TAHA Engineering Toolsby TAHA Knowledge Lab

Machining & Workshop

Thread Pitch, TPI & Lead Calculator

Convert pitch in mm to TPI and back, and find the lead of multi-start threads.

Inputs

Side view of a V-thread profile with pitch P measured between two neighbouring crests.P60° threadaxis
Pitch P is the distance from one thread crest to the next along the axis. TPI = 25.4 ÷ P (mm). On a single-start thread the lead equals the pitch; with n starts, lead = n × P. Diagram not to scale.

Distance from one thread crest to the next, measured along the axis.

Most screws are single-start (1). Multi-start threads have 2, 3 or more separate helices side by side.

Leave empty if you do not need the lead (helix) angle. For an M10 × 1.5 thread the pitch diameter is about 9.03 mm.

Result

Lead (advance per turn)
1.5
Pitch
1.5
Threads per inch
16.9333TPI
Working
TPI = 25.4 ÷ 1.5 mm = 16.933 TPI Lead = 1.5 mm × 1 start = 1.5 mm

A pitch of 1.5 mm is 16.9333 TPI. The thread advances 1.5 mm for each full turn.

Educational estimate — check the assumptions below.

About this calculator

Metric threads are specified by their pitch — the distance between neighbouring threads in millimetres, such as M10 × 1.5. Imperial (Unified) threads are specified in threads per inch (TPI), such as 3/8-16. This calculator converts between the two, which you need when cutting a metric thread on an imperial lathe (or the reverse), checking a thread with a pitch gauge, or matching a part from another country.

The lead is how far the nut moves in one full turn. For an ordinary single-start thread, lead equals pitch. Multi-start threads (common on lead screws, jar lids and fast-acting valves) have two or more helices, so the lead is the pitch multiplied by the number of starts. The lathe must be set up to cut the lead, then index for each start.

Formula

P (mm) = 25.4 ÷ TPI    TPI = 25.4 ÷ P (mm)

L = P × n    λ = arctan[L ÷ (π × d2)]

P = pitch, L = lead, n = number of starts, d2 = pitch diameter, λ = lead (helix) angle. 1 inch = 25.4 mm exactly.

Worked example

  • Pitch 1.5 mm → TPI = 25.4 ÷ 1.5 = 16.93 TPI (close to, but not the same as, 16 TPI).
  • 20 TPI → pitch = 25.4 ÷ 20 = 1.27 mm.
  • A 2-start thread with 1.5 mm pitch has a lead of 1.5 × 2 = 3 mm. At a pitch diameter of 9.026 mm the lead angle is arctan[3 ÷ (π × 9.026)] = 6.04°.

Assumptions and limitations

  • Conversion is exact (1 in = 25.4 mm). Most metric pitches do not convert to whole-number TPI, so a metric thread cannot be replaced by the “nearest” imperial thread — they will not fit properly.
  • The lead angle is calculated at the pitch diameter you enter. It is used, for example, to check tool side clearance; tool makers give the required clearance for their inserts.
  • Pitch diameters and tolerances of standard threads are defined in the thread standards (for example ISO 965 for metric, ASME B1.1 for Unified threads). They are not calculated here.

References

  • Inch–millimetre definition (1 in = 25.4 mm); lead = pitch × number of starts; lead angle tan λ = L ÷ (π·d₂).