Regular Roof Slope Angle
 Unit Rise Slope Angle atan(unitrise / 12 ) Hip Slope Angle atan(unitrise)/sqrt(288) Backing Angle atan(sin(hip slope angle))

 Angles for an Irregular Roof
 Major Roof Pitch Minor Roof Pitch Major Plan Angleatan(minor/major) angle in plan on the steeper side. working with the example of the 8/12, 10/12 8/10 =.8 , arc tan .8= 38.659 degrees = plan angle of 10/12 side Minor Plan Angleatan(major/minor)angle in plan of the shallower-pitched roof. 51.34 degrees = plan angle of 8/12 side Hip Run per Foot 8x10 divide 12= 6.666 =rise 8 divide 10 =.8 , arc tan .8 =38.65 degrees cos 1x 38.659 = 1.2806 1.2806 x 10 =12.806 = hip run for 8-10 runs Angle of Hip 6.666 divide 12.806 =.5205 arc tan .5205 =27.498 degrees = angle of hip Backing Angle Shallow Side of Hip sine 27.498 = .4617= rise of backing angles tan 51.34 degrees = 1.2499 .4617 divide 1.2499 = .369 arc tan .369 =20.27 degrees = saw backing bevel for 8/12 side of hip Backing Angle Steep side of Hip tan 38.659 = .799 , .4617 divide .799= .577 arc tan .577 =29.99 degrees = saw backing bevel of 10/12 side of hip.