Bowl Segment Calculator

Bowl Segment Calculator sizing each segmented ring to its flats, with the saw angle, long and short points, strip rip width and strip lengths, or a whole bowl planned ring by ring.

Cutting Segmented Rings With the Bowl Segment Calculator

Segmented turners build a bowl blank from rings of small mitered pieces glued edge to edge. The Bowl Segment Calculator gives the saw angle, segment lengths and strip rip width for one ring. It can also plan a whole bowl ring by ring, sizing each layer to cover its slice of the wall.

Diameters are finished sizes after turning, and the tool adds your turning margins on top. Lengths come out in decimal inches, inches to the nearest 1/64, or millimeters.

Segment Length: Tangent, Not Circumference

A glued ring is a polygon, not a circle. The finished bowl has to fit inside the flats of that polygon, so the flats must sit at the outer radius you need.

$$L_o=2R_o\tan \left(\frac{180^{\circ }}{N}\right)$$

Here $L_o$ is the long point length, $N$ is the segment count and $R_o$ is half the finished diameter plus the outer turning margin. A 10 in ring with 1/8 in margins and 12 segments gives $R_o$ of 5.125 in and a long point of 2.746 in.

Not every published method does this. Malcolm Tibbetts' segmented turning notes work from circumference divided by segment count. For the same ring that gives 2.683 in, which glues up 0.235 in small across the flats.

Some online calculators use diameter times the sine of the angle instead, which puts the corners on the circle rather than the flats. That gives 2.653 in here and a ring 0.349 in small. At 8 segments the gap widens to 0.532 in for the circumference method and 0.780 in for the sine method, which is why those methods only work with generous margins.

The short point and rip width follow from the inner radius $R_i$, which is the finished inside radius minus the inner margin.

$$L_i=2R_i\sin \left(\frac{180^{\circ }}{N}\right)$$

$$W=R_o-R_i\cos \left(\frac{180^{\circ }}{N}\right)$$

For the default ring with a 1/2 in finished wall, the short point is 2.265 in and the strip rips to 0.899 in wide. The ring measures 10.612 in across its corners, the widest point to check against your lathe swing and clamps.

Saw Settings and Angle Error

Each end of a segment is cut at half the angle each piece spans around the ring. The Bowl Segment Calculator shows that angle two ways, once for a miter saw and once for a miter gauge.

$$\theta =\frac{180^{\circ }}{N}$$

That is 15 degrees for 12 segments, the number a miter saw shows because its scale reads from square. A table saw miter gauge reads from the blade instead, so the same cut shows as 75 degrees. Some calculators that rank for this keyword list 90 minus 180/N as the miter angle, which is the gauge reading, not the saw setting.

Small angle errors add up because every segment has two cut faces. An error $e$ on each of $2N$ faces leaves a gap at the last joint.

$$g=2R_c\sin (Ne)$$

Here $R_c$ is half the across-corners width. A 0.1 degree error on the default 12-segment ring adds up to 2.4 degrees and a 0.222 in gap. The same error on 24 segments opens 0.433 in, so more segments demand a more accurate saw.

Turners on the AAW forum handle this by gluing segments into two half rings, then sanding the half-ring ends flat on a disc sander until they meet. The tool suggests half rings whenever the computed gap reaches 1/32 in. One member also warns that digital angle gauges showing 0.1 degree steps are often accurate to only plus or minus 0.3 degrees.

Before any glue goes on, clamp the dry ring with a hose clamp and hold it to a bright light, a check AAW members credit to Tibbetts. A gap at the outside means the angle is too small, and a gap at the inside means it is too large.

The same 180/N rule sets flat frame miters, and the Polygon Angle Calculator covers those along with interior and exterior angles.

Strip Length, Kerf and the Flip Cut

Flipping the strip after every cut lets the trapezoids nest end to end. Each segment then uses the average of its long and short points, plus the kerf measured along the angled cut.

$$s=\frac{L_o+L_i}{2}+\frac{k}{\cos (180^{\circ }/N)}$$

With a 0.098 in kerf, the default segment uses 2.607 in of strip, and one 12-segment ring needs 31.28 in. Grain-matched cutting keeps the long points on one edge so the grain flows around the ring. That costs a full long point per segment, plus a wedge of waste between every pair.

Small segments are a safety issue on a miter saw or table saw. When the shortest segment drops under 1 in long or the strip under 3/8 in wide, the tool warns you to use a sled with a hold-down and a stop block, never fingers near the blade.

Segment counts from 5 to 96 are accepted, and ring width must stay under half the diameter. Alternating woods need a segment count that divides evenly by the number of woods, so 12 works for two or three woods while 14 only works for two.

Planning a Whole Bowl Ring by Ring

In whole-bowl mode, the Bowl Segment Calculator asks for the rim and foot diameters, the height, the wall thickness and a base disc. It draws a straight or curved side between foot and rim, offsets it inward by the wall, and slices it into layers one board thick.

Each ring is sized to the widest outside and narrowest inside of its own layer, plus the turning margins. The curved option follows a smooth quarter-sine bulge from foot to rim, a working profile rather than a standard shape.

A 10 in curved bowl, 4-1/2 in tall on a 4 in foot with a 1/2 in wall, builds from a 5.803 in base disc and five 3/4 in rings. That comes to 60 segments, with rings growing from 7.250 in across the flats at the bottom to 10.250 in at the rim.

The bottom ring needs the widest rip at 1.756 in, and the rim ring the narrowest at 1.019 in. The tool lists the widest strip first, the order Tibbetts gives in his notes. Starting wide also lets offcuts be ripped down for the narrower rings.

The ring-by-ring cut list downloads as a CSV file you can open in a spreadsheet. The widest glued ring sets the lathe swing, and the Lathe Speed Calculator sets a safe starting speed for a blank that size.

Segmented Ring Questions From Turners

What angle do you cut for 8, 12 or 16 segments?

Divide 180 by the segment count to get the cut at each end. Eight segments take 22.5 degrees, 12 take 15 degrees and 16 take 11.25 degrees, set on a miter saw that reads from square.

On a table saw miter gauge that reads from the blade, set 90 minus those numbers, so 67.5, 75 and 78.75 degrees. Mixing up the two scales is the most common reason a first ring will not close at all.

How many segments should a bowl ring have?

More segments mean shorter pieces, a smaller saw angle and a narrower rip. At 10 in across the flats, the strip for one ring barely changes, from 31.23 in at 8 segments to 32.27 in at 24.

The cost is accuracy, since every extra segment adds two cut faces. A 0.1 degree error leaves a 0.155 in gap at 8 segments but 0.433 in at 24. The Segment Count Chart in the tool lays out angle, long point and rip width for 6 to 48 segments on your own ring.

Is there a segmented bowl chart, spreadsheet or PDF?

The Segment Count Chart covers 6 to 48 segments for whatever ring you enter, which replaces a printed chart for one diameter. Whole-bowl mode adds a ring-by-ring cut list with a CSV download that opens in Excel or Google Sheets.

Print Results opens every result card, the chart and the ring drawing on one sheet. That gives you a paper cut list to keep at the saw while you work through each ring.