Threading and thread measuring
Metric trapezoidal thread calculator
A Tr 20 x 4 cuts 2.250 mm deep: h3 = 0.5 x P + ac = 2.000 + 0.250, for a 15.500 mm external minor diameter and an 18.000 mm pitch diameter.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Trapezoidal thread dimensions
External thread depth (h3)
mm
h3 = 0.5 x P + ac = 0.5 x 4 + 0.25 = 2.250 mm
0.0886 in. Minor diameter d3 15.500 mm; pitch diameter d2 18.000 mm. Basic sizes; limits come from ISO 2903.
Helix angle at the pitch diameter
°
lambda = atan(Ph / (pi x d2)) = atan(4 / (3.1416 x 18.000)) = 4.0461°
4° 2' 46". Lead Ph = 1 x 4 = 4.000 mm (0.1575 in). Designation Tr 20 x 4.
| Dimension | Formula | Metric (mm) | Inch (in) |
|---|---|---|---|
| Pitch (P) | P | 4.000 | 0.1575 |
| Lead (Ph) | Ph = n x P | 4.000 | 0.1575 |
| Basic thread height (H1) | H1 = 0.5 x P | 2.000 | 0.0787 |
| Crest clearance (ac) | by pitch, ISO 2901 | 0.250 | 0.0098 |
| External thread depth (h3) | h3 = 0.5 x P + ac | 2.250 | 0.0886 |
| External major diameter (d) | d, nominal | 20.000 | 0.7874 |
| External minor diameter (d3) | d3 = d - P - 2 x ac | 15.500 | 0.6102 |
| Pitch diameter (d2 = D2) | d2 = d - 0.5 x P | 18.000 | 0.7087 |
| Internal thread depth (H4) | H4 = 0.5 x P + ac | 2.250 | 0.0886 |
| Internal major diameter (D4) | D4 = d + 2 x ac | 20.500 | 0.8071 |
| Internal minor diameter (D1) | D1 = d - P | 16.000 | 0.6299 |
| Basic crest and root flat (w) | w = 0.366 x P | 1.464 | 0.0576 |
| Tool tip flat, max (F) | F = 0.366 x P - 0.536 x ac | 1.330 | 0.0524 |
| Crest corner radius, max (R1) | R1 = 0.5 x ac | 0.125 | 0.0049 |
| Root radius, max (R2) | R2 = ac | 0.250 | 0.0098 |
| Compound travel at 15° | h3 / cos(15°) | 2.329 | 0.0917 |
Basic dimensions. Tolerance limits for d, d2, d3, D1 and D2 come from ISO 2903; the drawing governs.
Source: ISO 2901 (ISO metric trapezoidal screw threads, basic and design profiles); ISO 2904 (basic dimensions); DIN 103 (metric trapezoidal threads) size series; helix angle and tool flat derived by trigonometry as shown.
Basic dimensions from ISO 2901 and ISO 2904; tolerance limits come from ISO 2903 and the drawing governs.
How it works
Basic profile, ISO 2901
H1 = 0.5 x P; h3 = H4 = 0.5 x P + ac; d2 = D2 = d - 0.5 x P; d3 = d - P - 2 x ac; D1 = d - P; D4 = d + 2 x ac
| Symbol | Meaning | Unit |
|---|---|---|
| d | Nominal (external major) diameter | mm |
| P | Pitch | mm |
| H1 | Basic thread height (flank overlap) | mm |
| ac | Crest clearance, by pitch (table below) | mm |
| h3 | External thread depth | mm |
| H4 | Internal thread depth | mm |
| d2, D2 | Pitch diameter | mm |
| d3 | External minor diameter | mm |
| D1 | Internal minor diameter | mm |
| D4 | Internal major diameter | mm |
| Pitch P (mm) | Crest clearance ac (mm) |
|---|---|
| 1.5 | 0.15 |
| 2 to 5 | 0.25 |
| 6 to 12 | 0.50 |
| 14 to 44 | 1.00 |
Source: ISO 2901 (basic and design profiles)
Lead, helix angle and tool
Ph = n x P; lambda = atan(Ph / (pi x d2)); w = 0.366 x P; F = 0.366 x P - 0.536 x ac; R1 = 0.5 x ac; R2 = ac; compound travel = h3 / cos(15°)
| Symbol | Meaning | Unit |
|---|---|---|
| n | Number of starts | starts |
| Ph | Lead: axial travel per revolution | mm |
| lambda | Helix angle at the pitch diameter | ° |
| w | Basic flat at crest and root | mm |
| F | Largest tool tip flat for a sharp-cornered tool cut to d3 | mm |
| R1, R2 | Crest corner radius and root radius limits, maximum | mm |
| 15° | Half of the 30° included angle (flank angle) | ° |
The tool flat comes from the basic flat w and the 15° flank: every millimeter of extra depth narrows the groove by 2 x tan(15°) = 0.5359 mm, so cutting ac deeper than the basic profile takes 0.536 x ac off the tip. Wire size and the reading over wires for a finished Tr thread come from the trapezoidal 3-wire measuring calculator.
Worked example: Tr 20 x 4, single start
Tr 20 x 4 external, 1 start.
- Crest clearance: P 4 mm is in the 2 to 5 mm range, so ac = 0.25 mm.
- Height and depth: H1 = 0.5 x 4 = 2.000 mm; h3 = 2.000 + 0.250 = 2.250 mm (0.0886 in).
- Pitch diameter: d2 = 20 - 0.5 x 4 = 18.000 mm (0.7087 in). Minor diameter: d3 = 20 - 2 x 2.250 = 15.500 mm (0.6102 in).
- Nut: D4 = 20 + 2 x 0.25 = 20.500 mm; D1 = 20 - 4 = 16.000 mm.
- Tool: w = 0.366025 x 4 = 1.464 mm; F = 1.464 - 0.5359 x 0.25 = 1.464 - 0.134 = 1.330 mm (0.0524 in).
- Helix angle: 4 / (3.1416 x 18.000) = 4 / 56.549 = 0.070736; atan = 4.0461° (4° 2' 46").
- Compound travel at 15°: 2.250 / 0.96593 = 2.329 mm.
Result: h3 2.250 mm, d2 18.000 mm, d3 15.500 mm, D1 16.000 mm, D4 20.500 mm; tool flat no wider than 1.330 mm. These match the Tr 20 x 4 row in the ISO 2904:2020 table.
Worked example: Tr 40 x 14 (P7), two starts
Tr 40 x 14 (P7) external, 2 starts.
- Lead: Ph = 2 x 7 = 14.000 mm (0.5512 in).
- Crest clearance: P 7 mm is in the 6 to 12 mm range, so ac = 0.5 mm. H1 = 3.500 mm; h3 = 3.500 + 0.500 = 4.000 mm (0.1575 in).
- Diameters: d2 = 40 - 3.5 = 36.500 mm; d3 = 40 - 2 x 4.000 = 32.000 mm; D4 = 41.000 mm; D1 = 33.000 mm.
- Tool: w = 0.366025 x 7 = 2.562 mm; F = 2.562 - 0.5359 x 0.5 = 2.562 - 0.268 = 2.294 mm (0.0903 in).
- Helix angle: 14 / (3.1416 x 36.500) = 14 / 114.668 = 0.122091; atan = 6.9609° (6° 57' 39").
- Compound travel at 15°: 4.000 / 0.96593 = 4.141 mm. Index the second start by one pitch, 7 mm, along Z.
Result: lead 14.000 mm, h3 4.000 mm, d3 32.000 mm, helix angle 6.9609°.
Shop notes
- Basic sizes are not limits. External threads are cut under basic per the ISO 2903 tolerance class; check d2 over wires on the trapezoidal measuring page.
- The 30° flank is not the 29° flank of the Acme thread; Acme tools and gauges do not fit a Tr thread.
- Multi-start: the lathe feeds the lead (n x P) per revolution; index each start one pitch along Z. Grind the leading side clearance larger than the helix angle.
- Grind the tool tip no wider than F, or it cuts the flanks oversize before reaching full depth.
| Size | d (mm) | P (mm) | d2 = D2 (mm) | d3 (mm) | D1 (mm) | D4 (mm) | h3 = H4 (mm) | ac (mm) |
|---|---|---|---|---|---|---|---|---|
| Tr 8 x 1.5 | 8 | 1.5 | 7.250 | 6.200 | 6.500 | 8.300 | 0.900 | 0.15 |
| Tr 9 x 2 | 9 | 2 | 8.000 | 6.500 | 7.000 | 9.500 | 1.250 | 0.25 |
| Tr 10 x 2 | 10 | 2 | 9.000 | 7.500 | 8.000 | 10.500 | 1.250 | 0.25 |
| Tr 11 x 3 | 11 | 3 | 9.500 | 7.500 | 8.000 | 11.500 | 1.750 | 0.25 |
| Tr 12 x 3 | 12 | 3 | 10.500 | 8.500 | 9.000 | 12.500 | 1.750 | 0.25 |
| Tr 14 x 3 | 14 | 3 | 12.500 | 10.500 | 11.000 | 14.500 | 1.750 | 0.25 |
| Tr 16 x 4 | 16 | 4 | 14.000 | 11.500 | 12.000 | 16.500 | 2.250 | 0.25 |
| Tr 18 x 4 | 18 | 4 | 16.000 | 13.500 | 14.000 | 18.500 | 2.250 | 0.25 |
| Tr 20 x 4 | 20 | 4 | 18.000 | 15.500 | 16.000 | 20.500 | 2.250 | 0.25 |
| Tr 22 x 5 | 22 | 5 | 19.500 | 16.500 | 17.000 | 22.500 | 2.750 | 0.25 |
| Tr 24 x 5 | 24 | 5 | 21.500 | 18.500 | 19.000 | 24.500 | 2.750 | 0.25 |
| Tr 26 x 5 | 26 | 5 | 23.500 | 20.500 | 21.000 | 26.500 | 2.750 | 0.25 |
| Tr 28 x 5 | 28 | 5 | 25.500 | 22.500 | 23.000 | 28.500 | 2.750 | 0.25 |
| Tr 30 x 6 | 30 | 6 | 27.000 | 23.000 | 24.000 | 31.000 | 3.500 | 0.50 |
| Tr 32 x 6 | 32 | 6 | 29.000 | 25.000 | 26.000 | 33.000 | 3.500 | 0.50 |
| Tr 34 x 6 | 34 | 6 | 31.000 | 27.000 | 28.000 | 35.000 | 3.500 | 0.50 |
| Tr 36 x 6 | 36 | 6 | 33.000 | 29.000 | 30.000 | 37.000 | 3.500 | 0.50 |
| Tr 38 x 7 | 38 | 7 | 34.500 | 30.000 | 31.000 | 39.000 | 4.000 | 0.50 |
| Tr 40 x 7 | 40 | 7 | 36.500 | 32.000 | 33.000 | 41.000 | 4.000 | 0.50 |
| Tr 42 x 7 | 42 | 7 | 38.500 | 34.000 | 35.000 | 43.000 | 4.000 | 0.50 |
| Tr 44 x 7 | 44 | 7 | 40.500 | 36.000 | 37.000 | 45.000 | 4.000 | 0.50 |
| Tr 46 x 8 | 46 | 8 | 42.000 | 37.000 | 38.000 | 47.000 | 4.500 | 0.50 |
| Tr 48 x 8 | 48 | 8 | 44.000 | 39.000 | 40.000 | 49.000 | 4.500 | 0.50 |
| Tr 50 x 8 | 50 | 8 | 46.000 | 41.000 | 42.000 | 51.000 | 4.500 | 0.50 |
| Tr 52 x 8 | 52 | 8 | 48.000 | 43.000 | 44.000 | 53.000 | 4.500 | 0.50 |
| Tr 55 x 9 | 55 | 9 | 50.500 | 45.000 | 46.000 | 56.000 | 5.000 | 0.50 |
| Tr 60 x 9 | 60 | 9 | 55.500 | 50.000 | 51.000 | 61.000 | 5.000 | 0.50 |
| Tr 65 x 10 | 65 | 10 | 60.000 | 54.000 | 55.000 | 66.000 | 5.500 | 0.50 |
| Tr 70 x 10 | 70 | 10 | 65.000 | 59.000 | 60.000 | 71.000 | 5.500 | 0.50 |
| Tr 75 x 10 | 75 | 10 | 70.000 | 64.000 | 65.000 | 76.000 | 5.500 | 0.50 |
| Tr 80 x 10 | 80 | 10 | 75.000 | 69.000 | 70.000 | 81.000 | 5.500 | 0.50 |
| Tr 85 x 12 | 85 | 12 | 79.000 | 72.000 | 73.000 | 86.000 | 6.500 | 0.50 |
| Tr 90 x 12 | 90 | 12 | 84.000 | 77.000 | 78.000 | 91.000 | 6.500 | 0.50 |
| Tr 95 x 12 | 95 | 12 | 89.000 | 82.000 | 83.000 | 96.000 | 6.500 | 0.50 |
| Tr 100 x 12 | 100 | 12 | 94.000 | 87.000 | 88.000 | 101.000 | 6.500 | 0.50 |
One common pitch per diameter from the DIN 103 standard series; ISO 2904 lists other pitches for most diameters. Use Other for any d and P. Values computed from the ISO 2901 formulas above.
Source: ISO 2904 (basic dimensions); DIN 103 size series
FAQ
How deep is a Tr 20 x 4 thread?
2.250 mm on the external thread (0.5 x 4 + 0.25 mm clearance), leaving a 15.500 mm minor diameter.
What is the pitch diameter of Tr 20 x 4?
18.000 mm basic: d - 0.5 x P = 20 - 2. Check it over wires on the trapezoidal 3-wire page.
What does Tr 40 x 14 (P7) mean?
A 40 mm two-start trapezoidal thread: 7 mm pitch, 14 mm lead. It cuts 4.000 mm deep with a 6.9609° helix angle at the pitch diameter.
What drill or bore size for a Tr 20 x 4 nut?
The internal minor diameter D1 is 16.000 mm (d - P); bore to the D1 limit of the class from ISO 2903.
How wide is the tool tip for Tr 20 x 4?
No wider than 1.330 mm at the tip for a sharp-cornered tool cut to 2.250 mm depth.
Is a metric trapezoidal thread the same as Acme?
No. Tr is 30° and sized in mm (ISO 2904); Acme is 29° and sized in inches (ASME B1.5).
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