DIN 76 Thread Undercut & Runout Calculator (Metric)

How Does a DIN 76-1 Thread Relief Prevent Insert Breakage in CNC G76 Cycles?

When single-point threading on a CNC lathe using our Fanuc G76 threading cycle calculator, the Z-axis carriage travels locked to the spindle encoder at 100% feed rate (F = P mm/rev). At 1,200 RPM on a 1.5 mm pitch thread, the turret advances at 1,800 mm/min (30 mm/s). If the thread ends directly against a 90° shoulder without a relief groove, the threading tool has no free space to exit, so the thread runs out as a tapered, incomplete run x1 ≈ 2.5P long, and the carbide tip can chip against the shoulder face. DIN German Institute for Standardization DIN 76-1 avoids this with a circumferential undercut: a groove turned slightly deeper than the minor root d3 before threading begins, so the tool leaves the thread into free air. The runout x1 in Table 1 applies only to threads without a relief groove, where it sets the 30° lead-out at the thread end.

DIN 76-1 defines two axial width series for external threads: Form A (Normal) limits the overall relief width to g2 ≤ 3.5P with a minimum flat floor of roughly g1 ≈ 2.2P (5.2 mm and 3.2 mm for P = 1.5), suitable for general bolts, leadscrews, and dieheads, whereas Form B (Short) compresses the relief to the shorter g1 / g2 values of Table 1 when axial engagement length is restricted on compact hydraulic fittings or thin locknuts.

External Shaft Undercuts (d_g) and Tap Core Bore (D₁)

For external ISO metric threads governed by International Organization for Standardization (ISO) ISO 68-1, the external thread root lies at d3 = d − 1.22687P. To guarantee that the crest of the 60° threading insert clears the floor of the undercut across all tolerance classes in our metric tap drill and thread chart, DIN 76-1 Table 1 sets the external groove diameter one step below the root (d − 1.6 at P = 1, d − 2.3 at P = 1.5, d − 3.0 at P = 2, tolerance h13) with corner radii r ≈ 0.5P and a 30° entry chamfer matching the flank angle of the thread.

For internal blind-hole threads cut with a boring bar or single-point internal threading tool, the geometry inverts: the pre-bored hole is drilled to D1 = D − 1.08253P, and the internal relief groove at the bottom of the bore must expand outward past the major thread diameter to Dg read from DIN 76-1 Table 2 for the pitch row (H13; not published by this tool) so the internal threading tip drops into free air at the end of each pass. Internal relief widths (Forms C and D in DIN 76-1 Table 2) are longer than the external Form A/B values shown here, so this tool does not compute internal relief widths g1 and g2: take them from Table 2 of your edition. When tapping without an internal undercut, use our blind hole tap depth calculator to account for tap chamfer relief.

Worked Examples: M16×1.5 External Spindle Nose & M20×2.5 Blind Bore

Worked Example 1 (M16 × 1.5 External Shaft Thread): On an M16 × 1.5 shaft shoulder (not a Table 1 row, so its pitch-row value d − 2.3 is extrapolated), our engine computes external minor diameter d3 = 14.16 mm and DIN 76 Form A undercut diameter d_g = 13.70 mm (radial step 1.150 mm per side from major d, or 0.230 mm per side from minor d₃) with corner radius r = 0.80 mm. Program the grooving tool for flat bottom width g1 = 3.2 mm and total shoulder-to-chamfer width g2 = 5.2 mm. If axial space is tight, Form B reduces the groove to g₁ = 1.8 mm / g₂ = 3.8 mm.

Worked Example 2 (M20 × 2.5 Internal Blind Cylinder Bore): For an internal M20 × 2.5 thread bored in a manifold block, the core bore is D1 = 17.29 mm and the internal relief groove at the bottom of the hole takes D_g from DIN 76-1 Table 2 for the pitch row (not published by this tool), with widths g₁ / g₂ also read from Table 2; its corner radius is not yet verified, so it is not published here. For heavy power threads, check the Buttress thread calculator and DIN 103 trapezoidal thread calculator.

Thread pitches follow the International Organization for Standardization (ISO) ISO 261 metric series, and the h13 tolerance on the undercut diameter follows International Organization for Standardization (ISO) ISO 286.

Check the finished undercut before the first thread pass: measure the groove diameter dg with a depth micrometer or a go/no-go plug, confirm the corner radius r with a radius gage, and check that the flat width g1 clears the threading insert in the program. A groove that comes out shallower than the programmed dg leaves the thread running into the shoulder, so correct the groove before cutting the thread.

Next step: For plain bearing and grinding shoulders without threads see the DIN 509 undercut calculator, and generate your lathe threading passes in the Fanuc G76 threading cycle calculator.