Coopered Stave & Taper Angle Calculator
Enter the finished top and bottom diameters, height, stave count, wall thickness, and stock size. The calculator returns the compound bevel, taper layout, inner openings, and a simple board estimate.
Compound bevel angle14.7
- Included joint angle
- 29.4
- Top outer stave width
- 3.28
- Bottom outer stave width
- 2.21
- Stave face length
- 10.2
- Minimum blank length
- 10.7
- Side taper angle
- 3.01
- Taper-jig offset per side
- 0.54
- Top inner opening diameter
- 10.72
- Bottom inner opening diameter
- 6.72
- Staves per stock board
- 8
- Stock boards required
- 2
Stock fit
| Check | Value |
|---|---|
| Staves across board width | 1 |
| Blanks along board length | 8 |
Bevel angle is blade tilt away from a square 90-degree cut, not the table-saw miter gauge reading.
Stock use assumes rectangular blank positions and does not nest alternating trapezoids.
How to use this calculator
- Enter finished outside diameters, not the rough blank diameters.
- Measure height vertically, then choose the number of staves in the ring.
- Add the finished wall thickness, turning allowance, end trim, and saw kerf.
- Enter the usable width and length of one stock board.
- Use the bevel, taper offset, and blank length for test cuts before milling the full set.
How the stave angles are calculated
A tapered coopered vessel is not cut like a straight segmented ring. When the outside diameter changes from one end to the other, each stave is a sloped trapezoid and the joint between neighboring staves becomes a compound bevel. This calculator follows the splayed-joinery method: it starts from the finished outside dimensions, adds a radial turning allowance, and treats the outside faces as a regular polygon at each end.
Let DT and DB be the finished top and bottom outside diameters, H the vertical height, N the stave count, T the finished thickness, A the radial turning allowance, E the trim allowance per end, K the saw kerf, and BW and BL the usable board width and length.
The angle between stave centers is phi = 2 x pi / N. The rough outside apothems are aT = DT / 2 + A and aB = DB / 2 + A. The top and bottom outside stave widths are wT = 2 x aT x tan(pi / N) and wB = 2 x aB x tan(pi / N). The stave face length is L = sqrt(H^2 + (aT - aB)^2), and the minimum blank length is LR = L + 2E.
The wall slope is k = (aT - aB) / H. The compound bevel is beta = 0.5 x acos((cos(phi) + k^2) / (1 + k^2)), reported in degrees as blade tilt away from a square 90-degree cut. The included joint angle is 2 x beta. The side taper angle is atan(abs(wT - wB) / (2L)), and the taper-jig offset per side is abs(wT - wB) / 2.
What changes the result most
Stave count changes the bevel and stave width directly. More staves make each piece narrower and reduce the amount that must be turned away, but they also add glue joints. The difference between top and bottom diameter changes the wall slope, so it changes both the side taper and the compound bevel. Turning allowance increases the outside widths at both ends and can push the blank beyond the available board width.
Inner openings and stock estimates
Because thickness is measured normal to the stave face, the inner apothem reduction is T x sqrt(1 + k^2). The calculator subtracts that amount from each outside apothem and doubles the result for the top and bottom inner opening diameters across the flats. If an inner apothem is zero or negative, the wall thickness cannot fit the chosen diameter and taper.
The stock estimate uses the wider end of the trapezoid as a rectangular blank width. It computes floor((BW + K) / (W + K)) across the board and floor((BL + K) / (LR + K)) along the board, then rounds board count up from the stave count. This leaves out alternating or nested trapezoid layouts, jointing loss, blade calibration, wood movement, assembly gaps, and turning after glue-up.
Worked example
For a vessel with a 12 inch finished top diameter, 8 inch finished bottom diameter, 10 inch vertical height, 12 staves, 3/4 inch wall thickness, 1/8 inch radial turning allowance, 1/4 inch trim at each end, a 1/8 inch kerf, and 5.5 inch by 96 inch stock, the rough outside apothems are 6.125 inches and 4.125 inches.
The calculator gives a 14.70 degree compound bevel, so the included joint angle is 29.40 degrees. The outside stave widths are 3.28 inches at the top and 2.21 inches at the bottom. The stave face length is 10.20 inches, the minimum blank length is 10.70 inches, and the taper-jig offset is 0.54 inch per side. The inner opening diameters across flats are about 10.72 inches at the top and 6.72 inches at the bottom. With the entered board size, eight staves fit per board and two boards are required.
Common questions
What angle do I cut each stave?
Use the compound bevel angle as the blade tilt away from a square 90-degree cut. The included joint angle is twice that value and describes the angle between two neighboring stave faces after assembly.
Is the bevel measured from 90 degrees or from the saw table?
The calculator reports the bevel away from a square cut. If your saw scale reads from the table instead, convert it according to that saw's convention and verify with a scrap test joint.
Why is the bevel different for a tapered vessel?
A tapered vessel has sloping stave faces, so adjacent face normals are not separated by only the flat polygon angle. The wall slope enters the splayed-joinery formula and changes the compound bevel.
Can this design a cylinder as well as a cone?
Yes. When the top and bottom diameters are equal, the slope term is zero. The side taper and taper-jig offset become zero, while the bevel becomes the normal half-angle for the selected stave count.
How do I set a taper jig from the offset?
The offset is half the difference between the two outside end widths. Mark the centerline of the blank, set one end that amount farther from the cut line than the other end, and make a test piece before cutting the full set.
How thick will the wall be after turning?
The entered thickness is the finished stave thickness measured normal to the face before interior turning. The inner opening diameters describe the polygonal inside faces, not the final turned inside surface.