In a gable (rake) wall the length of the studs will increase by a certain amount based on the spacing of the studs and the slope of the wall.

Example calculation:

the formula used; rise ÷ run * S, where S = the stud spacing in inches
slope = 5" in 12"
the on-center stud spacing = 24"

(5 ÷ 12) * 24 = 0.41666666667 * 24 = 10

The stud length increases by 10 inches.

slope = 2 in 12
the on-center stud spacing = 16".

(2 ÷ 12) * 16 = 0.1666666667 * 16 = 2.666666666666666667

Converting the decimal to a fraction by multiplying it by 16 and thus making 16 the denominator

0.666666666666666667 * 16 = 10.667 rounded to 11
0.666666666666666667 = 11/16

The stud length increases by 2 ¹¹/₁₆ inches

Calculation

1. slope ratio of inches per foot
2. stud spacing in inches

Results

1. stud length increase in inches