# Trapezoidal lead screw threads Tr10 to Tr40 (ISO 2904 / DIN 103): Tr10x2, Tr12x3, Tr16x4, Tr20x4, Tr24x5, Tr30x6, Tr40x7: pitch, d2, D4, d3, D1

> What are the pitch diameter, minor diameter and nut major diameter of a Tr10x2, Tr12x3, Tr16x4, Tr20x4, Tr24x5, Tr30x6 or Tr40x7 trapezoidal thread?

- Category: Hardware › Bearings, rails & motion
- Kind: Standard part
- Basis: ISO 2904:2020 sample table (iTeh) with formula checks on every row; fasten.it, Roymech and AmesWeb as comparison; numbers only
- Page: https://xemstudio.com/objects/trapezoidal-threads-tr10-tr40-iso-2904/ · JSON: https://xemstudio.com/api/geometry?object=trapezoidal-threads-tr10-tr40-iso-2904 · Plain text: https://xemstudio.com/objects/trapezoidal-threads-tr10-tr40-iso-2904/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); files CC BY 4.0 or their publisher's license
- Use in every chat: add https://xemstudio.com/mcp as a connector (https://xemstudio.com/use-with-ai/)

**Exact dimensions.** True size, with no tolerance added.

## Notes

- Tr is the metric trapezoidal (30 degree flank angle) lead-screw thread: Tr10x2 means 10 mm nominal diameter and 2 mm pitch. For a single-start screw the lead equals the pitch; a multi-start thread has lead = P x starts and is written Tr d x lead (P pitch). The standard's formulas: D1 = d - P, d2 = D2 = d - 0.5 P, D4 = d + 2 ac, d3 = d - P - 2 ac (ac is the crest clearance, which differs by pitch).
- Numbers: the ISO 2904:2020 sample (iTeh) table for Tr10 to Tr40 (44 d x P combinations); the generator re-checks D1 = d - P, d2 = d - 0.5 P and d3 = d - P - 2 ac on every row (ac = (D4 - d) / 2). AmesWeb's limits tables print the same screw minor and nut major values where compared (Tr10x1.5: d3 8.200, D4 10.300; Tr16x4: d3 11.500; Tr40x7: d3 32.000).
- Disagreements kept: fasten.it's copy of the table (a cancelled-DIN reproduction) prints Tr10x1.5 with D4 11, d3 8 and D1 7.5, Roymech with D4 11, d3 2.000 and D1 3.000; the ISO 2904 sample and AmesWeb both give D4 10.3, d3 8.2, D1 8.5, which the formulas confirm. fasten.it, Roymech and AmesWeb also list Tr16x3 (and Tr18x3, Tr20x3 on AmesWeb), which the ISO 2904 sample table does not; Tr16x4 is in the ISO sample (and AmesWeb) but fasten.it and Roymech print Tr16x3 in its place. Those rows are not used here.
- Numbers only, no files: a lead screw's length, ends and start count are chosen by the user, and the helical thread is not a published envelope. For modelled lead screws see the T8 lead screw and the Tr10x2 screw pages.
- Left out: the external / internal tolerance classes (7e, 7H and so on), the multi-start leads, Tr sizes above 40 mm, ac / H4 / h3 values per pitch (not in the sample).

## Sizes

| thread | nominal Ø d, mm | pitch P, mm | pitch Ø d2 = D2, mm | nut major Ø D4, mm | screw minor Ø d3, mm | nut minor Ø D1, mm |
|---|---|---|---|---|---|---|
| Tr10x1.5 | 10 | 1.5 | 9.250 | 10.300 | 8.200 | 8.500 |
| Tr10x2 | 10 | 2 | 9.000 | 10.500 | 7.500 | 8.000 |
| Tr11x2 | 11 | 2 | 10.000 | 11.500 | 8.500 | 9.000 |
| Tr11x3 | 11 | 3 | 9.500 | 11.500 | 7.500 | 8.000 |
| Tr12x2 | 12 | 2 | 11.000 | 12.500 | 9.500 | 10.000 |
| Tr12x3 | 12 | 3 | 10.500 | 12.500 | 8.500 | 9.000 |
| Tr14x2 | 14 | 2 | 13.000 | 14.500 | 11.500 | 12.000 |
| Tr14x3 | 14 | 3 | 12.500 | 14.500 | 10.500 | 11.000 |
| Tr16x2 | 16 | 2 | 15.000 | 16.500 | 13.500 | 14.000 |
| Tr16x4 | 16 | 4 | 14.000 | 16.500 | 11.500 | 12.000 |
| Tr18x2 | 18 | 2 | 17.000 | 18.500 | 15.500 | 16.000 |
| Tr18x4 | 18 | 4 | 16.000 | 18.500 | 13.500 | 14.000 |
| Tr20x2 | 20 | 2 | 19.000 | 20.500 | 17.500 | 18.000 |
| Tr20x4 | 20 | 4 | 18.000 | 20.500 | 15.500 | 16.000 |
| Tr22x3 | 22 | 3 | 20.500 | 22.500 | 18.500 | 19.000 |
| Tr22x5 | 22 | 5 | 19.500 | 22.500 | 16.500 | 17.000 |
| Tr22x8 | 22 | 8 | 18.000 | 23.000 | 13.000 | 14.000 |
| Tr24x3 | 24 | 3 | 22.500 | 24.500 | 20.500 | 21.000 |
| Tr24x5 | 24 | 5 | 21.500 | 24.500 | 18.500 | 19.000 |
| Tr24x8 | 24 | 8 | 20.000 | 25.000 | 15.000 | 16.000 |
| Tr26x3 | 26 | 3 | 24.500 | 26.500 | 22.500 | 23.000 |
| Tr26x5 | 26 | 5 | 23.500 | 26.500 | 20.500 | 21.000 |
| Tr26x8 | 26 | 8 | 22.000 | 27.000 | 17.000 | 18.000 |
| Tr28x3 | 28 | 3 | 26.500 | 28.500 | 24.500 | 25.000 |
| Tr28x5 | 28 | 5 | 25.500 | 28.500 | 22.500 | 23.000 |
| Tr28x8 | 28 | 8 | 24.000 | 29.000 | 19.000 | 20.000 |
| Tr30x3 | 30 | 3 | 28.500 | 30.500 | 26.500 | 27.000 |
| Tr30x6 | 30 | 6 | 27.000 | 31.000 | 23.000 | 24.000 |
| Tr30x10 | 30 | 10 | 25.000 | 31.000 | 19.000 | 20.000 |
| Tr32x3 | 32 | 3 | 30.500 | 32.500 | 28.500 | 29.000 |
| Tr32x6 | 32 | 6 | 29.000 | 33.000 | 25.000 | 26.000 |
| Tr32x10 | 32 | 10 | 27.000 | 33.000 | 21.000 | 22.000 |
| Tr34x3 | 34 | 3 | 32.500 | 34.500 | 30.500 | 31.000 |
| Tr34x6 | 34 | 6 | 31.000 | 35.000 | 27.000 | 28.000 |
| Tr34x10 | 34 | 10 | 29.000 | 35.000 | 23.000 | 24.000 |
| Tr36x3 | 36 | 3 | 34.500 | 36.500 | 32.500 | 33.000 |
| Tr36x6 | 36 | 6 | 33.000 | 37.000 | 29.000 | 30.000 |
| Tr36x10 | 36 | 10 | 31.000 | 37.000 | 25.000 | 26.000 |
| Tr38x3 | 38 | 3 | 36.500 | 38.500 | 34.500 | 35.000 |
| Tr38x7 | 38 | 7 | 34.500 | 39.000 | 30.000 | 31.000 |
| Tr38x10 | 38 | 10 | 33.000 | 39.000 | 27.000 | 28.000 |
| Tr40x3 | 40 | 3 | 38.500 | 40.500 | 36.500 | 37.000 |
| Tr40x7 | 40 | 7 | 36.500 | 41.000 | 32.000 | 33.000 |
| Tr40x10 | 40 | 10 | 35.000 | 41.000 | 29.000 | 30.000 |

## Where the files are

- iTeh Standards: [ISO 2904:2020 sample: ISO metric trapezoidal screw threads, basic dimensions, formulas and the d, P, d2, D4, d3, D1 table (Tr10 to Tr40)](https://cdn.standards.iteh.ai/samples/78729/7d158726108b478c889fa887d460ba78/ISO-2904-2020.pdf) — web — Publisher's page; dimensions are facts
- fasten.it: [ISO 2904 (cancelled DIN 103 successor) trapezoidal thread table, reproduced by permission of DIN](https://fasten.it/en/Norms/Norm/ISO%202904) — web — Publisher's page; dimensions are facts
- Roymech: [Trapezoidal threads: metric table d, P, d2, D4, d3, D1](https://roymech.org/Useful_Tables/Screws/Trapezoidal.html) — web — Publisher's page; dimensions are facts
- AmesWeb: [Trapezoidal thread chart: external / internal major, pitch, minor diameter limits](https://amesweb.info/Screws/trapezoidal-thread-chart.aspx) — web — Publisher's page; dimensions are facts

## Questions

**What are the dimensions of a Tr10x2 thread?**

Nominal diameter 10, pitch 2: pitch diameter d2 = 9.000, nut minor D1 = 8.000, screw minor d3 = 7.500, nut major D4 = 10.500 mm (ISO 2904).

**What are the dimensions of a Tr12x3 thread?**

d2 = 10.500, D1 = 9.000, d3 = 8.500, D4 = 12.500 mm.

**What are the dimensions of a Tr16x4 thread?**

d2 = 14.000, D1 = 12.000, d3 = 11.500, D4 = 16.500 mm.

**What are the dimensions of a Tr20x4 thread?**

d2 = 18.000, D1 = 16.000, d3 = 15.500, D4 = 20.500 mm.

**What is the formula for the pitch diameter of a Tr thread?**

d2 = d - 0.5 P; the nut minor diameter is D1 = d - P (ISO 2904).

## Fits with

- [T8 lead screw Tr8×8 envelope, 100 to 400 mm](https://xemstudio.com/objects/t8-lead-screw/)
- [Lead screw Tr10×2, 80 mm thread, Ø6 journals, Ø20 head with Ø6 cross hole](https://xemstudio.com/objects/lead-screw-tr10x2-l80-journals-6/)
- [Lead screw and nut-slide (rotation to straight travel), Tr10×2](https://xemstudio.com/objects/lead-screw-and-slide-mechanism/)
- [Acme threads 1/4-16 to 2-4 (ASME B1.5): 1/2-10, 5/8-8, 3/4-6, 1-5, 1-1/2-4, 2-4: major, pitch and minor diameter, pitch](https://xemstudio.com/objects/acme-threads-asme-b1-5-1-4-to-2-in/)
- [Thrust ball bearings 51100 series (51100 to 51130): bore, outside diameter, height, housing washer bore + STEP/STL envelopes](https://xemstudio.com/objects/thrust-ball-bearings-51100-series/)
- [Thrust ball bearings 51200 and 51300 series (51204, 51205, 51206, 51305, 51306 and more): bore, OD, height, r, housing washer bore + 11 ring-envelope STEP/STL files](https://xemstudio.com/objects/thrust-ball-bearings-51200-51300-series/)
- [Ball screw end supports BK10, BK12, BK15, BF10, BF12, BF15, FK, FF: bore, bearing, base hole spacing, height (HIWIN tables)](https://xemstudio.com/objects/ball-screw-end-supports-bk-bf-fk-ff/)