Hip and Valley Rafter Calculator
Free Hip valley rafter Calculator for roofing projects. Enter dimensions to get material lists and cost estimates. Enter your values for instant results.
Reviewed by Abdullah, Technical Content Specialist
Formula
Hip Length = sqrt((Run x sqrt(2))² + Rise²)
The hip rafter runs diagonally at 45 degrees in plan view. Its horizontal run is the common rafter run times the square root of 2. The hip rafter length is the hypotenuse of a triangle formed by the hip run and the common rise. The hip pitch per 12 inches of run equals the common pitch divided by the square root of 2. Jack rafters decrease in length by a constant difference based on spacing and pitch.
Worked Examples
Example 1: Standard Hip Roof — 6/12 Pitch
Problem:Calculate hip and valley rafter lengths for a roof with 12 ft common run and 6/12 pitch, 16 in OC jack spacing.
Solution:Common rise = 12 x (6/12) = 6 ft\nCommon rafter = sqrt(144 + 36) = 13.42 ft\nHip run = 12 x 1.414 = 16.97 ft\nHip rafter = sqrt(287.88 + 36) = 17.99 ft\nJack diff = sqrt(1.333² + 0.667²) = 1.49 ft
Result:Hip rafter = 17.99 ft, Common = 13.42 ft, Jack diff = 1.49 ft
Example 2: Steep Hip Roof — 10/12 Pitch
Problem:Calculate for 10 ft common run, 10/12 pitch, 24 in OC spacing.
Solution:Common rise = 10 x (10/12) = 8.33 ft\nCommon rafter = sqrt(100 + 69.44) = 13.02 ft\nHip run = 10 x 1.414 = 14.14 ft\nHip rafter = sqrt(200 + 69.44) = 16.42 ft\nJack diff = sqrt(4 + 2.778) = 2.60 ft
Result:Hip rafter = 16.42 ft, Common = 13.02 ft, Jack diff = 2.60 ft
Frequently Asked Questions
How do you calculate a hip rafter length?
A hip rafter runs diagonally from the ridge to the corner of the building at 45 degrees in plan view. Its horizontal run is the common rafter run multiplied by the square root of 2 (approximately 1.414). The hip rafter length equals the square root of the hip run squared plus the common rise squared. For a building with a 12-foot common run and 6/12 pitch, the common rise is 6 feet, the hip run is 16.97 feet, and the hip rafter length is approximately 18.0 feet before shortening adjustments.
What is the difference between a hip rafter and a valley rafter?
A hip rafter runs from the ridge down to an outside corner of the building where two roof planes meet at a convex angle. A valley rafter runs from the ridge down to an inside corner where two roof planes meet at a concave angle, such as where a dormer or wing intersects the main roof. Mathematically, hip and valley rafters have the same length and angle calculations when both roof sections have the same pitch. The key difference is in the backing bevel direction and the connection details at the ridge and bearing points.
What is the jack rafter difference and how is it calculated?
The jack rafter difference is the consistent length change between consecutive jack rafters spaced equally along the hip or valley. For equal-pitch hip roofs, each jack rafter is shorter than the previous one by a fixed amount that depends on the rafter spacing and roof pitch. The difference equals the square root of the spacing squared plus the rise-per-spacing squared. For 16-inch on-center spacing with a 6/12 pitch, the difference is approximately 17.9 inches. This makes layout efficient because you cut each subsequent jack rafter shorter by the same amount.
What is the hip rafter backing angle?
The backing angle is the bevel cut applied to the top edges of a hip rafter so the roof sheathing sits flat against it. Without backing, the sheathing would sit on the sharp top corners of the hip rafter, creating gaps at the hip line. The backing angle depends on the roof pitch and gets steeper as the pitch increases. For a 6/12 pitch, the backing angle is approximately 14.5 degrees. Some framers drop the hip rafter instead of backing it, which achieves the same result by lowering the rafter seat cut rather than beveling the top edges.
References
Reviewed by Abdullah, Technical Content Specialist · Editorial policy