Hip Rafter Plumb Line Shift

Math for equal pitched roofs for Hip Rafter Plumb Line Shift 
(1/2 of hip rafter width) * tan( 90° - plan angle) = Hip Rafter Plumb Line Shift  dimension
(0.75) * tan( 90° - 45) = 0.75

Hip Rafter Shift Dimension in Decimal Inches 

Hip Rafter Width	1.5	1.75	2.5	3	3.125	3.5	5.125	5.5
Rectangle - 90°	0.75	0.875	1.25	1.5	1.5625	1.75	2.5625	2.75
Pentagon - 108°	0.54491	0.63572	0.90818	1.08981	1.13522	1.27145	1.86177	1.99799
Hexagon - 120°	0.43301	0.50518	0.72169	0.86603	0.90211	1.01036	1.47946	1.58771
Octagon - 135°	0.31066	0.36244	0.51777	0.62132	0.64721	0.72487	1.06142	1.13909

Hip Rafter Shift Dimension in Fractions of Inches

Hip Rafter Width	1 1/2	1 3/4	2 1/2	3	3 1/8	3 1/2	5 1/8	5 1/2
Rectangle - 90°	3/4	7/8	1 1/4	1 1/2	1 9/16	1 3/4	2 9/16	2 3/4
Pentagon - 108°	9/16	5/8	15/16	1 1/16	1 1/8	1 1/4	1 7/8	2
Hexagon - 120°	7/16	1/2	3/4	7/8	7/8	1	1 1/2	1 9/16
Octagon - 135°	5/16	3/8	1/2	5/8	5/8	3/4	1 1/16	1 1/8

Hip Rafter Shift Dimension in Millimeters (mm)

Hip Rafter Width	40	60	80	90	100	110	120	130
Rectangle - 90°	20	30	40	45	50	55	60	65
Pentagon - 108°	14.53085	21.79628	29.06170	32.69441	36.32713	39.95984	43.59255	47.22526
Hexagon - 120°	11.54701	17.32051	23.09401	25.98076	28.86751	31.75426	34.64102	37.52777
Octagon - 135°	8.28427	12.42641	16.56854	18.63961	20.71068	22.78175	24.85281	26.92388