Every angle the calculator reports, drawn to its true value for your parameters. Change the numbers below (or arrive here from the calculator link) and every diagram redraws.
Looking straight down at the pot: the rim is a regular n-gon. Each board spans one side, which subtends the central angle θ at the pot’s axis:
θ = 360°/n =
The apothem a is the distance from the center to the middle of a face. Half a side subtends the half-angle g = θ/2, so the outside face width follows from simple trigonometry:
w = 2 a tan(θ/2)
w₂ = w₁ =
Solid outline: top rim at apothem a₂. Dashed: bottom rim at a₁.
Seen from the side, each board leans outward. Going from bottom rim to top rim it rises h while stepping outward by d = a₂ − a₁ = . That right triangle gives both the lean angle and the true board length along the slope:
β = atan( d / h ) =
L = √(d² + h²) =
β shows up twice: it is how far the board leans from vertical, and it is the blade tilt for the top and bottom cuts (section 4), because those cuts must end up horizontal.
This is a section cut perpendicular to the sloped seam where two neighboring boards meet. Their inside faces open up at the dihedral angle Φ:
cos Φ = −(h²cos θ + d²) / (h² + d²) ⇒ Φ =
For a snug glue joint, each board gives up half of the corner. The bevel is measured from a square cut (dashed line, 90° to the board face):
B = 90° − Φ/2 =
Section through one board’s thickness, viewed from the side. The board leans β from vertical, so a square end cut (dashed) would leave the rim tilted. Tilting the blade the same β makes the top and bottom faces horizontal — a level rim and a base that sits flat.
end bevel = β =
A straight-sided planter (a₁ = a₂) has β = 0° — plain square end cuts.
Laid flat, each board is an isosceles trapezoid. When you mark it out, the two long edges converge toward the bottom. Each long edge makes the in-plane angle δ with the board’s centerline:
δ = atan( (w₂ − w₁) / 2L ) =
The top and bottom edges are drawn square to the centerline — all the top/bottom trickiness is in the blade tilt β, not in the layout.
| Cut | Mark on the face | Blade tilt (bevel) |
|---|---|---|
| Two long edges | lines converging at δ = to the centerline | B = |
| Top & bottom edges | square across the face (90° to centerline) | β = |
In woodworking terms: the long edges are beveled rips along a tapered layout line; the ends are square crosscuts with the blade tilted. None of the angles depend on the board thickness — thickness only changes how wide the beveled faces are. Cut list: .