With a “standard” jack rafter, one that connects a 45° hip with the plate, the way to calculate the common difference is pretty straight forward. Since the common difference is also the length of the first jack, you can use this formula to quickly find the rafters “unadjusted” length for any o.c. measurement.

Common Difference = o.c./cos (common rafter pitch angle)

16" (o.c.)

For a 7 inch rise it would be 16/cos(30.26°) = 18.52"
For a 8 inch rise it would be 16/cos(33.69°) = 19.22"
For a 9 inch rise it would be 16/cos(36.87°) = 20"
For a 12 inch rise it would be 16/cos(45.00°) = 22.63"

24" (o.c.)

For a 7 inch rise it would be 24/cos(30.26°) = 27.79"
For a 8 inch rise it would be 24/cos(33.69°) = 28.84"
For a 9 inch rise it would be 24/cos(36.87°) = 30"
For a 12 inch rise it would be 24/cos(45.00°) = 33.94"

Each one of the example above is the length of the first jack rafter coming out from the corner of the hip. To find the length of the next jack rafter just add the length of the first with the length of the first to find the second. Then you and the length of the second to the length of the first to find the third and so on. The length or the first is always the common difference.