Sample HAP Calculations PLUMB LINE DEPTH = RAFTER DEPTH / cos PITCH ANGLE        Diagram detailing the relationship between rafter depth, rafter pitch angle, and total plumb line depth. The pitch angle, given as 45° on the diagram, may actually assume any value. For a rafter depth of 11.25, and a pitch angle of 45°: (1) PLUMB LINE DEPTH = 11.25 / cos 45° = 15.9099 (2) Factoring by 2/3 gives a HAP of 10.6066. Value for the HAP returned by CAD The sum of the angles is the rafter pitch angle, 45° Angle A = 27.84943° Angle B = 17.15057° Sample Calculations (1) Length along bottom = RAFTER DEPTH / sin PITCH ANGLE (2) Subtract the plate width (3) Multiply this result by tan PITCH ANGLE        Substituting the numbers in the diagram above: (1) 11.25 / sin 45° = 15.9099 (2) 15.9099 - 5.5 = 10.4099 (3) 10.4099 (tan 45°) = 10.4099 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Changing the variables:        Another example, using a rafter depth of 13.25, and a pitch of 8/12, giving a pitch angle of arctan (8/12) = 33.69007°. (1) 13.25 / sin 33.69007° = 23.88678 (2) 23.88678 - 5.5 = 18.38678 (3) 18.38678 (tan 33.69007°) = 12.25785        Same initial variables as the last calculation, but this time solving for the plumb line depth, and factoring by 2/3. (1) 13.25 / cos 33.69007° = 15.92452 (2) 15.92452 (2/3) = 10.61635 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Triangle lengths instead of trig functions:        The final pair of calculations repeated using the lengths of the 8/12 pitch triangle. This is exactly the same as using the trig functions of 33.69007°. (1) Since the rise is 13.25, the run = 13.25 (12/8) = 19.875 (2) Hypotenuse = Square Root ( 13.25 ² + 19.875 ² ) = 23.88678 (3) 23.88678 - 5.5 = 18.38678 (4) 18.38678 (8/12) = 12.25785        Solving for the plumb line depth, and factoring by 2/3. (1) 13.25 (23.88678 / 19.875) = 15.92452 (2) 15.92452 (2/3) = 10.61635