SFMm)
SFCm = arccos (sin 4.93408° sin 22.40659°) = 88.12123°


Adjacent Span Angles

ADJACENT SPAN COMPLEMENT of ANGLE between HIP RIDGE and EAVE
arctan (cos Adjacent Common Pitch Angle ÷ tan Adjacent Deck Angle)
P2a = arctan (cos S ÷ tan D)
P2a = arctan (cos 36.86990° ÷ tan 50.70741°) = 33.20954°


ADJACENT SPAN FASCIA MITER ANGLE
arctan (sin Adjacent Common Pitch Angle ÷ tan Main Deck Angle)
SFMa = arctan (sin S ÷ tan DD)
SFMa = arctan (sin 36.86990° ÷ tan 84.29259°) = 3.43171°


ADJACENT SPAN HIP RAFTER MITER ANGLE
arctan (cos Adjacent Common Pitch Angle sin Adjacent Common Pitch Angle cos Adjacent Deck Angle ÷ tan Adjacent Deck Angle)
R2a = arctan (cos S sin S cos D ÷ tan D)
R2a = arctan (cos 36.86990° sin 36.86990° cos 50.70741° ÷ tan 50.70741°) = 13.96800°


ADJACENT SPAN FASCIA BEVEL ANGLE
arcsin (cos Main Common Pitch Angle cos Adjacent Deck Angle)
SFBa = arcsin (cos SS cos D)
SFBa = arcsin (cos 30.25644° cos 50.70741°) = 33.16244°
Check :
arctan (cos Adjacent Span Fascia Miter Angle tan Adjacent Span Complement of Angle between Hip Ridge and Eave)
SFBa = arctan (cos SFMa tan P2a)
SFBa = arctan (cos 3.43171° tan 33.20954°) = 33.16244°


ADJACENT SPAN HIP RAFTER BEVEL ANGLE
arcsin (cos Adjacent Common Pitch Angle cos Adjacent Deck Angle)
C1a = arcsin (cos S cos D)
C1a = arcsin (cos 36.86990° cos 50.70741°) = 30.43926°


ADJACENT SPAN ANGLE between MATCHING FACES of FASCIA
arccos (sin Adjacent Span Complement of Angle between Hip Ridge and Eave sin Adjacent Span Fascia Miter Angle)
SFCa = arccos (sin P2a sin SFMa)
SFCa = arccos (sin 33.20954° sin 3.43171°) = 88.12123°

Check :
The angles on the faces created by cutting the Compound Angle on both fascia are always equal :
SFCm = SFCa  OR  arccos (sin P2m sin SFMm) = arccos (sin P2a sin SFMa)

Matching Fascia Dimensions

Main Span Fascia Width = Adjacent Span Fascia Width × cos SFMm ÷ cos SFMa
7.75" = 8.36786" × cos 22.40659° ÷ cos 3.43171°
7 3/4" = 8 3/8" × cos 22.40659° ÷ cos 3.43171°

Main Span Fascia Thickness = Adjacent Span Fascia Thickness × cos SFBm ÷ cos SFBa
.75" = .62984" × cos 4.56320° ÷ cos 33.16244°
3/4" = 5/8" × cos 4.56320° ÷ cos 33.16244°

Adjacent Span Fascia Width = Main Span Fascia Width × cos SFMa ÷ cos SFMm
8.36786" = 7.75" × cos 3.43171° ÷ cos 22.40659°
8 3/8" = 7 3/4" × cos 3.43171° ÷ cos 22.40659°

Adjacent Span Fascia Thickness = Main Span Fascia Thickness × cos SFBa ÷ cos SFBm
.62984" = .75" × cos 33.16244° ÷ cos 4.56320°
5/8" = 3/4" × cos 33.16244° ÷ cos 4.56320°

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Joe Bartok

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