Bowl Segment Calculator
Calculate precise dimensions and cutting angles for segmented wood bowl turning projects
Bowl Design Parameters
Number of wood pieces per ring (minimum 3)
Radius from center to outer edge of bowl
Finished wall thickness of the bowl
Calculated: R₀ - Tᵣ = 11.00 cm
Extra material on outer edge for turning allowance
Extra material on inner edge for turning allowance
Segment Cutting Specifications
Formulas used:
• Cutting angle: α = 180°/n = 22.50°
• Outer length: L₀ = 2 × tan(α) × (R₀ + a₀) = 10.355 cm
• Inner length: Lᵢ = 2 × sin(α) × (Rᵢ - aᵢ) = 8.419 cm
• Thickness: Tₛ = (R₀ + a₀) - cos(α) × (Rᵢ - aᵢ) = 2.337 cm
Example Calculation
8-Segment Salad Bowl
Project: Medium salad bowl with 8 segments
Outer radius: R₀ = 12.5 cm (10 inch diameter bowl)
Ring thickness: Tᵣ = 1.5 cm (finished wall thickness)
Inner radius: Rᵢ = 11.0 cm (calculated)
No fudge factors: a₀ = aᵢ = 0
Step-by-step Calculation
1. Cutting angle: α = 180°/8 = 22.5°
2. Outer length: L₀ = 2 × tan(22.5°) × 12.5 = 2 × 0.4142 × 12.5 = 10.355 cm
3. Inner length: Lᵢ = 2 × sin(22.5°) × 11.0 = 2 × 0.3827 × 11.0 = 8.419 cm
4. Thickness: Tₛ = 12.5 - cos(22.5°) × 11.0 = 12.5 - 0.9239 × 11.0 = 2.337 cm
Result: Cut 8 pieces at 22.5° with dimensions 10.4×8.4×2.3 cm
Common Segment Numbers
6 Segments
30° cuts, beginner-friendly
Larger pieces, easier to handle
8 Segments
22.5° cuts, most common
Good balance of aesthetics
12 Segments
15° cuts, advanced
Fine pattern, smaller pieces
Woodworking Tips
Safety Reminders
Always wear safety glasses and hearing protection
Double-check all measurements and angles
Use proper clamping and gluing techniques
Keep cutting tools sharp and well-maintained
Make test cuts on scrap wood first
Understanding Segmented Wood Bowl Turning
What is Segmented Wood Turning?
Segmented wood turning is a woodworking technique where individual wood pieces (segments) are cut at precise angles and glued together to form rings. These rings are then stacked and turned on a lathe to create beautiful, patterned bowls with geometric designs.
Process Overview
- 1.Calculate segment dimensions and cutting angles
- 2.Cut wood pieces at precise miter angles
- 3.Glue segments together to form rings
- 4.Stack and glue rings with base
- 5.Mount on lathe and turn to final shape
Mathematical Formulas
Cutting Angle
α = 180° / n
Where n = number of segments
Outer Length
L₀ = 2 × tan(α) × (R₀ + a₀)
Length of outer edge of segment
Inner Length
Lᵢ = 2 × sin(α) × (Rᵢ - aᵢ)
Length of inner edge of segment
Segment Thickness
Tₛ = (R₀ + a₀) - cos(α) × (Rᵢ - aᵢ)
Minimum board thickness needed
Fudge Factors Explained
Outer Fudge Factor (a₀)
Extra material added to the outer edge of segments. This provides turning allowance for final shaping and accounts for slight variations in cutting accuracy. Typically 1-3mm for small bowls, up to 6mm for larger projects.
Inner Fudge Factor (aᵢ)
Material removed from the inner edge calculation. This accounts for potential over-cutting during turning and ensures adequate wall thickness. Usually smaller than outer fudge factor, typically 0-2mm for most projects.