Hopper Miter Angle and Saw Blade Bevel Angle Settings


Hopper Angles for 80 slope angleHopper Angles for 38 slope angles
Enter Hopper Slope Angle
or Enter Roof Angle

Hopper angles are the same angles that are use for cutting roof sheathing. The hopper miter angle is the same as the jack rafter side cut angle and the hopper saw blade bevel angle is the same as the hip rafter backing angle.
Hopper Miter Angle = arctan (cos(Roof Pitch Angle) tan (Plan Angle))
Hopper Saw Blade Bevel Angle for Mitered Hopper = arctan( sin ( Hip Rafter Angle ) tan ( Plan Angle ))
Hopper Saw Blade Bevel Angle for Butt Joint Hopper = arctan( 90 - (sin ( Hip Rafter Angle ) tan ( Plan Angle )*2))
See the bottom of this page for more formulas for the hopper miter and bevel angles.

The first column in the table is the corner angle in degrees. The second column is the miter angle for cutting the hopper material laying flat in the compound miter saw. The third column is the bevel angle for cutting the hopper material laying flat in the compound miter saw. The fourth column is the Hip Rafter angle for the referenced wall angle. The Hip Rafter Angle is for reference only. The fifth column is the miter for a butt joint hopper and the sixth column is the bevel angle for the butt joint hopper.

Hopper Slope Angle = 33.69


 
Hopper Slope Angle = 33.69
Corner Angle Mitered Hopper
Hopper Material Laying Flat in Miter Saw
Hip Rafter Butt Joint Hopper
Hopper Material Laying Flat in Miter Saw
or Wall Angle
in Degrees
Miter Angle Bevel Angle Hip Rafter Angle Butt Joint Miter Angle Butt Joint Bevel Angle
1 89.39908 33.68855 0.33332 89.39908 22.62291
2 88.79820 33.68418 0.66660 88.79820 22.63163
3 88.19741 33.67691 0.99978 88.19741 22.64618
4 87.59673 33.66673 1.33282 87.59673 22.66653
5 86.99622 33.65365 1.66566 86.99622 22.69269
6 86.39591 33.63767 1.99827 86.39591 22.72466
7 85.79585 33.61878 2.33059 85.79585 22.76243
8 85.19607 33.59700 2.66258 85.19607 22.80599
9 84.59661 33.57233 2.99418 84.59661 22.85534
10 83.99751 33.54477 3.32536 83.99751 22.91046
11 83.39881 33.51433 3.65606 83.39881 22.97135
12 82.80056 33.48101 3.98624 82.80056 23.03799
13 82.20278 33.44481 4.31585 82.20278 23.11037
14 81.60553 33.40575 4.64485 81.60553 23.18849
15 81.00883 33.36384 4.97319 81.00883 23.27233
16 80.41272 33.31907 5.30083 80.41272 23.36187
17 79.81725 33.27145 5.62772 79.81725 23.45709
18 79.22244 33.22100 5.95382 79.22244 23.55799
19 78.62834 33.16773 6.27908 78.62834 23.66454
20 78.03498 33.11164 6.60346 78.03498 23.77673
21 77.44240 33.05274 6.92692 77.44240 23.89453
22 76.85063 32.99104 7.24941 76.85063 24.01793
23 76.25970 32.92655 7.57090 76.25970 24.14690
24 75.66965 32.85929 7.89134 75.66965 24.28142
25 75.08051 32.78926 8.21069 75.08051 24.42148
26 74.49232 32.71648 8.52892 74.49232 24.56704
27 73.90511 32.64096 8.84597 73.90511 24.71809
28 73.31891 32.56270 9.16182 73.31891 24.87459
29 72.73374 32.48174 9.47642 72.73374 25.03653
30 72.14965 32.39807 9.78974 72.14965 25.20387
31 71.56665 32.31171 10.10174 71.56665 25.37658
32 70.98478 32.22267 10.41238 70.98478 25.55465
33 70.40407 32.13098 10.72164 70.40407 25.73804
34 69.82453 32.03664 11.02946 69.82453 25.92672
35 69.24621 31.93967 11.33582 69.24621 26.12066
36 68.66913 31.84009 11.64069 68.66913 26.31982
37 68.09330 31.73790 11.94404 68.09330 26.52419
38 67.51876 31.63314 12.24582 67.51876 26.73373
39 66.94553 31.52580 12.54601 66.94553 26.94839
40 66.37363 31.41592 12.84458 66.37363 27.16816
41 65.80308 31.30350 13.14150 65.80308 27.39300
42 65.23391 31.18857 13.43674 65.23391 27.62286
43 64.66614 31.07114 13.73027 64.66614 27.85773
44 64.09978 30.95122 14.02207 64.09978 28.09756
45 63.53485 30.82885 14.31210 63.53485 28.34231
46 62.97138 30.70402 14.60034 62.97138 28.59195
47 62.40938 30.57678 14.88676 62.40938 28.84645
48 61.84886 30.44712 15.17135 61.84886 29.10576
49 61.28985 30.31508 15.45407 61.28985 29.36985
50 60.73235 30.18066 15.73491 60.73235 29.63868
51 60.17639 30.04390 16.01383 60.17639 29.91221
52 59.62197 29.90480 16.29083 59.62197 30.19040
53 59.06911 29.76339 16.56587 59.06911 30.47322
54 58.51783 29.61969 16.83894 58.51783 30.76062
55 57.96812 29.47371 17.11002 57.96812 31.05257
56 57.42001 29.32549 17.37909 57.42001 31.34902
57 56.87350 29.17503 17.64613 56.87350 31.64994
58 56.32860 29.02236 17.91112 56.32860 31.95529
59 55.78533 28.86749 18.17405 55.78533 32.26501
60 55.24368 28.71046 18.43490 55.24368 32.57908
61 54.70366 28.55127 18.69366 54.70366 32.89745
62 54.16529 28.38996 18.95031 54.16529 33.22008
63 53.62857 28.22653 19.20484 53.62857 33.54693
64 53.09349 28.06102 19.45722 53.09349 33.87796
65 52.56007 27.89344 19.70746 52.56007 34.21313
66 52.02831 27.72381 19.95554 52.02831 34.55238
67 51.49821 27.55215 20.20145 51.49821 34.89569
68 50.96978 27.37849 20.44517 50.96978 35.24301
69 50.44301 27.20285 20.68670 50.44301 35.59430
70 49.91791 27.02524 20.92602 49.91791 35.94952
71 49.39448 26.84569 21.16313 49.39448 36.30861
72 48.87271 26.66422 21.39802 48.87271 36.67155
73 48.35261 26.48086 21.63068 48.35261 37.03829
74 47.83417 26.29561 21.86110 47.83417 37.40878
75 47.31739 26.10851 22.08928 47.31739 37.78299
76 46.80228 25.91957 22.31520 46.80228 38.16087
77 46.28882 25.72881 22.53888 46.28882 38.54238
78 45.77701 25.53626 22.76028 45.77701 38.92748
79 45.26685 25.34194 22.97942 45.26685 39.31612
80 44.75834 25.14587 23.19629 44.75834 39.70826
81 44.25146 24.94807 23.41089 44.25146 40.10387
82 43.74621 24.74855 23.62320 43.74621 40.50289
83 43.24260 24.54735 23.83323 43.24260 40.90529
84 42.74060 24.34448 24.04098 42.74060 41.31103
85 42.24021 24.13997 24.24644 42.24021 41.72006
86 41.74143 23.93383 24.44960 41.74143 42.13234
87 41.24424 23.72608 24.65048 41.24424 42.54783
88 40.74865 23.51675 24.84906 40.74865 42.96649
89 40.25463 23.30586 25.04535 40.25463 43.38828
90 39.76218 23.09343 25.23935 39.76218 43.81315
91 39.27129 22.87947 25.43104 39.27129 44.24106
92 38.78196 22.66401 25.62045 38.78196 44.67198
93 38.29416 22.44707 25.80756 38.29416 45.10587
94 37.80789 22.22867 25.99238 37.80789 45.54267
95 37.32314 22.00882 26.17490 37.32314 45.98236
96 36.83989 21.78756 26.35513 36.83989 46.42488
97 36.35814 21.56490 26.53307 36.35814 46.87021
98 35.87787 21.34085 26.70873 35.87787 47.31830
99 35.39907 21.11545 26.88209 35.39907 47.76911
100 34.92173 20.88870 27.05317 34.92173 48.22260
101 34.44583 20.66064 27.22197 34.44583 48.67873
102 33.97136 20.43127 27.38849 33.97136 49.13746
103 33.49831 20.20062 27.55274 33.49831 49.59876
104 33.02666 19.96871 27.71470 33.02666 50.06258
105 32.55641 19.73556 27.87440 32.55641 50.52888
106 32.08752 19.50118 28.03183 32.08752 50.99763
107 31.62000 19.26560 28.18700 31.62000 51.46879
108 31.15382 19.02884 28.33991 31.15382 51.94232
109 30.68897 18.79091 28.49056 30.68897 52.41818
110 30.22543 18.55183 28.63895 30.22543 52.89634
111 29.76320 18.31163 28.78510 29.76320 53.37675
112 29.30225 18.07031 28.92900 29.30225 53.85938
113 28.84257 17.82791 29.07067 28.84257 54.34419
114 28.38414 17.58443 29.21009 28.38414 54.83114
115 27.92694 17.33990 29.34729 27.92694 55.32020
116 27.47096 17.09433 29.48225 27.47096 55.81133
117 27.01619 16.84775 29.61500 27.01619 56.30450
118 26.56261 16.60017 29.74552 26.56261 56.79966
119 26.11019 16.35161 29.87383 26.11019 57.29678
120 25.65892 16.10208 29.99994 25.65892 57.79583
121 25.20879 15.85162 30.12384 25.20879 58.29677
122 24.75978 15.60022 30.24553 24.75978 58.79956
123 24.31187 15.34791 30.36504 24.31187 59.30417
124 23.86505 15.09472 30.48235 23.86505 59.81056
125 23.41928 14.84065 30.59748 23.41928 60.31870
126 22.97457 14.58572 30.71043 22.97457 60.82856
127 22.53089 14.32995 30.82121 22.53089 61.34009
128 22.08822 14.07337 30.92981 22.08822 61.85327
129 21.64654 13.81597 31.03625 21.64654 62.36806
130 21.20584 13.55779 31.14052 21.20584 62.88442
131 20.76610 13.29884 31.24265 20.76610 63.40232
132 20.32730 13.03913 31.34262 20.32730 63.92173
133 19.88942 12.77869 31.44044 19.88942 64.44262
134 19.45244 12.51753 31.53612 19.45244 64.96495
135 19.01635 12.25566 31.62967 19.01635 65.48868
136 18.58112 11.99311 31.72108 18.58112 66.01379
137 18.14674 11.72988 31.81037 18.14674 66.54024
138 17.71319 11.46600 31.89753 17.71319 67.06800
139 17.28045 11.20148 31.98257 17.28045 67.59703
140 16.84851 10.93635 32.06550 16.84851 68.12731
141 16.41733 10.67060 32.14632 16.41733 68.65880
142 15.98691 10.40427 32.22504 15.98691 69.19147
143 15.55722 10.13736 32.30165 15.55722 69.72528
144 15.12825 9.86990 32.37617 15.12825 70.26021
145 14.69998 9.60189 32.44860 14.69998 70.79622
146 14.27238 9.33336 32.51893 14.27238 71.33328
147 13.84544 9.06432 32.58718 13.84544 71.87137
148 13.41915 8.79478 32.65335 13.41915 72.41044
149 12.99347 8.52477 32.71745 12.99347 72.95047
150 12.56839 8.25429 32.77947 12.56839 73.49142
151 12.14390 7.98337 32.83942 12.14390 74.03327
152 11.71997 7.71201 32.89730 11.71997 74.57598
153 11.29659 7.44024 32.95312 11.29659 75.11953
154 10.87372 7.16806 33.00688 10.87372 75.66388
155 10.45137 6.89550 33.05859 10.45137 76.20900
156 10.02950 6.62257 33.10824 10.02950 76.75486
157 9.60810 6.34928 33.15584 9.60810 77.30143
158 9.18714 6.07566 33.20140 9.18714 77.84869
159 8.76661 5.80171 33.24491 8.76661 78.39659
160 8.34649 5.52744 33.28637 8.34649 78.94511
161 7.92676 5.25289 33.32580 7.92676 79.49423
162 7.50740 4.97805 33.36319 7.50740 80.04390
163 7.08839 4.70295 33.39855 7.08839 80.59411
164 6.66971 4.42759 33.43188 6.66971 81.14481
165 6.25135 4.15201 33.46317 6.25135 81.69599
166 5.83327 3.87620 33.49244 5.83327 82.24760
167 5.41547 3.60018 33.51968 5.41547 82.79963
168 4.99792 3.32398 33.54489 4.99792 83.35204
169 4.58060 3.04760 33.56808 4.58060 83.90480
170 4.16350 2.77106 33.58925 4.16350 84.45789
171 3.74660 2.49437 33.60840 3.74660 85.01126
172 3.32987 2.21755 33.62554 3.32987 85.56490
173 2.91329 1.94061 33.64065 2.91329 86.11878
174 2.49685 1.66357 33.65374 2.49685 86.67286
175 2.08053 1.38644 33.66482 2.08053 87.22711
176 1.66431 1.10924 33.67389 1.66431 87.78152
177 1.24816 0.83198 33.68094 1.24816 88.33603
178 0.83208 0.55468 33.68597 0.83208 88.89064
179 0.41603 0.27735 33.68899 0.41603 89.44531
180 0.00000 0.00000 33.69000 0.00000 90.00000
or Wall Angle
in Degrees
Miter Angle Bevel Angle Hip Rafter Angle Butt Joint Miter Angle Butt Joint Bevel Angle

   
   Roof Pitch Angle = Hopper Slope Angle
   
   Use any of these formulas to find the Hopper Miter Angle (Jack Rafter Side cut Angle) for Mitered or Butt Joint Hoppers
Hopper Miter Angle  = arccos( sin ( Plan Angle )     cos ( Hip Rafter Backing Angle ))
Hopper Miter Angle  = arccos( sin ( Hip Rafter Angle )     sin ( Roof Pitch Angle ))
Hopper Miter Angle  = arcsin ( cos ( Plan Angle )    cos ( Hip Rafter Angle ))
Hopper Miter Angle  = arcsin ( tan ( Hip Rafter Backing Angle )     tan ( Roof Pitch Angle ))
Hopper Miter Angle  = arctan( cos  ( Roof Pitch Angle )    tan ( Plan Angle ))
Hopper Miter Angle  = arctan( sin  ( Hip Rafter Backing Angle )     tan ( Hip Rafter Angle ))

Use any of these formulas to find the Hopper Saw Blade Bevel Angle (Hip Rafter Backing Angle)for Mitered Hoppers
Hopper Saw Blade Bevel Angle  = arccos( sin ( Plan Angle )    cos ( Jack Rafter Side Cut Angle ))
Hopper Saw Blade Bevel Angle  = arccos( cos ( Roof Pitch Angle )    cos ( Hip Rafter Angle ))
Hopper Saw Blade Bevel Angle  = arcsin ( sin ( Roof Pitch Angle )    cos ( Plan Angle ))
Hopper Saw Blade Bevel Angle  = arcsin ( tan ( Jack Rafter Side Cut Angle )    tan ( Hip Rafter Angle ))
Hopper Saw Blade Bevel Angle  = arctan( tan  ( Roof Pitch Angle )    sin ( Jack Rafter Side Cut Angle ))
Hopper Saw Blade Bevel Angle  = arctan( sin  ( Hip Rafter Angle )    tan ( Plan Angle )) 


The saw blade bevel angle for butt joint hoppers is 90 - (2   Hip Rafter Backing Angle)
or  90 - (2   Mitered Hopper Saw Blade Bevel Angle)


Hopper Miter Angle = arctan (cos(Roof Pitch Angle)    tan (Plan Angle)) 
Hopper Saw Blade Bevel Angle  = arctan( sin  ( Hip Rafter Angle )    tan ( Plan Angle )) 
example: 
Roof Pitch Angle = 38 
Wall Angle = 90
Plan Angle = 45
Hip Rafter Angle  = arctan( tan  ( 38 )    sin ( 45 )) = 28.91856

Hopper Miter Angle = arctan (cos( 38 )    tan( 45 )) = 38.23849 
Hopper Saw Blade Bevel Angle  = arctan( sin( 28.91856 )    tan( 45 )) = 25.80683

or
Hopper Miter Angle = arctan (cos(Roof Pitch Angle)  tan (Plan Angle)) 
Hopper Saw Blade Bevel Angle  = arccos( sin ( Plan Angle )    cos ( Hopper Miter Angle ))
Hopper Miter Angle = arctan (cos( 38 )    tan( 45 )) = 38.23849 
Hopper Saw Blade Bevel Angle  = arccos( sin( 45 )    cos( 38.23849 )) = 25.80683