Gazebo Rafter Calculator

The gazebo rafter calculator models the roof as a regular polygon: it converts your width into the apothem (center-to-wall distance, the common rafter's run) and the circumradius (center-to-corner distance, the hip rafter's run), applies your face pitch to both runs, and returns two right triangles. Example — a 10' hexagon measured across corners at 6/12: apothem 4' 3-15/16", rise 2' 2", common rafter 4' 10-1/8", hip run the full 5', hip pitch 5.2/12, hip rafter 5' 5-3/8". It also outputs the hip pitch conversion, the jack cheek-cut miter, and a rafter count for your spacing.

Work two triangles from one rise. Step 1: apothem = (width across flats ÷ 2). Step 2: rise = apothem × (face pitch ÷ 12). Step 3: common rafter = apothem ÷ cos(face pitch angle). Step 4: hip run = apothem ÷ cos(180° ÷ sides). Step 5: hip pitch in X/12 = face pitch × cos(180° ÷ sides), and hip rafter = hip run ÷ cos(hip pitch angle). Worked on a 12' octagon across flats at 8/12: apothem 6', rise 4', common rafter 7' 2-9/16", hip run 6' 5-15/16", hip pitch 7.39/12 (31.62°), hip rafter 7' 7-1/2". The gazebo roof rafter calculator above runs all five steps at once and adds the overhang tails.

In plan view it is exact: the hip run is 1 ÷ cos(30°) = 1.1547 times the common run — 15.47% longer, every hexagon, every pitch. Along the slope the length ratio is smaller because the hip pitch is shallower: at a 6/12 face pitch the hexagon hip is 1.125× the common length, and at 12/12 it is 1.080×. Octagons: the plan ratio is 1.0824 and the 6/12 length ratio is 1.058. Use the plan ratio for layout marks on the plate and the length ratio when ordering stock.

Three numbers change. The plan angle from hip to wall is 67.5° on an octagon instead of 45° on a square, so the hip is only 8.24% longer in run than the commons (1 ÷ cos 22.5° = 1.0824) rather than 41.4% longer. The hip pitch multiplier is cos(22.5°) = 0.9239 instead of cos(45°) = 0.7071, so an octagon hip stays much closer to the face pitch — an 8/12 face pitch gives a 7.39/12 octagon hip versus 5.66/12 on a square roof. And jacks land on the hip from only one side at a shallower plan angle, which shrinks their cheek-cut miter (20.3° at 6/12 versus 35.3° on a square roof). An octagon hip rafter calculator bakes those three substitutions in automatically.

The jack cheek-cut miter = arctan(cos(face pitch angle) × tan(180° ÷ sides)). At a 6/12 face pitch: 27.3° on a hexagon, 20.3° on an octagon, 13.5° on a 12-side roof. At 12/12: 22.2° hexagon, 16.3° octagon, 10.7° 12-side. Pair the miter with a bevel equal to arctan(sin(face pitch angle) × sin(180° ÷ sides)) on a compound saw — or do what most gazebo crews do: cut the first jack long at the miter-only setting, hold it against the hip, scribe the bevel by eye, and use that test piece as the pattern for the rest.

The pitch measured along the hip line at the center (the 'center pitch' you set with a string line from hub to corner) is always shallower than the pitch of the roof face. Conversion: hip pitch X/12 = face pitch X/12 × cos(180° ÷ sides), and back the other way: face pitch = center pitch ÷ cos(180° ÷ sides). A 6/12 center pitch means a 6.93/12 face pitch on a hexagon, 6.49/12 on an octagon, and 6.21/12 on a 12-side roof. This is the trap the octagon hip rafter calculator exists to catch: setting the face pitch on the hip line makes the faces come out too steep and the hip rafter too long.

Count three families. Hips: one per corner (6, 8, or 12). Commons: one per face, centered (6, 8, or 12). Jacks: two per spacing bay per face — jacks per face = 2 × floor(half-side ÷ spacing). A 12' octagon across flats has a 4'-11 3/4" side (half-side 29.8"), so at 16" o.c. it takes 1 jack per half-face: 8 hips + 8 commons + 16 jacks = 32 rafters. A 12' hexagon across flats has an 83-1/8" side: 2 jacks per half-face at 16" — 6 + 6 + 24 = 36 rafters. A 14' 12-side roof: 12 + 12 + 24 = 48 rafters. Add 10% stock for test cuts and mis-scribes.

A hip rafter runs taller than the jack planes it carries, so its top edges would stand above the sheathing and telegraph through the roofing. On the 12' octagon example, a 1.5"-thick hip at the 31.62° hip pitch needs a drop of (1.5 ÷ 2) × tan(31.62°) = 7/16" — the seat cut sits that much deeper than a jack's birdsmouth so the hip's top corners land on the sheathing plane. The alternative is backing: beveling the hip's top edges down to a knife edge at the pitch-line plane. Drop the seat for exposed rafter tails; back the hip where the look of a flat-topped ridge line matters.

Match the pitch to the roofing. Asphalt shingles: 3/12 minimum for standard laminates, and 2/12 to 4/12 requires double underlayment. Exposed-fastener metal panels: 3/12 minimum. Standing-seam metal: down to 1/4:12 to 3/12 depending on the seam type. Cedar shakes: 4/12 minimum. Most gazebo builders run a 6/12 to 10/12 face pitch — steep enough to shed under trees, shallow enough to stand on for staining. On polygons, remember the face pitch is what the material sees; the hip pitch runs one multiplier shallower (×0.866 hexagon, ×0.924 octagon, ×0.966 12-side).

Commons and jacks do: a standard seat cut on the level plate with a plumb shoulder, laid out with the face pitch on your square. Keep the seat depth within about one-third of the rafter depth so the remaining web carries the load, and verify against your local code. The hips are the exception — their seat is rotated to the hip pitch and dropped (see the hip-drop answer) so the corners of the hip, not its crown, bear on the plate. Skipping the drop leaves every hip floating 3/8" to 1/2" above its seat with a visible shadow line under the eave.

Yes — the geometry is identical. A yurt roof is a 12-to-30-side polygon whose rafters run from a compression ring instead of a point: subtract the ring's radius from both the apothem and the circumradius runs, then run the same two triangles. A bay-window or turret cone is a 5-to-8-side polygon sitting on curved or segmental walls — mark hips to the corners and treat each wall segment as a face. Treehouse crowns and belvedere roofs are the same math at small radius. Any of these the calculator handles by setting the side count from 5 to 16 and entering the width the same way.

Commons and jacks sized like house rafters for the same snow and dead loads — a 2x6 carries most gazebo common runs under 10', with 2x8 for longer runs or heavy snow country; run your load and span through a rafter load calculator and span table rather than guessing. Hips: one size deeper than the jacks they carry (2x8 hips over 2x6 jacks is the classic pairing) because the hip collects jack loads along its whole length. The center hub: a fabricated steel hub or a built-up 2x ring block; never rely on fasteners alone in a single-point connection. Use pressure-treated lumber anywhere the wood meets posts or concrete.