A 1/8 inch cutter is 3.175 mm across, so the relief radius R is 1.5875 mm. Every number on this page comes from that radius, not from a fudge factor someone read off a CAM screenshot.
Check the collet before you trust the label. A 3 mm bit and a 1/8″ bit differ by 0.175 mm in diameter, which is enough to leave a tenon corner touching. Type the diameter you are actually going to cut with.
The only number that matters: R = 1.5875 mm
Relief geometry is driven entirely by the cutter radius. Diameter 3.175 mm gives R = 1.5875 mm, and all three styles place an arc of exactly that radius — they only disagree about where the centre goes.
Because the arc radius equals the cutter radius, the relief is exactly the shape the bit will leave when it plunges at that point. There is no approximation and no safety margin baked in. If you want extra clearance for paint or swelling, get it by choosing a more aggressive style, not by inflating the bit number.
Minimal dogbone with a 1/8″ bit
The centre sits 1.5875 mm from the vertex along the bisector. The bulge past the original corner is 1.5875 × (1 − 1/√2) ≈ 0.465 mm — about the thickness of six sheets of paper.
Each adjoining edge is consumed by √2 × 1.5875 ≈ 2.245 mm. Two minimal dogbones on the same wall therefore need 4.49 mm plus the 0.05 mm tolerance, so call it 4.6 mm of clear edge before the tool will export.
This is the right default for small joinery, inlay pockets, and anything where the corner will be visible. Half a millimetre of bulge disappears into a glue line.
Full corner with a 1/8″ bit
Overcut depth is the full 1.5875 mm and each edge is consumed by 1.5875 mm, so two full corners on one wall need about 3.23 mm — comfortably less than the 4.6 mm two minimal dogbones want.
That makes the full corner the fallback for genuinely tiny pockets. You pay for it with a 3.175 mm circle bitten out of each corner, which on a small part is a large fraction of the whole feature.
T-bone with a 1/8″ bit
The wall the T-bone faces is consumed by 2R = 3.175 mm; the other wall is consumed by nothing. On a 6 mm wide slot cut with a 1/8″ bit, T-bones placed on the long walls leave the 6 mm width completely intact.
Point the same T-bone at the 6 mm wall instead and two of them need 6.35 mm, which does not fit, and the generator refuses. Leaving the axis on auto lets the tool pick the wall that still has slack after the opposite corner is reserved.
Worked examples: which pockets actually fit
A 20 × 10 mm pocket with minimal dogbones on all four corners is comfortable: the 20 mm sides need 4.6 mm and the 10 mm sides need the same, both with room to spare.
An 8 × 40 mm slot still passes on all four corners — 8 mm is well above 4.6 mm. Take the short dimension down to 4 mm and the short walls fail, at which point you have three options: disable one corner on that wall, switch to full corners (3.23 mm needed), or run T-bones along the 40 mm axis so the 4 mm walls are untouched.
A 4.5 mm wide slot is right at the edge for full corners and beyond reach for minimal dogbones. At that width the honest answer is usually a smaller cutter.
Matching the bit in CAM
In LightBurn, Carbide Create, or Easel, set the tool diameter to 3.175 mm (or 0.125 in) and create an inside or pocket toolpath. The exported contour already contains the dogbones.
Do not offset the geometry by 1.5875 mm before cutting. Your CAM already applies cutter compensation; adding your own doubles the clearance and the joint will rattle.
A 1/8″ bit is small enough that a unit mistake hides in the preview. Treating 3.175 as inches produces a relief you can barely see on screen and a crater on the machine. Check the output size readout in the tool against the size you expect, then dry-run above the stock.