How this calculation works
Threads per inch and millimetre pitch describe the same axial spacing in reciprocal units. A multi-start thread adds another distinction: one turn advances by the lead, which is the pitch multiplied by the number of starts.
Pitch mm = 25.4/TPI; lead = pitch × starts; helix angle = atan(lead/(π × pitch diameter))A worked example
A pitch of 1.27 mm corresponds to twenty threads per inch because 25.4/1.27 equals twenty. With two starts, the lead is 2.54 mm per revolution. At a ten-millimetre pitch diameter, the ideal helix angle is arctan(2.54/(10 pi)), about 4.622 degrees. Switching to TPI mode and entering twenty must reproduce the same quantities.
Good to know
Exact inch conversion and ideal cylindrical helix geometry only; no thread standard identification, taper, fit class, handedness or compatibility approval. Use axial pitch for conversions and thread preparation formulas. Use lead for advance per revolution; confusing those quantities is especially consequential on multi-start screws.
Reference: OpenStax — right-triangle trigonometry (opens in a new tab) ↗
What this model answers
Threads per inch and millimetre pitch describe the same axial spacing in reciprocal units. A multi-start thread adds another distinction: one turn advances by the lead, which is the pitch multiplied by the number of starts.
Helix angle depends on both lead and the diameter at which the helix is considered. This page uses the entered pitch diameter rather than silently substituting major diameter. It describes an ideal cylindrical helix.
The Lead screw speed and command pulse calculator turns multi-start lead into nominal travel and control pulses. Axial pitch alone understates travel per revolution when the screw has several starts.
Measure the right inputs
Choose the known convention before entering the value. In pitch mode the value is millimetres per adjacent thread spacing. In TPI mode it is the number of those spacings per inch.
The conversion uses exactly 25.4 millimetres per inch. Starts must be a whole number. Pitch diameter must come from an appropriate specification or measurement; the calculator does not derive it from a nominal thread label.
Read the result in context
Changing starts leaves TPI and axial pitch unchanged but multiplies lead. Helix angle then increases because the thread climbs farther axially per circumference.
Converting pitch does not identify a thread standard. Similar pitch values can still belong to incompatible nominal diameters, flank forms, taper conventions, tolerances or handedness. A numeric spacing match is only one dimension of compatibility.
Work through the numbers
A pitch of 1.27 mm corresponds to twenty threads per inch because 25.4/1.27 equals twenty. With two starts, the lead is 2.54 mm per revolution.
At a ten-millimetre pitch diameter, the ideal helix angle is arctan(2.54/(10 pi)), about 4.622 degrees. Switching to TPI mode and entering twenty must reproduce the same quantities.
Where the model stops
Exact inch conversion and ideal cylindrical helix geometry only; no thread standard identification, taper, fit class, handedness or compatibility approval.
Use axial pitch for conversions and thread preparation formulas. Use lead for advance per revolution; confusing those quantities is especially consequential on multi-start screws.
A few questions, answered
Does a two-start thread have half the TPI?
No. TPI still describes adjacent axial pitch spacing. Lead doubles at the same pitch.
Can matching pitch prove two parts fit?
No. Diameter, profile, tolerance, taper and handedness must also match the relevant specification.