Hip & Valley Calculator
Calculate hip and valley rafter lengths from pitch and plan dimensions. Get diagonal length, backing angle, and compound cut angles. Free, no signup.
Rafter / Hip & Valley
Calculate rafter and hip/valley lengths from pitch and span
Plan-view distance from wall to ridge (one rafter)
Related Free tools
Hip & valley — did you know?
What makes hip rafters different
Hip rafter runs diagonally corner-to-ridge at 45° plan view, longer than common rafter. hip = hip_run × sqrt((1/cos(pitch°))² + 1). At 35°, 4m hip run = 6.31m.
Valleys — mirror of hips
Valley is the internal equivalent — where two slopes meet in a V. Same length formula. Hips carry weight; valleys carry water and need waterproofing.
The backing angle
Top edge of hip must be bevelled so roofing lies flat both sides. backing = arctan(sin(pitch°) ÷ sqrt(2)). At 35°: ~24.2°.
Compound angle cuts
Hip top cut is compound — pitch angle AND 45° plan bevel. side_cut = arctan(cos(pitch°) ÷ sin(45°)). At 35°: 49.2°. One of roofing's trickiest cuts.
Formulas used
Hip/valley length
hip = hip_run × sqrt((1/cos(pitch°))² + 1)
Backing angle
backing = arctan(sin(pitch°) ÷ sqrt(2))
Side cut angle
side_cut = arctan(cos(pitch°) ÷ sin(45°))
Common rafter
rafter = run ÷ cos(pitch°)
Frequently asked questions
How do I calculate hip rafter length?
hip_run × sqrt((1/cos(pitch°))² + 1). At 35°, 4m hip run = 6.31m.
Difference between hip and valley?
Hip = external ridge (corner). Valley = internal junction (V channel for water). Same length formula.
What is the backing angle?
arctan(sin(pitch°) ÷ sqrt(2)). At 35°: ~24.2°. Bevels the hip top so both roof planes lie flat.
Best free hip and valley calculator?
One that gives hip length, backing angle, and side cut. This tool does all, free.