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Thread Pitch Diameter and Helix Angle

Guide · Updated October 28, 2026

The pitch diameter is where a 60° thread is measured and where the thread fit is controlled. For both Unified (ASME B1.1) and ISO metric (ISO 68-1 and ISO 724) 60° threads, the basic pitch diameter is the basic major diameter minus 0.649519 × pitch, because 0.649519P is 3/4 of the sharp V height (0.866025P × 0.75). The helix angle, also called lead angle, is the angle the thread makes with a plane square to the axis: tan λ = lead ÷ (π × pitch diameter). It decides how much side clearance a lathe threading tool needs.

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Step by step

Find the pitch: P = 1 ÷ TPI in inches, or read it in mm.
Calculate basic PD: d2 = D − 0.649519 × P.
Find the lead: Lead = pitch × number of starts.
Calculate helix angle: λ = atan(lead ÷ (π × d2)).
Set tool clearance: Grind the leading side clearance at the helix angle plus a few degrees.
Measure: Check PD with three wires or a thread mic against the class tolerance.

Basic pitch diameter and helix angle: UN inch

#10-24: basic pitch diameter 0.1629 in, helix angle 4.65°
#10-32: basic pitch diameter 0.1697 in, helix angle 3.35°
1/4-20: basic pitch diameter 0.2175 in, helix angle 4.18°
1/4-28: basic pitch diameter 0.2268 in, helix angle 2.87°
5/16-18: basic pitch diameter 0.2764 in, helix angle 3.66°
3/8-16: basic pitch diameter 0.3344 in, helix angle 3.40°
3/8-24: basic pitch diameter 0.3479 in, helix angle 2.18°
1/2-13: basic pitch diameter 0.4500 in, helix angle 3.11°
1/2-20: basic pitch diameter 0.4675 in, helix angle 1.95°
3/4-10: basic pitch diameter 0.6850 in, helix angle 2.66°
1-8: basic pitch diameter 0.9188 in, helix angle 2.48°

Values are basic sizes. Actual external threads in class 2A have an allowance and tolerance below basic; get the class limits from ASME B1.1 or the UNC/UNF chart before you measure.

Basic pitch diameter and helix angle: ISO metric coarse

M3 x 0.5: basic d2 2.675 mm, helix angle 3.40°
M4 x 0.7: basic d2 3.545 mm, helix angle 3.60°
M5 x 0.8: basic d2 4.480 mm, helix angle 3.25°
M6 x 1: basic d2 5.350 mm, helix angle 3.40°
M8 x 1.25: basic d2 7.188 mm, helix angle 3.17°
M10 x 1.5: basic d2 9.026 mm, helix angle 3.03°
M12 x 1.75: basic d2 10.863 mm, helix angle 2.94°
M16 x 2: basic d2 14.701 mm, helix angle 2.48°
M20 x 2.5: basic d2 18.376 mm, helix angle 2.48°

These d2 values match the basic pitch diameters tabulated in ISO 724, for example 5.350 mm for M6 and 9.026 mm for M10. Tolerance class 6g or 6H limits come from ISO 965-1.

Why helix angle matters on the lathe

The thread flank climbs at the helix angle, so the side of the tool that leads into the cut must be ground with at least that much clearance or it rubs. Fine threads on big diameters have small angles (a 1-8 is under 2.5°), while coarse threads on small diameters and multiple-start threads have large ones. For a 4-start thread the lead is 4 × pitch and the helix angle roughly quadruples. Insert holders handle this with shims that tilt the insert.

Worked example: 1/2-13 UNC

P = 1 ÷ 13 = 0.076923 in. d2 = 0.5000 − 0.649519 × 0.076923 = 0.5000 − 0.049963 = 0.4500 in. Helix angle = atan(0.076923 ÷ (π × 0.4500)) = atan(0.05441) = 3.11°. Grind about 3° + 3° = 6° leading side clearance.

Worked example: M10 x 1.5 two-start

d2 = 10 − 0.649519 × 1.5 = 9.026 mm. Single start lead = 1.5 mm, helix angle 3.03°. With two starts, lead = 3.0 mm, so λ = atan(3.0 ÷ (π × 9.026)) = atan(0.1058) = 6.04°. Tool clearance must roughly double.

Common problems

Using major diameter in the helix formula (small error, but it adds up), forgetting starts when calculating lead, and comparing a measured PD to basic instead of the class limits. Check the wire set or thread mic against a gage block or setting plug before measuring.

FAQ

What is the pitch diameter formula?

d2 = D − 0.649519 × P for 60° UN and ISO metric threads.

What is the pitch diameter of 1/4-20?

Basic is 0.2175 in.

What is the pitch diameter of M6 x 1?

Basic is 5.350 mm.

What is the helix angle formula?

tan λ = lead ÷ (π × pitch diameter).

Is lead the same as pitch?

Only for single-start threads; lead = pitch × starts.

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