Shop Notes · Build Guide
Give a planter, tub, or vase sloping walls and every corner needs two cuts at once — a miter across the board and a bevel through its thickness. Both come straight out of two short formulas that take the number of sides and how far the walls lean. Here’s where the numbers come from, a table to start from, and how to cut and glue the staves.
A flat, straight-walled box needs one angle at each corner: a miter of 180°/N — 45° for four sides, 30° for six — with the blade left square. Lean the walls in or out and that single angle splits in two. The miter (how far you swing the fence) shrinks a little, and a bevel (how far you tilt the blade) appears. Cut both on the mating edges and the leaning walls pull into a closed ring.
Say you want a six-sided planter whose walls lean out 15°. Six sides puts A at 30°. Drop the two into the formulas and you get a miter near 29° and a bevel near 13° — set the fence to 29°, tilt the blade to 13°, and the six staves close up. The table covers the common cases. Read a row, then fine-tune on scrap.
| Sides (N) | A = 180°/N | Lean 10° — miter / bevel | Lean 20° — miter / bevel |
|---|---|---|---|
| 4 | 45° | 44.6° / 7.1° | 43.2° / 14.0° |
| 6 | 30° | 29.6° / 8.6° | 28.5° / 17.2° |
| 8 | 22.5° | 22.2° / 9.2° | 21.3° / 18.4° |
| 12 | 15° | 14.8° / 9.7° | 14.1° / 19.3° |
A compound joint multiplies a small mistake by the number of sides — half a degree off, across twelve corners, leaves a gap you can see. Cut every setting in scrap and dry-fit the whole ring before you touch the real stock.
Cut both angles in one pass: tilt the table-saw blade to the bevel and set the miter gauge to the miter, or set both on a sliding compound miter saw. Keep one face — the outside — as your reference for every cut, so the bevels all lean the same way.
If the container tapers, each stave is a trapezoid, a little wider at the top than the bottom; its width sets the size of the rim. Glue the ring up with the bevels working for you: lay the staves outside-face-down in a row, run tape across each seam, then roll the strip up so the tape becomes a hinge and the joints close. A band or strap clamp pulls the last seam tight.
Nothing here needs the sides to be equal. For an irregular shape, A isn’t 180°/N — use half the turn at each individual corner in the same two formulas, and every joint can carry its own pair of numbers.