Calculateur Avancé d'Arêtier, Noue & Empannon

How to use it: enter your roof pitch (rise and run), the common rafter's run (wall plate to ridge) and jack rafter spacing, for a standard 45° hip corner where two equally pitched roof planes meet. This extends ToolHuts' basic hip rafter calculator with the seat and side/cheek cuts a framer needs beyond the plumb cut and length alone. Valley rafters use the exact same numbers - same math, opposite (concave rather than convex) corner.

Seat cuts. Every rafter's seat cut (where it sits on the wall plate) is simply 90° minus its own plumb-cut angle, since the seat and plumb cuts together always make a right angle across the rafter.

Cheek (side) cuts. Where a jack rafter butts into the hip, or the hip meets the ridge, the cut isn't a simple single bevel - it's a compound angle because the meeting line runs at 45° in plan. For a 45°-in-plan intersection, the side-cut angle (measured across the rafter, in addition to the plumb cut) is: cheek angle = atan(cos(plumb angle)). Check the limits: at a flat (near-0°) pitch this gives 45° (a plain flat miter, as expected), and as pitch steepens toward vertical it shrinks toward 0° - matching published rafter-square side-cut tables.

Worked example. With the defaults (6-in-12 pitch, 3600 mm common run, 600 mm jack spacing): common pitch angle ≈ 26.57°, hip length = 5400 mm at a hip plumb angle ≈ 19.47°. The hip cheek cut is atan(cos 19.47°) ≈ 43.31°, and the jack cheek cut is atan(cos 26.57°) ≈ 41.81°.

Le résultat ci-dessus utilise exactement ces valeurs. Cet instantané est inclus à l’impression pour comparer la sortie aux mesures d’origine.

Roof pitch rise

6

Roof pitch run

12

Common rafter run

3600 mm

Jack rafter spacing

600 mm

Résultat principal: Hip/valley length: 5400 mm.

• Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
• Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
• When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.

This does not compute the hip/valley backing angle (the extra bevel that keeps the hip's top edge flush with both roof planes rather than standing proud) - that's a separate step, typically set with a bevel gauge on site or left "unbacked" and planed flush after framing. It also assumes equal pitches on both sides and a true 45° plan corner.

Roof framing is structural work. Cross-check these angles against a rafter table, framing square, or local carpenter, and verify all cuts on a test piece before committing lumber - this tool does not adjudicate building code or account for snow/wind load, engineered lumber requirements, or local span tables.