Article — Thread Pitch Calculator
Thread Pitch Calculator — TPI, Metric Pitch, Lead, and Helix Angle
Thread pitch is the distance between adjacent thread crests, measured parallel to the screw axis. In metric it is given in millimeters (M10 × 1.5 has a 1.5 mm pitch); in imperial it is given as TPI — threads per inch. The exact conversion: pitch in mm = 25.4 / TPI.
The 25.4 mm-per-inch factor is exact by definition (since 1959), so the TPI-to-mm conversion is mathematically clean. What is messy is that the two systems use slightly different nominal sizes, which means a 20 TPI thread and a 1.27 mm pitch thread are mathematically identical but physically incompatible because the matching bolt diameters differ. Always specify both.
Thread pitch basics
Pitch controls how far the screw advances per turn (for a single-start thread, advance = pitch). A fine pitch (small mm or high TPI) gives more thread engagement per inch of length, which is desirable for vibration resistance and pressure-tight joints. A coarse pitch (large mm or low TPI) tolerates damage better — a slightly bunged-up coarse thread still starts; a damaged fine thread often does not.
Manufacturers specify pitch as part of the fastener callout. "M10 × 1.5" is M10 nominal diameter with 1.5 mm pitch. "1/4-20 UNC" is 1/4 inch diameter with 20 TPI. The second number is always the pitch indicator, and it is what tells you whether two fasteners can mate.
Pitch vs TPI conversion
The math: pitch (mm) = 25.4 / TPI, and TPI = 25.4 / pitch (mm). 20 TPI gives 1.27 mm pitch. 16 TPI gives 1.5875 mm. 13 TPI gives 1.954 mm. The reverse: 1.5 mm pitch is 16.93 TPI, 2.0 mm is 12.7 TPI.
These conversions are exact but rarely give round numbers in both systems simultaneously. ISO metric threads were designed to give clean mm values; Unified threads were designed to give clean TPI values; and the two systems do not overlap. The 1.27 mm thread pitch you get by converting 20 TPI is not a standard metric pitch, so a 1/4-20 bolt has no metric equivalent.
The pound was redefined as exactly 0.45359237 kg in 1959, and the inch as exactly 25.4 mm. Before that, US and UK inches differed slightly — meaning pre-1959 1/4-20 UNC bolts from the US would not match UK 1/4-20 BSW. The 1959 treaty fixed the mismatch.
Pitch vs lead
Pitch and lead are often confused, but they describe different things. Pitch is the distance between thread crests. Lead is the distance the screw advances per full rotation. For a single-start thread, pitch and lead are equal. For multi-start threads (2 or more independent helices wound around the same shaft), lead = pitch × number of starts.
A 3-start thread with 2 mm pitch has 6 mm lead — three times faster advance per turn than a single-start version, but each thread carries one-third the axial load. Multi-start threads show up on bottle caps, jar lids, camera tripod quick-release mounts, and CNC lead screws. They trade load capacity for assembly speed.
Metric vs imperial thread pitch
Metric coarse pitches were chosen so each diameter has one "default" pitch that gives similar strength to the UNC equivalent. M6 × 1.0 corresponds roughly to 1/4-20 UNC; M10 × 1.5 to 3/8-16 UNC; M12 × 1.75 to 1/2-13 UNC. Fine metric pitches exist too — M10 × 1.25 is the fine version, used where vibration is a concern.
UNC and UNF dominate in the US for legacy reasons: when the world switched to metric in the 1960s, the US balked because billions of dollars of hardware would have to be replaced. Today aerospace, defense, and US automotive heritage parts still use Unified; everything else has gone metric. European cars, modern bicycles, computer components, and any product designed after about 1990 default to metric.
If you cannot remember whether a bolt is metric or imperial, check the head. Metric bolts are usually marked with a class number like "8.8" or "10.9" on the head; Unified bolts use radial slash marks (3 marks = Grade 5, 6 marks = Grade 8).
Helix angle and self-locking
The helix angle β is the angle the thread makes with a plane perpendicular to the screw axis. For M10 × 1.5: β = arctan(1.5 / (π × 10)) ≈ 2.73°. Standard machine screws sit between 2° and 5°. Below about 5° the thread is self-locking under most conditions — vibration alone cannot back the bolt out.
Above 15° the thread becomes a power screw (lead screw) that needs a brake or counterweight to stop it from back-driving under axial load. Power screws are common on CNC machines, jack stands, and clamp mechanisms — anywhere you need to convert rotation into translation efficiently.
Multi-start threads
Multi-start threads pack two or more independent helices into the same shaft. The thread profile looks normal from the side, but if you traced a single thread, it would only be one of several wound around the screw together. Each start has its own root and crest; the pitch stays the same, but the lead multiplies by the number of starts.
Applications: 2-start camera mounts (faster setup), 3-start ball-valve quick connects, 4-start CNC ball screws, jar lids that close in a half-turn. The cost is reduced strength per thread (each carries 1/n the load), so multi-start is rarely used where load is critical.
Measuring thread pitch in the field
The cleanest tool is a thread pitch gauge — a stack of metal leaves, each etched with a specific pitch. You hold the gauge against the thread; the leaf that fits without rocking is your pitch. Sets cover both metric (0.5 to 6 mm) and imperial (4 to 80 TPI) ranges.
Without a gauge: measure across 10 thread crests with calipers, then divide by 9 (the gap count between 10 crests). For metric, the result is your pitch in mm. For imperial, 1 divided by your result is TPI. The 10-crest method is accurate to about ±0.05 mm with cheap calipers.
- 20 TPI = 1.27 mm pitch (UNC 1/4 inch, the most common US thread)
- M6 coarse = 1.0 mm pitch, β ≈ 3.0° (metric equivalent of UNC 1/4)
- M10 × 1.5 = 16.93 TPI equivalent, β ≈ 2.73° (automotive default)
- 1/2-13 UNC = 1.954 mm pitch (US structural standard)
- Self-locking limit = roughly β < 5° in dry steel-on-steel
- 3-start camera = lead is 3 × pitch, advances 3× faster per turn
Bicycle pedals (left side), LPG gas fittings, propane tanks, and turnbuckles use left-hand threads. The pitch and major diameter look identical to a normal right-hand thread, but the spiral runs the opposite direction. Forcing a right-hand tool onto a left-hand thread strips the part instantly. Look for "LH" stamped on the head before applying torque.