Why is the hip rafter on a gazebo flatter than the roof pitch?

Because the pitch is measured square to an eave, from the middle of a side, and the hip starts at a corner, which is further from the centre. It climbs the same height over a longer run. The hip's rise per foot is the roof's times cos(180° ÷ N): on a 12' gazebo at 8:12, an octagon's hips are 7.39:12 and a hexagon's 6.93:12. On a square building the same rule gives the familiar 17" of hip run for every 12" of common run.

Why do gazebos have a king post in the middle?

Because hips that meet each other at a point need a cheek cut on each side of the point, at a bevel of 90° less 180° ÷ N. On a square hip roof that is the 45° every framer cuts; on a hexagon it is 60.0° and on an octagon 67.5° — past the bevel stop on any saw. Landing the hips on the faces of a six- or eight-sided post turns every one of those into a plain plumb cut, and gives the roof something to nail to while it goes up.

How big does the king post need to be?

Big enough that each face is at least as wide as a hip, or neighbouring hips collide where they land. For 1 1/2" hip stock that means at least 3 5/8" across the flats for an octagon and 2 5/8" for a hexagon, rounded up. A 4x4 is 3 1/2", short of an octagon's, which is why a post cut from 6x6 stock is the usual choice. The calculator checks the faces against your hip thickness.

Does this calculator size the rafters, beams and posts?

No. It works out the geometry — lengths, angles and counts — and none of the engineering. How deep a hip, a beam or a king post has to be depends on its span, the species and grade, and the snow load where you live, and a guessed figure would look exactly as authoritative as a right one. Take member sizes from a span table, and ring your building department before you buy.

Gazebo roof calculator: hip rafters, angles and the king post

Enter the size of a hexagonal or octagonal gazebo and the pitch of its roof. This works out the hip rafters — which are flatter than the roof — their cuts at the king post, and the posts and beams under them.

Shape

Measured

Size

Outside of the beams

Pitch

:12

Of each roof facet

Advanced settings12" overhang · 5 1/2" king post · 1 1/2" hips

Overhang

Past the beams, level, square to the eave

King post, across flats

= 5.5"

Hip thickness

= 1.5"

Each of 8 hip rafters

103 9/16"long

Plumb cut

31.6°

Hip pitch

7.375:12

Buy

10 ft

Cutting one hip

Hip pitchFlatter than the 8:12 facets: the hip climbs the same 48" from a corner, further out than the middle of a side: 7.375:12
Line lengthOutside corner of the plate to the face of the king post, along the hip: 88 5/16"
TailFrom the plate out to the eave corner: 15 1/4"
Plumb cutAt the king post — a plain plumb cut, square in plan, against a face: 31.6° off square
Seat cutWhere the hip bears on the beams at the corner: 58.4° off square
Per foot of common runThe hip's own figure, the way a framing square's hip table reads: 15.25"

Commons, posts and beams

Common rafterMiddle of a side to the centre line at 8:12, plus 14 7/16" of tail. Shorten it to land on whatever it meets: 86 9/16"
Height of the roofTop of the plate to the peak, on the centre line: 48"
PostsOne under every corner: 8
8 beamsLong point to long point on the outside, 22.5° miter both ends: 59 5/8"
Roof surfaceThe eave outline times the slope factor, for sheathing and shingles: 195 sq ft

All 2 checks passShow the numbers

Each hip fits on a face of the king post — passesA 5 1/2" king post has 2 1/4" faces, room for 1 1/2" hip stock.
At least 2:12 for asphalt shingles — passesThis roof is 8:12 on each facet. The hips are flatter, but shingles go on the facets.

This is the geometry of the roof, not its engineering. How deep the hips, beams and king post have to be depends on the span, the species and grade, and your snow load — take those from a span table and ring your building department before you buy.

Hip plumb cut, at true size

Print at 100% and check the ruler. Lay the hip's top edge on the baseline and the second line is plumb — the cut at the king post, marked straight onto the board or set into a bevel gauge for all 8 hips.

Check this first

Put a tape on the printed ruler. If it does not read exactly 6 inches, the print was scaled — set the print dialog to 100% or “Actual size” and print it again. Do not cut wood from a template that failed this.

octagon hip plumb cut

Baseline along the hip's top edge; the second line is plumb.

Printing this properly

In the print dialog, set the scale to 100% or “Actual size” and turn off “Fit to page”. Measure the printed ruler with a tape before you trust the angle.

Worked example: a 12' octagon at 8:12

A 12' octagon gazebo, measured across the flats at the beams, rises 48" to its peak at 8:12. Its hips start at the corners, further out than the middle of a side, so they run flatter: 7.39:12, 31.6°.

Landing on a 5 1/2" king post, each of the 8 hips is 88 5/16" plate to post plus a 15 1/4" tail — 103 9/16" in all, out of 10 ft stock — with a 31.6° plumb cut and a 58.4° seat cut.

Underneath it are 8 posts and 8 beams of 59 5/8", mitered 22.5°. It passes all 2 of the geometry checks the calculator applies.

Hip rafter: 103 9/16"
Hip pitch: 7.39:12
Plumb cut: 31.6°
Roof height: 48"
Beams: 8 × 59 5/8"

These are the figures the calculator above opens on. Change any field and it works the same problem for your numbers.

Embed this calculator on your site

Free to use. Paste this HTML into your page; the calculator runs in a frame, with no ads and nothing to sign up for.

<iframe src="https://carpentrycalculators.xyz/embed/gazebo-calculator" width="100%" height="850" style="border:0" loading="lazy" title="Gazebo roof calculator"></iframe>
<p><a href="https://carpentrycalculators.xyz/gazebo-calculator">Gazebo roof calculator</a> from Carpentry Calculators</p>

About gazebo roofs

Why is the hip rafter on a gazebo flatter than the roof pitch?: Because the pitch is measured square to an eave, from the middle of a side, and the hip starts at a corner, which is further from the centre. It climbs the same height over a longer run. The hip's rise per foot is the roof's times cos(180° ÷ N): on a 12' gazebo at 8:12, an octagon's hips are 7.39:12 and a hexagon's 6.93:12. On a square building the same rule gives the familiar 17" of hip run for every 12" of common run.
Why do gazebos have a king post in the middle?: Because hips that meet each other at a point need a cheek cut on each side of the point, at a bevel of 90° less 180° ÷ N. On a square hip roof that is the 45° every framer cuts; on a hexagon it is 60.0° and on an octagon 67.5° — past the bevel stop on any saw. Landing the hips on the faces of a six- or eight-sided post turns every one of those into a plain plumb cut, and gives the roof something to nail to while it goes up.
How big does the king post need to be?: Big enough that each face is at least as wide as a hip, or neighbouring hips collide where they land. For 1 1/2" hip stock that means at least 3 5/8" across the flats for an octagon and 2 5/8" for a hexagon, rounded up. A 4x4 is 3 1/2", short of an octagon's, which is why a post cut from 6x6 stock is the usual choice. The calculator checks the faces against your hip thickness.
Does this calculator size the rafters, beams and posts?: No. It works out the geometry — lengths, angles and counts — and none of the engineering. How deep a hip, a beam or a king post has to be depends on its span, the species and grade, and the snow load where you live, and a guessed figure would look exactly as authoritative as a right one. Take member sizes from a span table, and ring your building department before you buy.