CROWN MOLDING: Formulas and Example Calculations

SPRING ANGLES are equal, the WALL ANGLE measured in PLAN is bisected
EXAMPLE : SPRING ANGLE = 38° , WALL ANGLE = 135°

 MITER ANGLE = arctan (sin SPRING ANGLE ÷ WALL ANGLE) MITER ANGLE = arctan (sin 38.00000° ÷ tan 67.50000°) = 14.30638° BEVEL ANGLE = arcsin (cos SPRING ANGLE cos WALL ANGLE) BEVEL ANGLE = arcsin (cos 38.00000° cos 67.50000°) = 17.55124° Alternate BEVEL ANGLE Formulas: (cos BEVEL ANGLE) ² = (sin SPRING ANGLE cos WALL ANGLE) ² + (sin WALL ANGLE) ² (cos BEVEL ANGLE) ² = (sin 38.00000° cos 67.50000°) ² + (sin 67.50000°) ² Solving for the arccosine of the square root of the right side: BEVEL ANGLE = 17.55124° (cos BEVEL ANGLE) ² = (cos SPRING ANGLE sin WALL ANGLE) ² + (sin SPRING ANGLE) ² (cos BEVEL ANGLE) ² = (cos 38.00000° sin 67.50000°) ² + (sin 38.00000°) ² Solving for the arccosine of the square root of the right side: BEVEL ANGLE = 17.55124° Calculate the MITER ANGLE first, and: BEVEL ANGLE = arctan (sin MITER ANGLE ÷ tan SPRING ANGLE) BEVEL ANGLE = arctan (sin 14.30638° ÷ tan 38.00000°) = 17.55124° BEVEL ANGLE = arccos (sin WALL ANGLE ÷ cos MITER ANGLE) BEVEL ANGLE = arccos (sin 67.50000° ÷ cos 14.30638°) = 17.55124° BEVEL ANGLE = arccos (sin SPRING ANGLE cos WALL ANGLE ÷ sin MITER ANGLE) BEVEL ANGLE = arccos (sin 38.00000° cos 67.50000° ÷ sin 14.30638°) = 17.55124° BEVEL ANGLE = arcsin (tan MITER ANGLE sin WALL ANGLE ÷ tan SPRING ANGLE) BEVEL ANGLE = arcsin (tan 14.30638° sin 67.50000° ÷ tan 38.00000°) = 17.55124° Calculate the BEVEL ANGLE first, and: MITER ANGLE = arctan (sin BEVEL ANGLE tan SPRING ANGLE ÷ sin WALL ANGLE) MITER ANGLE = arctan (sin 17.55124° tan 38.00000° ÷ sin 67.50000°) = 14.30638° MITER ANGLE = arccos (sin WALL ANGLE ÷ cos BEVEL ANGLE) MITER ANGLE = arccos (sin 67.50000° ÷ cos 17.55124°) = 14.30638° MITER ANGLE = arcsin (tan BEVEL ANGLE tan SPRING ANGLE) MITER ANGLE = arcsin (tan 17.55124° tan 38.00000°) = 14.30638° MITER ANGLE = arcsin (sin SPRING ANGLE cos WALL ANGLE ÷ cos BEVEL ANGLE) MITER ANGLE = arcsin (sin 38.00000° cos 67.50000° ÷ cos 17.55124°) = 14.30638°

SPRING ANGLES are equal, the WALL ANGLE measured in ELEVATION is bisected
EXAMPLE : SPRING ANGLE = 38° , WALL ANGLE = 120°

 MITER ANGLE = arctan (cos SPRING ANGLE ÷ tan WALL ANGLE) MITER ANGLE = arctan (cos 38.00000° ÷ tan 60.00000°) = 24.46355° BEVEL ANGLE = arcsin (sin SPRING ANGLE cos WALL ANGLE) BEVEL ANGLE = arcsin (sin 38.00000° cos 60.00000°) = 17.92855° Alternate BEVEL ANGLE Formulas: (cos BEVEL ANGLE) ² = (cos SPRING ANGLE cos WALL ANGLE) ² + (sin WALL ANGLE) ² (cos BEVEL ANGLE) ² = (cos 38.00000° cos 60.00000°) ² + (sin 60.00000°) ² Solving for the arccosine of the square root of the right side: BEVEL ANGLE = 17.92855° (cos BEVEL ANGLE) ² = (sin SPRING ANGLE sin WALL ANGLE) ² + (cos SPRING ANGLE) ² (cos BEVEL ANGLE) ² = (sin 38.00000° sin 60.00000°) ² + (cos 38.00000°) ² Solving for the arccosine of the square root of the right side: BEVEL ANGLE = 17.92855° Calculate the MITER ANGLE first, and: BEVEL ANGLE = arctan (sin MITER ANGLE tan SPRING ANGLE) BEVEL ANGLE = arctan (sin 24.46355° tan 38.00000°) = 17.92855° BEVEL ANGLE = arccos (sin WALL ANGLE ÷ cos MITER ANGLE) BEVEL ANGLE = arccos (sin 60.00000° ÷ cos 24.46355°) = 17.92855° BEVEL ANGLE = arccos (cos SPRING ANGLE cos WALL ANGLE ÷ sin MITER ANGLE) BEVEL ANGLE = arccos (cos 38.00000° cos 60.00000° ÷ sin 24.46355°) = 17.92855° BEVEL ANGLE = arcsin (tan MITER ANGLE sin WALL ANGLE tan SPRING ANGLE) BEVEL ANGLE = arcsin (tan 24.46355° sin 60.00000° tan 38.00000°) = 17.92855° Calculate the BEVEL ANGLE first, and: MITER ANGLE = arctan (sin BEVEL ANGLE ÷ (tan SPRING ANGLE sin WALL ANGLE)) MITER ANGLE = arctan (sin 17.92855° ÷ (tan 38.00000° sin 60.00000°)) = 24.46355° MITER ANGLE = arccos (sin WALL ANGLE ÷ cos BEVEL ANGLE) MITER ANGLE = arccos (sin 60.00000° ÷ cos 17.92855°) = 24.46355° MITER ANGLE = arcsin (tan BEVEL ANGLE ÷ tan SPRING ANGLE) MITER ANGLE = arcsin (tan 17.92855° ÷ tan 38.00000°) = 24.46355° MITER ANGLE = arcsin (cos SPRING ANGLE cos WALL ANGLE ÷ cos BEVEL ANGLE) MITER ANGLE = arcsin (cos 38.00000° cos 60.00000° ÷ cos 17.92855°) = 24.46355°