Segmented Bowl Calculator

Segmented Bowl Geometry: Understanding the Formulas

Segmented bowl turning constructs wooden bowls from many precisely cut trapezoidal pieces—called segments—glued edge-to-edge into rings, then stacked and shaped on a lathe. Because every joint must close perfectly before gluing, accurate segment dimensions are not optional: even a fraction of a millimeter of error per joint multiplies across all segments in the ring, opening visible gaps in the finished piece. This calculator applies regular polygon geometry to compute the exact outer length, inner length, and miter angle for any ring configuration.

The Core Formulas

Every ring of a segmented bowl is a regular polygon with n equal sides. When the outer diameter D is measured flat-to-flat—the standard shop measurement taken across the widest face of the finished ring—the segment dimensions follow directly from trigonometry:

• Outer segment length: L_outer = D × tan(π/n)
• Inner segment length: L_inner = (D − 2t) × tan(π/n)
• Miter angle: θ_miter = 180° ÷ n

In these expressions, t is the radial wall thickness and n is the segment count per ring. The tangent function converts the apothem—half the flat-to-flat diameter—into the half-length of one polygon side; multiplying by 2 (already embedded in the D×tan form) yields the full segment length. For the inner chord, the effective diameter shrinks by twice the wall thickness, one offset on each side of the ring. According to the Wikipedia article on regular polygons, a regular n-gon with apothem a has side length s = 2a × tan(π/n). Because the flat-to-flat diameter D = 2a, this reduces directly to s = D × tan(π/n), confirming the formula above.

Variable Definitions

• n — Segments per Ring: Typical values range from 8 (bold, faceted appearance) through 12, 16, and 20 (progressively smoother, more circular profile). Higher counts produce less turning waste but demand finer angular accuracy at the saw.
• D — Outer Diameter (flat-to-flat): The outside diameter of the finished ring measured across the flats, not the corners. A ruler or caliper laid across the polygon face gives this value directly—it is the measurement most turning plans specify.
• t — Wall Thickness: The radial depth of wood remaining in the bowl wall after turning. Values of 3/8 in (9.5 mm) suit thin decorative walls; 3/4 in (19.1 mm) suits heavier utility bowls.
• Waste Allowance (%): Extra length added to each blank to cover saw kerf—typically 0.10–0.13 in per cut on a table saw—and end trimming. A 5%–10% allowance covers most production work.

Worked Example

Consider a 12-segment ring with a 10-inch flat-to-flat outer diameter and 0.75-inch wall thickness:

• Miter angle: 180° ÷ 12 = 15.00° — set the saw fence to 15° from the blade face.
• Outer length: 10 × tan(π/12) = 10 × 0.2679 = 2.679 in
• Inner length: (10 − 1.50) × 0.2679 = 8.5 × 0.2679 = 2.277 in
• With 7% waste allowance: cut blank to 2.679 × 1.07 = 2.867 in

Twelve blanks at 2.867 in from 3/4-in-thick stock yield one complete ring with material to spare for trimming and fitting before glue-up.

Choosing the Right Segment Count

The American Association of Woodturners recommends that beginners start with 12 segments per ring. The 15° miter is straightforward to dial in, individual pieces are large enough to handle safely at the saw, and the resulting 12-sided polygon is close enough to circular that the lathe removes minimal waste. Sixteen- and 24-segment rings approach a true circle more closely but require correspondingly finer angular accuracy: a 0.5° miter error on a 24-segment ring produces 12° of cumulative gap error around the full ring circumference.

Waste Allowance in Practice

Blade kerf on a standard cabinet table saw removes 0.10–0.13 in of wood per pass. For a 12-segment ring, 12 miter cuts consume 1.20–1.56 in of total board length before accounting for end trim. A 5% blanket waste factor on a 2.679-in segment adds 0.134 in per piece—sufficient for most kerf widths—while a 10% allowance (0.268 in extra) suits wide-kerf blades or rough-sawn stock requiring face jointing. The SegEasy segmented bowl design reference advises calculating waste per individual cut rather than per full ring to avoid over-ordering lumber on large multi-ring projects with varied ring diameters.