Workshop Calculators - Real calculations for real work Workshop Calculators. Real calculations for real work.

Woodworking calculator

Segmented Ring Calculator

Lay out a segmented ring with equal pieces, correct miter angles, and useful chord dimensions before cutting expensive stock.

Sage dressed as a carpenter
equal segments

Enter the known values, choose the units or options, then calculate. Required or invalid entries will be identified before a result is shown.

Sage’s guided lesson

Let’s understand the result before using it

Calculate segment miter angle, outside and inside chord lengths, ring circumference, and stock requirements for segmented turning rings. I’ll show you what the numbers mean, how to check the math yourself, and where real-world conditions can change the answer.

Sage dressed as an architect with plans

Start with the real job

What this calculator is actually doing

A ring made from equal trapezoid segments divides a full circle into equal central angles. Each joint shares half of that angle, which determines the saw miter. The outside and inside chord lengths give practical segment widths at the two radii.

Sage’s rule

Every segment must use the same angle and orientation. A tiny error repeated around the ring becomes a visible gap at closure.

Now for the arithmetic

How to do the math yourself

Central angle = 360° ÷ segment count. Miter angle = 180° ÷ segment count. Chord length = 2 × radius × sin(central angle ÷ 2).

Worked example

A 12 segment ring has a 12 in outside diameter.Central angle = 360 ÷ 12 = 30°Miter setting = 30 ÷ 2 = 15°Outside chord = 2 × 6 × sin 15° ≈ 3.106 in

Set the cutting jig from the full precision angle, then use stop blocks so segment length does not drift.

Sage dressed as a carpenter

I know this is off topic, but this reminds me of a joke I heard when teaching this to one of my interns, Why did the jellybean go to school? To become a smarty-pants. Yeah, I don’t see the connection either, but I think it is cute!

Sage dressed as a Roman engineer

Before you cut, mix, or order

Tips, shortcuts, and mistakes to avoid

  • Make a test ring from inexpensive stock to verify the saw fence, stop, and accumulated angle error.
  • Cut all segments from stock of identical thickness and width; tiny differences become gaps during glue up.
  • Keep grain direction and color sequence planned before cutting, then number the segments.
Do one reality check

Saw kerf, sanding, glue lines, and stock width can change the finished diameter from the ideal geometry.

How we got here

A little history and background

Segmented turning combines polygon geometry with lathe work. Craftspeople used rings and staves long before digital calculators, relying on dividers, full size drawings, and angle tables to create vessels larger or more decorative than available solid wood.

What the result does not tell you

The ideal geometry does not include saw kerf, sanding, glue line compression, intentional oversize, wall taper, or the extra material needed for truing the ring on a lathe.

Sage dressed as a Roman engineer

Frequently asked questions

What miter angle do I use for 12 segments?

Fifteen degrees on each segment end, because 180 divided by 12 equals 15.

Why do small angle errors matter so much?

The error repeats at every joint and accumulates around the full ring.

Should the calculated diameter be the finished diameter?

Usually no. Leave enough extra material to true and finish the ring safely.

That wraps up the lesson

Class is over. It is officially cheese fries time.

You now know more about how the Segmented Ring Calculator actually works, not just which buttons to press. That earns cheese fries, Sage’s favorite way to celebrate a finished lesson.

Sage dressed as a chef
Sage pointing while explaining something

Before you use the result

Verify segment count, outer diameter, ring width, stock thickness, saw calibration, and safe jig setup.

Read the full disclaimer