Ring Segment Calculator
Calculate miter angle, chord length, kerf correction, radial depth and volume for segmented bowls, vases, wheels and arches. Any segment count 3–72.
Why this calculation matters
Segment angle decides whether the ring closes. Errors accumulate around the circle, so the last joint is where they all arrive at once.
Ring Segment — Calculator
Calculate miter angle, chord length, kerf correction, radial depth and volume for segmented bowls, vases, wheels and arches. Any segment count 3–72.
🔄 Ring Segment Calculator
Computes precise dimensions for wedge-shaped segments that form a perfect circle. Essential for segmented woodturning — bowls, vases, rings, wheels — where even 0.1° error per segment creates visible gaps. Includes automatic saw kerf correction.
Where Used?
Formulas
Miter angle: theta = 90 - (180 / N) where N = number of segmentsOuter chord: L = 2 x R_outer x sin(PI / N)Kerf correction: dL = kerf / sin(theta) [material lost per cut end]Cut length: L_cut = outer_chord - kerf_correctionVolume/seg: V = PI x (Rout2 - Rin2) x H / NAbout the Ring Segment Calculator
Segmented rings are how you build round work — bowls, planters, columns and curved frames — from straight pieces of timber glued edge to edge. Each segment has to be cut to a precise angle and length so the ring closes cleanly with no gaps, and the saw kerf has to be accounted for or the ring comes out too small. This calculator gives you the segment angle, length and count for your diameter and segment number, with allowance for the blade kerf. Turners get the segment cutting angle and strip lengths for any segmented bowl ring without doing trigonometry at the saw.
Where Is This Used?
- Segment geometry: miter = 90 − 180/N, chord = 2R·sin(π/N)
Formula checked against the sources above by an automated regression test (tests/verify-phase2.js) that derives each expected value independently of this page. Last reviewed .
FAQ
Wood species data
Density, hardness and movement for 60 timbers
How the calculation works
Each segment is a chord of the circle, so its length follows from the radius and how many segments share the ring. The kerf correction matters because the saw removes material at an angle across the joint, not square to it, so the loss is larger than the blade width.
Show the formula
Miter angle = 90 - 180/N for N segments. Outer chord = 2 x outer radius x sin(pi/N). Inner chord = 2 x inner radius x sin(pi/N). Segment depth = (outer diameter - inner diameter)/2. Kerf correction = kerf / sin(miter angle).True-circle geometry. Cumulative saw-setting error around the ring is the practical limiting factor and is not modelled — cut a test ring.
References
No external standard governs this calculation — it is arithmetic from your inputs. Take product-dependent figures from the manufacturer data sheet, not from here.
Limitations of this calculation
Calculates segment geometry for a true circle. It does not account for saw setting error accumulating around the ring, wood movement after glue-up, or the material lost to turning the ring true.
Do not use this for Production cutting without a test ring.
Figures are engineering estimates from the inputs and assumptions shown. Verify against the actual material and, where the result affects structure or safety, against a qualified professional.
How to use this tool
- Enter your stock sizes below, then press Calculate.
- Fill in number of segments, outer diameter, inner diameter, ring height / thickness.
- Press Calculate.
Worked example
Common mistakes to avoid
- Cutting segment angles to the calculator value with a mitre saw that is 0.2° off. Tiny angle errors multiply by the segment count — test with a dry ring first.
- Forgetting the kerf when cutting segments from one strip. Each cut eats blade width.
- Gluing the whole ring in one go. Glue up in halves, then flatten the two half-ring faces before the final joint.