Bowl Segment Calculator

Calculate cut angles, segment lengths, and generate templates for segmented bowl turning projects

Project Parameters

Inches
Millimeters
Minimum 3, maximum 360 segments per ring
Diameter (Dₒ)
Radius
Radial thickness of the ring
If provided, overrides ring thickness calculation
Extra material on outer side for finishing
Extra material on inner side for finishing
Width of material removed by saw blade
1/16″
1/8″
1/32″
Decimal

Calculation Results

Last calculated: Just now
Cut Angle (α)
22.5°
Outer Length (Lₒ)
6.128″
Inner Length (Lᵢ)
5.354″
Segment Thickness (Tₛ)
1.000″

Segment Diagram

Diagram showing bowl segment with outer length, inner length, and cut angle Refresh page if diagram doesn’t load

Multi-Ring Project Manager

No rings added yet. Use “Add Ring to Project” above.
Cut List
Templates
Export

Add rings to see the cut list

Add rings to generate templates

Export your project data for backup or sharing

How the Bowl Segment Calculator Works

The Bowl Segment Calculator uses geometric formulas to determine the precise measurements needed for creating segmented bowls. Here are the exact formulas used in the calculations:

Formulas

  • Interior Angle (θ): θ = 360° / n (where n is the number of segments)
  • Cut Angle (α): α = 180° / n (this is half of the interior angle)
  • Outer Radius (Rₒ): Rₒ = Dₒ / 2 (if using diameter input)
  • Inner Radius (Rᵢ): Rᵢ = Rₒ – Tᵣ (or Dᵢ / 2 if inner diameter is provided)
  • Outer Segment Length (Lₒ): Lₒ = 2 × (Rₒ + aₒ) × sin(θ / 2)
  • Inner Segment Length (Lᵢ): Lᵢ = 2 × (Rᵢ – aᵢ) × sin(θ / 2)
  • Segment Thickness (Tₛ): Tₛ = Rₒ – Rᵢ (plus any allowance adjustments)

These calculations ensure that your segmented bowl will have precisely fitting pieces that form a perfect ring when assembled.

Quick Usage Steps

  1. Select your preferred measurement units (inches or millimeters)
  2. Enter the number of segments for your bowl ring
  3. Specify the outer diameter (or radius) of your bowl
  4. Set the ring thickness or inner diameter
  5. Adjust allowances and kerf as needed
  6. View the calculated cut angle and segment lengths
  7. Add multiple rings to create a complete bowl project
  8. Export cut lists and templates for your workshop

Common Mistakes & Tips

  • Accounting for Kerf: Always include your saw blade kerf in calculations to avoid pieces that are too short.
  • Grain Matching: For visual appeal, consider grain direction when cutting segments.
  • Glue-up Order: Assemble rings one at a time, allowing glue to set before adding the next ring.
  • Segment Count: More segments create a smoother curve but increase cutting and assembly time.
  • Test Cuts: Always make test cuts with scrap wood to verify your settings before cutting valuable material.

Frequently Asked Questions

What angle do I set my miter saw to?

Set your miter saw to the cut angle (α) calculated by the tool. This is typically half of the interior angle. For example, for an 8-segment ring, the cut angle is 22.5°.

How do I account for saw kerf?

Enter your saw blade kerf in the appropriate field. The calculator will adjust segment lengths to account for material lost to the kerf. For accuracy, measure your actual blade kerf rather than relying on manufacturer specifications.

How many segments are recommended per ring?

For most bowls, 8-16 segments per ring provides a good balance between visual appeal and construction complexity. Smaller bowls may use fewer segments, while larger bowls or those seeking a more circular appearance may use more.

What’s the difference between outer and inner segment length?

The outer segment length (Lₒ) is the measurement along the outside edge of the segment, while the inner segment length (Lᵢ) is along the inside edge. In a tapered ring, these will be different values.

Should I use diameter or radius measurements?

Either works fine. The calculator can use both diameter and radius inputs interchangeably. Use whichever measurement is more convenient for your project planning.

What are allowances used for?

Allowances add extra material to account for finishing processes. Outer allowance adds material to the outside of the bowl for shaping, while inner allowance adds material to the inside for hollowing.