This online calculator can be used for unequal pitched roofs, Platonic Solids, Archimedean Solids, Polyhedrons or Parallelogram Roofs. The main objective of the calculator is to find the bevel angles on the top edge of unbacked hip rafter that will produce equal length miter lines on the roof surface.

To calculate the equal length miter line on the roof surface the calculator needs 3 roof slope angles that are perpendicular to the eave/gutter line and 2 eave/deck angles. The bevel angles returned by the calculator are only for one side of the hip rafter. If the roof is an equal sloped roof then the bevel angle can be used on both sides of the hip rafter. However, the bevel angles can be different for hip rafter A and hip rafter B.

Link to the online calculator:

Here's an example print out of the calculations returned for an unequal sloped roof.

Hip Rafter Miter Angles Hip Rafter Width = 6.00000 Roof Eave Angle for Hip Rafter A = 90.00000 Hip Rafter A Slope Angle = 40.89339 Roof Slope Angle A = 60.00000 Roof Slope Angle B = 45.00000 Plan Angle on Side A = 30.00000 Plan Angle on Side B = 60.00000 Roof Eave Angle for Hip Rafter B = 90.00000 Hip Rafter B Slope Angle = 35.26439 Roof Slope Angle B = 45.00000 Roof Slope Angle C = 45.00000 Plan Angle on Side B = 45.00000 Plan Angle on Side C = 45.00000 Plan Miter Peak Angle = 75.00000 Hip Rafter A Offset Perpendicular = 4.50000 Hip Rafter B Offset Perpendicular = 3.00000 Hip Rafter A Miter Line Peak Plan Angle 1 = 46.22485 Hip Rafter A Miter Line Peak Plan Angle 2 = 43.77515 Hip Rafter B Miter Line Peak Plan Angle 1 = 28.77515 Hip Rafter B Miter Line Peak Plan Angle 2 = 61.22485 Hip Rafter A Miter Line Slope Angle R5P = 30.92761 Hip Rafter B Miter Line Slope Angle R5P = 31.79022 Hip Rafter A R5B = 23.41322 Hip Rafter A R5B = 26.56505 Hip Rafter A - R4P Angle = 38.27203 Hip Rafter B - R4P Angle = 24.15202 Hip Rafter A Compound Miter Angle and Saw Blade Bevel Angle Settings for Cutting Material Laying Flat-- Side Face Hip Rafter A Miter Angle = 40.89339 Hip Rafter A Saw Blade Bevel Angle = 43.77515 Hip Rafter B Compound Miter Angle and Saw Blade Bevel Angle Settings for Cutting Material Laying Flat-- Side Face Hip Rafter B Miter Angle = 35.26439 Hip Rafter B Saw Blade Bevel Angle = 61.22485 Hip Rafter A Compound Miter Angle and Saw Blade Bevel Angle Settings for Cutting Material On Top Edge Hip Rafter A Tetrahedron Angles D Angle = 49.10661 A Angle = 46.22485 C Angle = 38.27203 E Angle = 30.92761 B Angle = 28.20967 90-D Angle = 40.89339 90-A Angle = 43.77515 90-C Angle = 51.72797 90-E Angle = 59.07239 90-B Angle = 61.79033 Saw Miter Angle = 51.72797 Saw Blade Bevel Angle = 28.20967 Bevel Angle (Compound Angle) = 40.89339 Hip Rafter B Compound Miter Angle and Saw Blade Bevel Angle Settings for Cutting Material On Top Edge Hip Rafter B Tetrahedron Angles D Angle = 54.73561 A Angle = 28.77515 C Angle = 24.15202 E Angle = 31.79022 B Angle = 16.13617 90-D Angle = 35.26439 90-A Angle = 61.22485 90-C Angle = 65.84798 90-E Angle = 58.20978 90-B Angle = 73.86383 Saw Miter Angle = 65.84798 Saw Blade Bevel Angle = 16.13617 Bevel Angle (Compound Angle) = 35.26439

Calculations for the hip rafter miter & bevel angles:

- Calculate the plan angles for both hip rafters using the 3 different roof slope angles.
- There will be 4 plan angles. 2 for each hip rafter. We're interested in plan angles 2 & 3.
- Calculate the plan angle at the peak of the hip rafters in plan view.
- 180 - (plan_angle_h2 + plan_angle_h3)
- Calculate the hip rafter offset perpendicular to the hip rafter run line based on the width of the hip rafter and plan angles.
- HROP_A = ((hip_rafter_width × sin(plan_angle_h2)) ÷ sin(180 - plan_angle_h1 - plan_angle_h2)) × cos(plan_angle_h1)
- HROP_B = ((hip_rafter_width × sin(plan_angle_h3)) sin(180 - plan_angle_h3 - plan_angle_h4)) × cos(plan_angle_h4)
- Calculate the 2 triangles at the peak of the hip rafters in plan view, based off the hip rafter offset perpendicular line to the hip rafter run line.
- After calculating the 2 triangles at the peak, the plan angles at the peak are determined.
- Then we calculate R5B & R5P using the plan angles at the peak.
- R5P_A = arctan(tan(R1_A) × cos(peak_plan_A_angle_1))
- R5P_B = arctan(tan(R1_B) × cos(peak_plan_B_angle_1))
- R5B_A = arctan(tan(R1_A) × cos(plan_angle_h2))
- R5B_B = arctan(tan(R1_B) × cos(plan_angle_h3))
- Calculate the bevel angles on the top edge of the unbacked hip rafters.
- R4P_A = arctan(cos(R1_A) ÷ tan(peak_plan_A_angle_2))
- R4P_B = arctan(cos(R1_B) ÷ tan(peak_plan_B_angle_2))
- Then calculate the saw blade bevel angles for each hip rafter.
- SBBA_A = arctan(cos(R1_A) ÷ tan(R4P_A))
- SBBA_B = arctan(cos(R1_B) ÷ tan(R4P_B))

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