Thread depth and passes calculator
Pick a thread from the list or enter your own diameter and pitch to get the thread depth, bolt minor or nut bore diameter and the diameter of every pass.
Quick answer
External thread: depth h = 0.6134 × P, minor diameter d3 = d − 1.2269 × P. For 1/2-13 UNC (P = 0.0769″): h ≈ 0.0472″, minor ≈ 0.4056″. For M12×1.75: h ≈ 1.07 mm.
Internal: h = 0.5413 × P, bore D1 = D − 1.0825 × P. For M12×1.75: bore ≈ 10.11 mm.
Result
- Pitch
- —
- Thread depth
- —
- Bolt minor diameter
- —
Passes
| Pass | Depth, mm | Diameter X (G7), mm |
|---|
Who needs it and why
A thread can't be cut in one pass: the depth is split into several, each thinner than the last. To write them in G-code you need the depth and diameter of every pass — the calculator lists them in a table.
- Threading with G33/G32 passes — by hand or on a control without a threading cycle: the X diameter of each pass is ready.
- Nuts — which diameter to bore for the thread and which diameter the last pass reaches.
- Non-standard threads — your own diameter and pitch that no chart lists: the formulas are the same.
- Inch threads — UNC/UNF by TPI on a metric machine, and the other way round.
The formulas
ISO metric and UNC/UNF threads share the same 60° profile, so the formulas are the same (P is the pitch, D the major diameter):
- external: depth
h = 0.6134 · P, minor diameterD − 1.2269 · P - internal: depth
h = 0.5413 · P, bore diameterD − 1.0825 · P - depth after pass n of N:
h · √(n / N)— constant chip area
These are calculated values. For critical parts check the standard's tables or a gauge; the bolt OD is usually turned slightly under nominal. Common sizes are tabulated in UNC/UNF thread chart for CNC lathe, and every G76 and G33 word is explained in Threading in LinuxCNC: G33 and G76.
In the Turn G-code app the threading cycle splits the depth into passes itself, adds lead-in and run-out, multi-start and left-hand threads, and shows every pass in the 2D simulator before you get the code.