Segmented Turning Ring Calculator
A ring has 2N cut faces, so error multiplies by 2N. Half a degree out on 12 segments leaves a 12 degree gap — more segments is worse.
More segments is less forgiving, not more
A ring of N segments has 2N cut faces, and an angular error on every cut accumulates all the way round rather than averaging out. So the gap that greets you when you dry-fit the ring is your per-cut error multiplied by 2N.
| Segments | Mitre each end | Cuts | ¼° error leaves | ½° error leaves |
|---|---|---|---|---|
| 6 | 30.00° | 12 | 3° | 6° |
| 8 | 22.50° | 16 | 4° | 8° |
| 10 | 18.00° | 20 | 5° | 10° |
| 12 | 15.00° | 24 | 6° | 12° |
| 16 | 11.25° | 32 | 8° | 16° |
| 18 | 10.00° | 36 | 9° | 18° |
| 24 | 7.50° | 48 | 12° | 24° |
| 36 | 5.00° | 72 | 18° | 36° |
Half a degree out on a twelve-segment ring leaves a twelve-degree gap. And the relationship runs the wrong way from intuition: going to twenty-four segments for a smoother curve doubles the amplification. Finer is harder, exactly twice as hard, and no amount of care with the individual pieces changes the multiplier.
Which is why the sled matters more than the saw
If the error were random it would partly cancel — some cuts long, some short. It does not, because a mis-set sled or fence is systematically off by the same amount on every single cut, and systematic errors add. That is the whole argument for cutting a test ring in cheap stock, closing it, and measuring the gap before touching the good timber: the gap tells you your per-cut error to a precision you could never measure on one joint. Divide it by 2N and correct the sled by that.
Notes
- Segment length is the outer diameter times tan(180/N). That is the side of a polygon circumscribing the circle, which is what you want — the ring must contain the finished diameter, not sit inside it.
- Cut alternately from both edges of the strip. Segments nest, so a strip yields considerably more than its length divided by the segment length. The board count here is the simple figure and will be pessimistic.
- Sand the ring flat before stacking. Any cup in one ring becomes a gap in the glue line of the next, and it compounds up the vessel exactly as the angular error compounds around it.
- Offset each ring from the one below. Rotating each layer by half a segment staggers the joints, which is stronger and looks deliberate rather than like a seam running up the side.
How to use
- Pick the segment count and the ring diameter you want.
- Read the mitre — it is 180 divided by the segment count.
- Enter your real per-cut accuracy to see the gap it leaves.
- Cut a test ring in cheap stock and measure the gap before starting.
Frequently asked questions
What angle do I cut segments for a ring?
180 divided by the number of segments, at each end. Twelve segments is 15 degrees a side, sixteen is 11.25. The two ends together turn 360/N, which is what closes the circle.
How long should each segment be?
The outer diameter times the tangent of 180/N. That is the side of a polygon circumscribing the circle, which is what you want — the ring has to contain the finished diameter rather than sit inside it.
Why will my segmented ring not close?
Because the error multiplies. A ring of N segments has 2N cut faces, so being half a degree out per cut leaves a 12 degree gap on a twelve-segment ring and 24 on a twenty-four. It is not that any one joint is bad — it is that they all add.
Does using more segments make it easier?
No, exactly the reverse, and this catches people out. Going from twelve segments to twenty-four for a smoother curve doubles the error amplification from 24x to 48x. Finer is precisely twice as hard.
Why does the error not average out?
Because it is systematic, not random. A mis-set sled or fence is off by the same amount on every cut in the same direction, so the errors add rather than cancelling. That is why the fix is to correct the sled rather than to cut more carefully.
How do I find my actual cutting error?
Cut a full test ring in cheap stock, close it, and measure the gap. Divide by 2N and you have your per-cut error to a precision you could never measure on a single joint — then adjust the sled by that amount.
How many boards will I need?
Fewer than the simple arithmetic says, because segments nest when you cut alternately from both edges of a strip. The figure here is the pessimistic one, which is the safe direction to be wrong in.
Should the rings line up between layers?
No — rotate each ring by half a segment so the joints stagger. It is stronger, and it stops a seam appearing to run straight up the side of the vessel.
Does this send anything anywhere?
No. Everything is calculated in your browser and nothing is stored or uploaded.
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