Worked example
A 1.5 mm pitch is 25.4 / 1.5 = 16.93 TPI. A 20 TPI thread has a pitch of 25.4 / 20 = 1.27 mm. No standard inch thread has exactly 16.93 TPI – the nearest are 16 and 18 – which is why cutting a metric thread on an inch lead screw needs a transposing gear set or a control that can do it.
Cutting a metric thread on an inch lathe
- The pitch conversion is the core of the gear ratio: the ratio of 25.4 to the pitch. Many lathes have a 127-tooth transposing gear for this, since 127 = 5 × 25.4.
- On a lathe with a thread dial, keep the half-nut engaged for metric pitches rather than releasing it between passes, as the dial positions are not valid.
- For the thread depth and tap drill sizes you need the thread standard – these pages do not reproduce standard tables.
Frequently asked questions
How do I convert TPI to pitch in mm?
Pitch = 25.4 / TPI. A 20 TPI thread has a pitch of 1.27 mm.
How do I convert pitch in mm to TPI?
TPI = 25.4 / pitch. A 1.5 mm pitch is 16.93 TPI.
Can I swap a metric thread for an inch thread with the same pitch?
No. Even if the pitch matches, thread form, diameter and tolerance differ, so the parts will not fit. The conversion is only arithmetic.
How do I cut a metric thread on an inch lathe?
The lead screw is in inches, so the gear train must supply the factor 25.4 / pitch; many lathes use a 127-tooth transposing gear, because 127 = 5 × 25.4.
More free machinist calculators
- Inch to mm – Convert inches to millimetres and back, fractions like 1 3/8 included. Exact factor 25.4, with a chart of every 1/64 inch.
- RPM and feed – Calculate spindle RPM from surface speed and diameter, surface speed from RPM, and feed rate from chip load – metric and imperial, with formulas.
- Taper – Taper ratio, half angle and taper per foot from the large and small diameter and the length, or the small diameter from the angle.
- Bolt circle – X and Y coordinates of evenly spaced holes on a bolt circle, with the hole spacing, start angle and centre offset. Copy the table into your program.
- Sine bar – Gauge block height for a sine bar angle, or the angle from a known stack, for 5 in, 10 in, 100 mm, 200 mm or any other bar length.
- Metal removal rate – Metal removal rate in cm³/min or in³/min from depth, width and feed – milling and turning, metric and imperial, with the formulas.
- Drill point depth – Length of a drill's point cone from diameter and point angle, and the total depth needed for a full-diameter hole to depth.
- Right triangle – Hypotenuse and angles from two legs, or the legs from the hypotenuse and an angle – for chamfers, dovetails, tapers and hole positions.
- Machining time – Cutting time from length, feed and spindle speed – turning with feed per revolution, milling with feed rate and number of passes.
- Decimal to fraction – Turn a decimal inch or a millimetre value into the nearest fraction – 8ths to 128ths – with the error in millimetres.
- Degrees to DMS – Convert decimal degrees to degrees, minutes and seconds and back, with the angle in radians.
- SFM to m/min – Convert surface feet per minute to metres per minute and back, and inches per minute to mm per minute, with the exact factors.
- Cpk calculator – Paste measurements from Excel, enter USL and LSL and get Cp, Cpk, Pp and Ppk. Says plainly when 25 values are too few for an index.
- Tolerance stack-up – Add up the tolerances of a chain of parts: closing gap, worst case and statistical RSS for up to eight dimensions. Free, in your browser.
- Fit clearance – Enter hole and shaft limits and get minimum and maximum clearance and the kind of fit – clearance, transition or interference.
- Chip thinning – Feed per tooth to program when the radial width of cut is below half the cutter diameter, so the real chip thickness stays right.
- Ball-nose stepover – Scallop height left by a ball-nose cutter from the stepover, or the stepover for a wanted scallop height, on a flat surface.
- Surface finish – Theoretical Rt and estimated Ra of a turned surface from the feed per revolution and the tool nose radius.
- Torque and power – Torque from power and speed in newton-metres or pound-feet, and power from torque and speed. The formulas with worked examples.
- Spur gear – Pitch and outside diameter, centre distance, ratio and circular pitch of a pair of external spur gears from the module and the tooth numbers.
Making parts for a customer who wants paperwork?
Automotive and aerospace customers ask for proof that the parts match the drawing. See first article inspection (FAI), PPAP explained and the true position calculator.