N-Sided Flower Pot Calculator

Design a tapered flower pot built from n identical mitered boards. The top and bottom are regular n-gons. Enter the apothems (center-to-face distance) and height, and get the board widths, the cut angles, an exploded 3 D model, and a fully-dimensioned board diagram.

Inputs

Number of sides

Top apothem (center → face, top)

a₂

Bottom apothem (center → face, bottom)

a₁

Height

Results

Board dimensions
w₂	Outside width, top edge
w₁	Outside width, bottom edge
L	Board length (along slope)
Cut angles
B	Long-side bevel (joint)
β	Top & bottom bevel (level)
δ	Side taper (board outline)
Reference
Φ	Dihedral between boards

3 D model & exploded view

Explode

Drag to orbit · scroll to zoom · slide to separate the boards.

One board — flat outline

The board is an isosceles trapezoid. Long edges get bevel B; the top & bottom edges get bevel β.

Elevation (cross-section)

Vertical section through the pot's center showing a₁, a₂, h and the lean angle β.

How the angles are defined (all measured from a square cut, i.e. 0° = straight through the board):

Long-side bevel B — tilt the saw blade this much for the rip cut along each of the two long edges, so neighboring boards close up into the polygon. B = 90° − Φ/2.
End bevel β — tilt for the top and bottom cuts so the rim and base sit level. β = atan((a₂−a₁)/h).
Side taper δ — in-plane angle of the long edges when you mark the trapezoid on the board face.