CALCULATING CROWN MOLDING ANGLES

Definition of Crown Molding Angles
DIAGRAM 1
Set the Select Entry Mode to Angle
MAIN PITCH Rise : Enter the SPRING ANGLE
ADJACENT PITCH Rise : Enter the SPRING ANGLE
TOTAL DECK ANGLE : Enter the WALL ANGLE
The Run fields are disregarded in Angle calculation mode.
Click on the or button.
Fascia Miter = Crown Molding Miter
Fascia Bevel = Crown Molding Bevel

EXAMPLE CALCULATIONS

Inside Corner
MAIN PITCH Rise = SPRING ANGLE = 38°
ADJACENT PITCH Rise = SPRING ANGLE = 38°
TOTAL DECK ANGLE = WALL ANGLE = 90°
Fascia Miter = Crown Molding Miter = 31.61901°
Fascia Bevel = Crown Molding Bevel = 33.86291°

Outside Corner
MAIN PITCH Rise = SPRING ANGLE = 38°
ADJACENT PITCH Rise = SPRING ANGLE = 38°
TOTAL DECK ANGLE = WALL ANGLE = 270°
Fascia Miter = Crown Molding Miter = 31.61901°
Fascia Bevel = Crown Molding Bevel = 33.86291°

Irregular Corner
MAIN PITCH Rise = SPRING ANGLE = 45°
ADJACENT PITCH Rise = SPRING ANGLE = 45°
TOTAL DECK ANGLE = WALL ANGLE = 135°
Fascia Miter = Crown Molding Miter = 16.32495°
Fascia Bevel = Crown Molding Bevel = 15.69986°

Miter and Bevel for Inside and Outside Corners
DIAGRAM 2


Crown Molding along Vaulted Ceiling
DIAGRAM 3

If the Crown Molding follows an angle measured on the wall in elevation as per DIAGRAM 3 above the entries are made as follows:

Set the Select Entry Mode to Angle
MAIN PITCH Rise : Enter the COMPLEMENT of the SPRING ANGLE
ADJACENT PITCH Rise : Enter the COMPLEMENT of the SPRING ANGLE
TOTAL DECK ANGLE : Enter the angle measured on the PLANE of the WALL

EXAMPLE CALCULATION

MAIN PITCH Rise = COMPLEMENT of the SPRING ANGLE = 52°
ADJACENT PITCH Rise = COMPLEMENT of the SPRING ANGLE = 52°
TOTAL DECK ANGLE = Angle measured on the PLANE of the WALL = 120°
Fascia Miter = Crown Molding Miter = 24.46355°
Fascia Bevel = Crown Molding Bevel = 17.92855°

CROWN MOLDING FORMULAS
Example Calculations

SPRING ANGLES are equal, the WALL ANGLE measured in PLAN is bisected
(refer to DIAGRAM 1 )

MITER ANGLE = arctan (sin SPRING ANGLE ÷ tan WALL ANGLE)
BEVEL ANGLE = arcsin (cos SPRING ANGLE cos WALL ANGLE)

Alternate Bevel Formulas:
(cos BEVEL ANGLE) ² = (sin SPRING ANGLE cos WALL ANGLE) ² + (sin WALL ANGLE) ²
(cos BEVEL ANGLE) ² = (cos SPRING ANGLE sin WALL ANGLE) ² + (sin SPRING ANGLE) ²

Calculate the MITER ANGLE first, and:
BEVEL ANGLE = arctan (sin MITER ANGLE ÷ tan SPRING ANGLE)
BEVEL ANGLE = arccos (sin WALL ANGLE ÷ cos MITER ANGLE)
BEVEL ANGLE = arccos (sin SPRING ANGLE cos WALL ANGLE ÷ sin MITER ANGLE)
BEVEL ANGLE = arcsin (tan MITER ANGLE sin WALL ANGLE ÷ tan SPRING ANGLE)

Calculate the BEVEL ANGLE first, and:
MITER ANGLE = arctan (sin BEVEL ANGLE tan SPRING ANGLE ÷ sin WALL ANGLE)
MITER ANGLE = arccos (sin WALL ANGLE ÷ cos BEVEL ANGLE)
MITER ANGLE = arcsin (tan BEVEL ANGLE tan SPRING ANGLE)
MITER ANGLE = arcsin (sin SPRING ANGLE cos WALL ANGLE ÷ cos BEVEL ANGLE)

SPRING ANGLES are equal, the WALL ANGLE measured in ELEVATION is bisected )
(refer to DIAGRAM 3 )

MITER ANGLE = arctan (cos SPRING ANGLE ÷ tan WALL ANGLE)
BEVEL ANGLE = arcsin (sin SPRING ANGLE cos WALL ANGLE)

Alternate Bevel Formulas:
(cos BEVEL ANGLE) ² = (cos SPRING ANGLE cos WALL ANGLE) ² + (sin WALL ANGLE) ²
(cos BEVEL ANGLE) ² = (sin SPRING ANGLE sin WALL ANGLE) ² + (cos SPRING ANGLE) ²

Calculate the MITER ANGLE first, and:
BEVEL ANGLE = arctan (sin MITER ANGLE tan SPRING ANGLE)
BEVEL ANGLE = arccos (sin WALL ANGLE ÷ cos MITER ANGLE)
BEVEL ANGLE = arccos (cos SPRING ANGLE cos WALL ANGLE ÷ sin MITER ANGLE)
BEVEL ANGLE = arcsin (tan MITER ANGLE sin WALL ANGLE tan SPRING ANGLE)

Calculate the BEVEL ANGLE first, and:
MITER ANGLE = arctan (sin BEVEL ANGLE ÷ (tan SPRING ANGLE sin WALL ANGLE))
MITER ANGLE = arccos (sin WALL ANGLE ÷ cos BEVEL ANGLE)
MITER ANGLE = arcsin (tan BEVEL ANGLE ÷ tan SPRING ANGLE)
MITER ANGLE = arcsin (cos SPRING ANGLE cos WALL ANGLE ÷ cos BEVEL ANGLE)

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Joe Bartok