1. The five elements of a thread
- Thread form: the flank angle defines the thread family — 60° triangular (metric / unified UN), 55° (Whitworth / pipe), 30° trapezoidal and so on.
- Major diameter D/d: the nominal diameter; M24 has a 24 mm major diameter.
- Pitch P / lead Ph: for a single-start thread Ph = P; for a two-start thread Ph = 2P.
- Number of starts n: power threads are often multi-start.
- Hand: right-hand is the default and is not marked; left-hand is marked "LH".
2. Thread parameter calculator
Enter a thread designation and the calculator works out the pitch, flank angle and major, pitch and minor diameters, draws the thread profile and recommends tolerances for the chosen material. Supports metric M, unified UNC/UNF, pipe G/R, NPT, trapezoidal Tr and round Rd (DIN 405).Decide first whether it is an external or an internal thread— the tolerance zone runs the other way (external threads below nominal, e/f/g/h; internal threads above nominal, G/H), and trapezoidal threads also differ in radial size.
Try:
M24 ·
M10×1.25 ·
1/2-13 UNC ·
5/16-18 ·
#10-32 UNF ·
G1/2 ·
NPT1/2 ·
Tr40×7 ·
Tr20×4 ·
Rd40×1/6
| Designation reading | — |
| Flank angle | — |
| Pitch P | — |
| Major diameter d (nominal) | — |
| Pitch diameter d₂ | — |
| Minor diameter d₁ | — |
| Thread height H (theoretical) | — |
Tolerance recommendation (by material): Calculate a thread designation first.
3. Common thread types and designations
| Type | Flank angle | Designation example | Use |
|---|---|---|---|
| Metric thread M (coarse) | 60° | M24-6H (pitch 3 omitted) | the most common fastening thread |
| Metric thread M (fine) | 60° | M24×1.5-6g | thin-wall parts, fine adjustment, vibration resistance |
| 55° non-sealing pipe thread G | 55° | G1/2 A | water and air fittings (sealed by a gasket) |
| 55° sealing pipe thread Rp/Rc | 55° | Rc1/2 (tapered internal)Rp1/2 (parallel internal) | piping sealed by the thread itself |
| 60° tapered pipe thread NPT | 60° | NPT1/4 | US pressure piping and hydraulic fittings |
| Trapezoidal thread Tr | 30° | Tr40×7-7H | lead screws, jacks, valves |
| Buttress thread B | 33°(3°/30°) | B40×7 | one-way heavy loads: presses, hooks |
| Tapping screws ST | 60° | ST4.8 | driven straight into sheet steel or plastic |
| Unified thread UNC/UNF | 60° | 1/4-20 UNC-2A | equipment built to inch standards (20 TPI) |
Tolerance class shorthand: internal threads use capitals (6H is the norm) and external threads lower case (6g is the norm); the smaller the number the tighter the class (4H > 6H > 7H); an assembly is written M24×1.5-6H/6g.
4. Reading designations — practice
M12-6H: coarse metric thread (pitch 1.75), internal, with both pitch and crest diameter zones at 6H.M20×2-5g6g-LH: fine pitch 2, external thread with 5g pitch diameter and 6g crest diameter, left-hand.G3/8 B: 55° non-sealing pipe thread, size code 3/8 (inch), class B external thread.Tr32×12(P6)-8e: trapezoidal thread, major diameter 32, lead 12 two-start (single-start pitch 6), external tolerance 8e.
5. Inspection methods
1. Functional inspection: thread gauges (first choice on the floor — "does it assemble?")
- Go gauge (T): must screw on freely through the full length, checking the functional pitch diameter (pitch diameter, pitch and flank angle combined).
- No-go gauge (Z): may be screwed on no more than 2 turns, checking whether the simple pitch diameter is oversize or undersize.
- Note: a no-go gauge must never be forced, and entering it at an angle gives a false verdict; calibrate gauges on schedule — a worn go gauge is the number one cause of accepting bad lots.
2. Measuring individual elements (for precision verdicts or finding the cause)
| Element | Method | Key point |
|---|---|---|
| Major diameter | Outside micrometer / caliper | Measure at several positions along the axis; check taper and ovality |
| Pitch | Pitch gauge comparison, or projector / vision system | Seat the gauge in the thread and check for light; for an accurate value measure 5–10 pitches and average |
| Flank angle | Projector / toolmaker's microscope / vision system | Magnified profile comparison; the 60° or 55° angle is held to about ±15′ |
| Pitch diameter | Three-wire method (the classic) or a thread micrometer | See the formula below; pick the best-size wire |
| Minor diameter | Caliper inside jaws / dedicated gauge | normally only for process control |
3. Pitch diameter by the three-wire method (the formula you must know)
- Metric 60° thread:M = d₂ + 3d₀ − 0.866P (M is the measurement over the wires, d₀ the wire diameter, P the pitch).
- 55° inch / pipe thread:M = d₂ + 3.1657d₀ − 0.9605P.
- Best wire diameter (the wire touches the flanks exactly at the pitch diameter): d₀ = 0.577P for a 60° form, 0.564P for 55°.
- Example: M24×3 bolt, best wire d₀ = 0.577 × 3 ≈ 1.732 mm (use the 1.732 standard wire); from the measured M, d₂ = M − 3×1.732 + 0.866×3.
- The two-wire method (three wires will not fit on coarse pitches) and the optical method (fixture the part and measure the flanks directly when wires are impractical) serve as alternatives.
4. Choosing the instrument
Quick screening on the floor with go/no-go gauges; all parameters as numbers with a vision system (flank angle, pitch, flank straightness); arbitration on pitch diameter with the three-wire method plus a micrometer or length measuring machine; for in-line batch checks add thread depth gauges and torque checks.
6. Coarse pitch table for common metric threads
| Size | M6 | M8 | M10 | M12 | M16 | M20 | M24 | M30 |
|---|---|---|---|---|---|---|---|---|
| Coarse pitch, mm | 1 | 1.25 | 1.5 | 1.75 | 2 | 2.5 | 3 | 3.5 |
| Usual tolerance class (external/internal) | 6g / 6H | 6g / 6H | 6g / 6H | 6g / 6H | 6g / 6H | 6g / 6H | 6g / 6H | 6g / 6H |
Basic dimensions follow GB/T 196 (sizes) and GB/T 197 (tolerances); pipe threads follow GB/T 7307 (G) and GB/T 7306 (Rp/Rc).
7. Fine pitch metric threads (basic dimensions per GB/T 196)
| Size | Pitch P (mm) | Pitch diameter d₂ (mm) | Minor diameter d₁ (mm) | Tap drill reference (mm) | Usual tolerance class (external/internal) |
|---|---|---|---|---|---|
| M8×1 | 1 | 7.350 | 6.917 | 7.000 | 6g / 6H |
| M8×0.75 | 0.75 | 7.513 | 7.188 | 7.250 | 6g / 6H |
| M10×1.25 | 1.25 | 9.188 | 8.647 | 8.750 | 6g / 6H |
| M10×1 | 1 | 9.350 | 8.917 | 9.000 | 6g / 6H |
| M10×0.75 | 0.75 | 9.513 | 9.188 | 9.250 | 6g / 6H |
| M12×1.5 | 1.5 | 11.026 | 10.376 | 10.500 | 6g / 6H |
| M12×1.25 | 1.25 | 11.188 | 10.647 | 10.750 | 6g / 6H |
| M12×1 | 1 | 11.350 | 10.917 | 11.000 | 6g / 6H |
| M14×1.5 | 1.5 | 13.026 | 12.376 | 12.500 | 6g / 6H |
| M14×1 | 1 | 13.350 | 12.917 | 13.000 | 6g / 6H |
| M16×1.5 | 1.5 | 15.026 | 14.376 | 14.500 | 6g / 6H |
| M16×1 | 1 | 15.350 | 14.917 | 15.000 | 6g / 6H |
| M18×2 | 2 | 16.701 | 15.835 | 16.000 | 6g / 6H |
| M18×1.5 | 1.5 | 17.026 | 16.376 | 16.500 | 6g / 6H |
| M20×2 | 2 | 18.701 | 17.835 | 18.000 | 6g / 6H |
| M20×1.5 | 1.5 | 19.026 | 18.376 | 18.500 | 6g / 6H |
| M22×2 | 2 | 20.701 | 19.835 | 20.000 | 6g / 6H |
| M22×1.5 | 1.5 | 21.026 | 20.376 | 20.500 | 6g / 6H |
| M24×2 | 2 | 22.701 | 21.835 | 22.000 | 6g / 6H |
| M24×1.5 | 1.5 | 23.026 | 22.376 | 22.500 | 6g / 6H |
| M27×2 | 2 | 25.701 | 24.835 | 25.000 | 6g / 6H |
| M30×2 | 2 | 28.701 | 27.835 | 28.000 | 6g / 6H |
| M30×1.5 | 1.5 | 29.026 | 28.376 | 28.500 | 6g / 6H |
| M36×3 | 3 | 34.051 | 32.752 | 33.000 | 6g / 6H |
| M36×2 | 2 | 34.701 | 33.835 | 34.000 | 6g / 6H |
Fine pitch notes: ① Fine threads lock better and resist vibration, so they suit thin walls, fine adjustment and vibrating service; ② d₂ = d − 0.6495P and d₁ = d − 1.0825P (same formula as coarse — a smaller pitch simply gives a shallower thread); ③ tap drill ≈ d − P (about 75% engagement, adjusted from shop experience); ④ the same tolerance system applies (6g external / 6H internal are the norm), written M20×1.5-6H/6g; for any size, type Mxx×P into the calculator in section 2.
8. UNF fine threads (ASME B1.1)
| Size | TPI (threads per inch) | Pitch P (mm) | Pitch diameter E (mm) | Minor diameter K (mm) | Tap drill reference | Usual tolerance class (external/internal) |
| #10-32 | 32 | 0.79 | 4.31 | 3.97 | #21 (4.0) | 2A / 2B |
| #12-28 | 28 | 0.91 | 4.9 | 4.5 | #14 (4.6) | 2A / 2B |
| 1/4-28 | 28 | 0.91 | 5.76 | 5.37 | #3 (5.4) | 2A / 2B |
| 5/16-24 | 24 | 1.06 | 7.25 | 6.79 | F(6.5) | 2A / 2B |
| 3/8-24 | 24 | 1.06 | 8.84 | 8.38 | Q(8.4) | 2A / 2B |
| 7/16-20 | 20 | 1.27 | 10.29 | 9.74 | 25/64 (9.9) | 2A / 2B |
| 1/2-20 | 20 | 1.27 | 11.88 | 11.33 | 29/64 (11.5) | 2A / 2B |
| 9/16-18 | 18 | 1.41 | 13.37 | 12.76 | 33/64 (13.1) | 2A / 2B |
| 5/8-18 | 18 | 1.41 | 14.96 | 14.35 | 37/64 (14.7) | 2A / 2B |
| 3/4-16 | 16 | 1.59 | 18.02 | 17.33 | 11/16 (17.5) | 2A / 2B |
| 7/8-14 | 14 | 1.81 | 21.05 | 20.26 | 51/64 (20.2) | 2A / 2B |
| 1-12 | 12 | 2.12 | 24.03 | 23.11 | 59/64 (23.4) | 2A / 2B |
| 1-1/8-12 | 12 | 2.12 | 27.2 | 26.28 | ≈26.9 | 2A / 2B |
| 1-1/4-12 | 12 | 2.12 | 30.38 | 29.46 | ≈30.0 | 2A / 2B |
| 1-1/2-12 | 12 | 2.12 | 36.73 | 35.81 | ≈36.4 | 2A / 2B |
UNF notes: ① UNF is the unified fine series (60° form, same formulas as metric: E = D − 0.6495P, K = D − 1.0825P, P = 25.4 ÷ TPI); ② coarse and fine are easily confused — #10-24 is UNC coarse while #10-32 is UNF fine, and 1/4-20 UNC pairs with 1/4-28 UNF, so check the TPI on the drawing before accepting goods; ③ 2A external / 2B internal are the norm (1A/1B loose, 3A/3B tight) and inspection uses GO/NOGO ring and plug gauges; ④ large sizes often use the constant pitch 8UN/12UN/16UN series (e.g. 1-3/4-8UN), which the calculator in section 2 handles with the UN formula; ⑤ pick the nearest standard drill for 75% engagement and follow the tap maker's data for critical parts.
9. BSF fine threads (BS 84, 55° Whitworth)
| Size (in – TPI) | Pitch P (mm) | Pitch diameter E (mm) | Minor diameter K (mm) | Tap drill reference (mm) | Usual tolerance class (external/internal) |
| 1/4-26 | 0.98 | 5.72 | 5.1 | ≈5.41 | External Medium / internal Normal (BS 84 medium class) |
| 5/16-22 | 1.15 | 7.2 | 6.46 | ≈6.83 | External Medium / internal Normal (BS 84 medium class) |
| 3/8-20 | 1.27 | 8.71 | 7.9 | ≈8.31 | External Medium / internal Normal (BS 84 medium class) |
| 7/16-18 | 1.41 | 10.21 | 9.31 | ≈9.76 | External Medium / internal Normal (BS 84 medium class) |
| 1/2-16 | 1.59 | 11.68 | 10.67 | ≈11.18 | External Medium / internal Normal (BS 84 medium class) |
| 9/16-16 | 1.59 | 13.27 | 12.25 | ≈12.76 | External Medium / internal Normal (BS 84 medium class) |
| 5/8-14 | 1.81 | 14.71 | 13.55 | ≈14.13 | External Medium / internal Normal (BS 84 medium class) |
| 3/4-12 | 2.12 | 17.69 | 16.34 | ≈17.02 | External Medium / internal Normal (BS 84 medium class) |
| 7/8-11 | 2.31 | 20.75 | 19.27 | ≈20.01 | External Medium / internal Normal (BS 84 medium class) |
| 1-10 | 2.54 | 23.77 | 22.15 | ≈22.96 | External Medium / internal Normal (BS 84 medium class) |
| 1-1/8-9 | 2.82 | 26.77 | 24.96 | ≈25.86 | External Medium / internal Normal (BS 84 medium class) |
| 1-1/4-9 | 2.82 | 29.94 | 28.14 | ≈29.04 | External Medium / internal Normal (BS 84 medium class) |
BSF notes: ① BSF is the Whitworth fine series (55° rounded crest and root, the same form as G pipe threads: E = D − 0.6403P, K = D − 1.2807P); ② it pairs with BSW coarse — 1/2-16 BSF against 1/2-12 BSW; ③ judge it by the 55° flank angle and never use 60° UNC/UNF gauges on it; ④ tolerances follow BS 84/BS 2779 medium fit and inspection uses Whitworth plug and ring gauges; ⑤ tap drills are estimated at 75% engagement and values marked ≈ are indicative.
10. Trapezoidal threads Tr (GB/T 5796, 30°)
| Size | Pitch P (mm) | Pitch diameter d₂ = D₂ (mm) | External minor diameter d₃ (mm) | Internal major diameter D₄ (mm) | Internal minor diameter D₁ (mm) | Usual tolerance class (external/internal) |
| Tr8×1.5 | 1.5 | 7.25 | 6 | 8.5 | 6.5 | External 7e / internal 7H (usual) |
| Tr10×2 | 2 | 9 | 7.5 | 10.5 | 8 | External 7e / internal 7H (usual) |
| Tr12×3 | 3 | 10.5 | 8.5 | 12.5 | 9 | External 7e / internal 7H (usual) |
| Tr14×3 | 3 | 12.5 | 10.5 | 14.5 | 11 | External 7e / internal 7H (usual) |
| Tr16×4 | 4 | 14 | 11.5 | 16.5 | 12 | External 7e / internal 7H (usual) |
| Tr18×4 | 4 | 16 | 13.5 | 18.5 | 14 | External 7e / internal 7H (usual) |
| Tr20×4 | 4 | 18 | 15.5 | 20.5 | 16 | External 7e / internal 7H (usual) |
| Tr22×5 | 5 | 19.5 | 16.5 | 22.5 | 17 | External 7e / internal 7H (usual) |
| Tr24×5 | 5 | 21.5 | 18.5 | 24.5 | 19 | External 7e / internal 7H (usual) |
| Tr26×5 | 5 | 23.5 | 20.5 | 26.5 | 21 | External 7e / internal 7H (usual) |
| Tr28×5 | 5 | 25.5 | 22.5 | 28.5 | 23 | External 7e / internal 7H (usual) |
| Tr30×6 | 6 | 27 | 23.5 | 30.5 | 24 | External 7e / internal 7H (usual) |
| Tr32×6 | 6 | 29 | 25.5 | 32.5 | 26 | External 7e / internal 7H (usual) |
| Tr36×6 | 6 | 33 | 29.5 | 36.5 | 30 | External 7e / internal 7H (usual) |
| Tr40×7 | 7 | 36.5 | 32.5 | 40.5 | 33 | External 7e / internal 7H (usual) |
| Tr44×7 | 7 | 40.5 | 36.5 | 44.5 | 37 | External 7e / internal 7H (usual) |
| Tr48×8 | 8 | 44 | 39.5 | 48.5 | 40 | External 7e / internal 7H (usual) |
| Tr52×8 | 8 | 48 | 43.5 | 52.5 | 44 | External 7e / internal 7H (usual) |
| Tr60×9 | 9 | 55.5 | 50.5 | 60.5 | 51 | External 7e / internal 7H (usual) |
| Tr70×10 | 10 | 65 | 59.5 | 70.5 | 60 | External 7e / internal 7H (usual) |
| Tr80×10 | 10 | 75 | 69.5 | 80.5 | 70 | External 7e / internal 7H (usual) |
Tr notes: ① Tr is the 30° metric trapezoidal power thread (GB/T 5796, matching ISO 2904) used for lead screws, jacks and valve stems; it carries load on the flanks and is not a fastening thread; ② basic dimensions (ac = 0.25): d₂ = d − 0.5P, external d₃ = d − P − 0.5 (thread height h₃ = 0.5P + ac), internal D₄ = d + 0.5 and D₁ = d − P; ③ tolerances per GB/T 5796.4 — internal 7H/8H/9H, external 7h/7e/8e/8c/9c, most often 7H/7e, written Tr40×7-7H (add LH for left-hand); ④ inspection: go/no-go gauges for batches; lead-screw pitch diameters by the three-wire method, best wire d₀ = 0.51764P for the 30° form; the 15° flank half-angle checked with a template or projector; ⑤ distinguish it from buttress thread B (33°: 3° on one flank, 30° on the other, one-way load) — check the symmetry first; ⑥ any size works in the calculator in section 2, e.g. Tr40×7, and sizes not listed above such as Tr26×5 or Tr34×6 behave the same way.
11. Round thread Rd (DIN 405-1, 30°)
| Size | TPI (threads per inch) | Pitch P (mm) | Pitch diameter d₂ (mm) | External minor diameter d₃ (mm) | Internal major diameter D₄ (mm) | Internal minor diameter D₁ (mm) | Usual tolerance class (external/internal) |
| Rd8×1/10″ | 10 | 2.54 | 6.73 | 5.46 | 8.25 | 5.71 | External 6h·7h / internal 7H·6H |
| Rd10×1/10″ | 10 | 2.54 | 8.73 | 7.46 | 10.25 | 7.71 | External 6h·7h / internal 7H·6H |
| Rd12×1/10″ | 10 | 2.54 | 10.73 | 9.46 | 12.25 | 9.71 | External 6h·7h / internal 7H·6H |
| Rd14×1/8″ | 8 | 3.17 | 12.41 | 10.82 | 14.32 | 11.14 | External 6h·7h / internal 7H·6H |
| Rd16×1/8″ | 8 | 3.17 | 14.41 | 12.82 | 16.32 | 13.14 | External 6h·7h / internal 7H·6H |
| Rd20×1/8″ | 8 | 3.17 | 18.41 | 16.82 | 20.32 | 17.14 | External 6h·7h / internal 7H·6H |
| Rd24×1/8″ | 8 | 3.17 | 22.41 | 20.82 | 24.32 | 21.14 | External 6h·7h / internal 7H·6H |
| Rd30×1/8″ | 8 | 3.17 | 28.41 | 26.82 | 30.32 | 27.14 | External 6h·7h / internal 7H·6H |
| Rd36×1/8″ | 8 | 3.17 | 34.41 | 32.83 | 36.32 | 33.14 | External 6h·7h / internal 7H·6H |
| Rd40×1/6″ | 6 | 4.23 | 37.88 | 35.77 | 40.42 | 36.19 | External 6h·7h / internal 7H·6H |
| Rd48×1/6″ | 6 | 4.23 | 45.88 | 43.77 | 48.42 | 44.19 | External 6h·7h / internal 7H·6H |
| Rd60×1/6″ | 6 | 4.23 | 57.88 | 55.77 | 60.42 | 56.19 | External 6h·7h / internal 7H·6H |
| Rd80×1/6″ | 6 | 4.23 | 77.88 | 75.77 | 80.42 | 76.19 | External 6h·7h / internal 7H·6H |
| Rd100×1/6″ | 6 | 4.23 | 97.88 | 95.77 | 100.42 | 96.19 | External 6h·7h / internal 7H·6H |
| Rd120×1/4″ | 4 | 6.35 | 116.83 | 113.65 | 120.64 | 114.28 | External 6h·7h / internal 7H·6H |
| Rd160×1/4″ | 4 | 6.35 | 156.82 | 153.65 | 160.63 | 154.28 | External 6h·7h / internal 7H·6H |
| Rd200×1/4″ | 4 | 6.35 | 196.82 | 193.65 | 200.63 | 194.28 | External 6h·7h / internal 7H·6H |
Rd notes: ① Rd is the DIN 405 knuckle thread: 30° straight flanks with large-radius crest and root (R₁ = 0.23851P). It resists dirt, impact and chip packing, and is used on fire hose couplings, trailer hitches (some European vehicles), respirator mask connectors, railway brake parts and oil line fittings; ② the diameter is metric but the pitch is imperial: designations look like Rd40×1/6″ (P = 4.233), with the common pitches 1/10″ = 2.54, 1/8″ = 3.175, 1/6″ = 4.233 and 1/4″ = 6.35. Distinguish it from DIN 20400 (all-metric pitches 3–16 mm, flat root with double radii) by how the pitch is written; ③ basic dimensions (ac = 0.05P): d₂ = d − 0.5P, d₃ = d − P, D₄ = d + 0.1P, D₁ = d − 0.9P. Bolt and nut radii differ (R₁ = 0.23851P / R₃ = 0.22105P), so profile templates are not interchangeable; ④ tolerances: external major 6h, pitch and minor 7h; internal pitch 7H, minor 6H (the table gives basic sizes — look up the limits in DIN 405-1); ⑤ the full round form must not be checked with 60° metric plug or ring gauges— use the dedicated round-thread gauges, or accept against basic dimensions with general measuring tools or vision systems; ⑥ DIN 405 also has series 2 sizes (avoid them in new designs); only series 1 is listed here. Any size can be entered in the calculator in section 2, e.g. Rd40×1/6.