Bowl Segment Calculator
Calculate precise measurements for segmented woodturning bowls. Enter your ring diameter, number of segments, and ring count to get exact miter angles, chord lengths, arc lengths, and material estimates. Whether you are making a 6-segment practice bowl or a 20-segment masterpiece, this calculator gives you the numbers you need for your miter saw setup.
Desired outer diameter of the ring in inches
Height/thickness of each ring in inches
Inner diameter if ring has a hollow center
Total rings stacked to form the bowl
Thickness of the lumber used for segments
Segment Angle = 360° / N
Chord Length = 2R × sin(π/N)
Arc Length = πD / N
Total Segments = N × Rings
Board Feet ≈ Segments × Length × Ring Thickness × Material Thickness / 144
Where: N = segments per ring, R = radius, D = diameter
Miter angle = 180/8 = 22.5°
Chord length = 2 × 6 × sin(22.5°) = 12 × 0.3827 = 4.592 in
Arc length = 12π/8 = 4.712 in
Total segments = 8 × 6 = 48
Board feet = 48 × 4.592 × 1 × 0.75 / 144 = 1.148 BF
Bowl height = 6 × 1 = 6 in
Set miter saw to 22.5° for both sides of each segment
What is segmented woodturning and how does it work?
Segmented woodturning is a technique where a bowl or vessel is constructed from multiple precisely-cut wooden segments glued together in rings, then turned on a lathe. Each ring consists of several identical trapezoidal segments that form a complete circle when assembled. The segments are cut at specific angles (360° ÷ number of segments ÷ 2 = miter angle). This method allows for spectacular patterns using different wood species, creates larger pieces than solid blanks, and uses smaller, less expensive wood pieces efficiently.
How do I calculate the miter angle and segment length for a bowl?
The miter (bevel) angle for each segment end = 360° / (2 × Number of Segments Per Ring). For an 8-segment ring: 360/(2×8) = 22.5°. For 12 segments: 360/(2×12) = 15°. For 16 segments: 360/(2×16) = 11.25°. The segment length (outside edge) = Ring Diameter × π / Number of Segments (then add a bit for the miter waste). The inside edge length = Inside Diameter × π / Number of Segments. You cut each piece as a trapezoid with these end angles.
What is the best number of segments to use for a bowl?
Common choices: 6 segments (60° miter) - Very chunky, rustic look, good for practice. 8 segments (22.5° miter) - Most common for beginners, good balance. 12 segments (15° miter) - Smoother appearance, more pieces to cut. 16+ segments (11.25° miter) - Near-circular shape, minimal waste on the lathe, requires precision cutting. More segments = more glue surface area (stronger) but more cutting and fitting. Start with 8 segments per ring for your first segmented bowl. The outer rings can have more segments than inner rings for design variety.
How do I account for saw kerf and glue lines when cutting segments?
Every saw cut removes material (kerf), typically 0.028-0.035 inches for a thin-kerf blade, 0.090-0.125 inches for a full-kerf blade. Kerf accumulates across cuts. For a 12-segment ring (24 cuts), a 0.035" kerf removes 0.84" total. To compensate: Cut segments slightly long, then use a jig with stop blocks for consistent length. For glue lines, allow 0.005-0.010 inches per joint. Use a segment length calculator or test assembly on a flat surface before final gluing. A disc sander with a miter jig is best for precise segment fitting.
🔗 Related Calculators
📐 Formula
Segment Angle = 360° / N
Chord Length = 2R × sin(π/N)
Arc Length = πD / N
Total Segments = N × Rings
Board Feet ≈ Segments × Length × Ring Thickness × Material Thickness / 144
Where: N = segments per ring, R = radius, D = diameter
📝 Example Calculation
Miter angle = 180/8 = 22.5°
Chord length = 2 × 6 × sin(22.5°) = 12 × 0.3827 = 4.592 in
Arc length = 12π/8 = 4.712 in
Total segments = 8 × 6 = 48
Board feet = 48 × 4.592 × 1 × 0.75 / 144 = 1.148 BF
Bowl height = 6 × 1 = 6 in
Set miter saw to 22.5° for both sides of each segment