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Hip/Valley Rafter Plumb Cut Angular Cutlist

Calculate hip or valley rafter length and plumb cut angle for a standard 45° hip/valley roof intersection.

Computed in your browser — nothing you enter is uploaded. Figures are presented for United States against IRC 2024, and every formula is cited under regulatory standards below.

Last verified 2026-08-26 · v1.0.0

Market
Imperial · sales tax
13.12 ft
Schematic, drawn to the proportions you entered — not to scale on screen.

Hip/valley rafter length

19.69 ft

High confidence
Plumb cut angle
19.47 °

Running these inputs gives 6 m as the hip/valley rafter length. Currently reading for United States under IRC 2024 — pick a different market above and the figures re-cast accordingly.

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This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.

Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — confirmed fixes become pinned regression tests.

[Schema Verified] Computed in alignment with American Concrete Institute (ACI 318-19) formulas and International Residential Code (IRC 2024) spatial boundaries.

Regulatory standards & verification citations

  • Standard carpentry hip/valley formula: for a 45° plan intersection, hip rafter length = common-rafter run × √(2 + (rise/12)²); plumb cut angle = arctan((rise/12)/√2)

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Frequently asked questions

Why does the hip/valley formula use √2 instead of the common rafter's √1?
This formula assumes a standard 45° plan intersection (equal-pitch roof planes meeting at a corner), where the hip or valley rafter runs diagonally in plan — its horizontal run is the common rafter run × √2, which is where the extra factor of 2 (instead of 1) inside the square root comes from.
What is the plumb cut angle used for?
The plumb cut angle is the angle at which the top end of the hip or valley rafter is cut to meet the ridge or another rafter — it's measured from vertical and is smaller than a common rafter's plumb cut angle because the hip/valley rafter's slope is 'flattened' by its diagonal run.
Does this apply to unequal-pitch or non-45° hip roofs?
No — this formula assumes a standard 45° plan intersection where both adjoining roof planes share the same pitch. Irregular hips (different pitches or non-45° plan angles) require a different, more involved layout method.