Threading and thread measuring
Metric trapezoidal thread 3-wire measuring calculator
For 30° trapezoidal threads, best wire W = 0.51764 x P and M = d2 + 4.8637 x W - 1.8660 x P.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Best wire and measurement over wires
Measurement over wires at basic d2 (M)
mm
M = d2 + 4.8637 x W - 1.8660 x P = 18.000 + 4.8637 x 2.0706 - 1.8660 x 4 = 20.607 mm
0.8113 in. Best wire 2.071 mm (0.0815 in), used above. Basic d2 18.000 mm.
| Dimension | Formula | Metric (mm) | Inch (in) |
|---|---|---|---|
| Basic pitch diameter (d2 = D2) | d - 0.5 x P | 18.000 | 0.7087 |
| Best wire | 0.51764 x P | 2.071 | 0.0815 |
| Over wires at basic d2 (M) | d2 + 4.8637 x W - 1.8660 x P | 20.607 | 0.8113 |
| Basic flank height (H1) | 0.5 x P | 2.000 | 0.0787 |
| Crest clearance (ac) | ISO 2904, by pitch | 0.250 | 0.0098 |
| External thread depth (h3) | 0.5 x P + ac | 2.250 | 0.0886 |
| External minor diameter (d3) | d - 2 x h3 | 15.500 | 0.6102 |
| Internal minor diameter (D1) | d - P | 16.000 | 0.6299 |
| Internal major diameter (D4) | d + 2 x ac | 20.500 | 0.8071 |
Basic values, single start, lead angle ignored. M uses the wire in the calculator.
Pitch diameter from measurement over wires
Pitch diameter (d2)
mm
d2 = M - 4.8637 x W + 1.8660 x P = 32.910 - 4.8637 x 3.1058 + 1.8660 x 6 = 29.000 mm
1.1417 in. Basic d2 for Tr32 x 6 is 29.000 mm; this reading is 0.000 mm from basic.
Source: ISO 2904 (metric trapezoidal screw threads, basic profile); Machinery's Handbook (measuring threads over wires)
How it works
Three-wire formula for 30° trapezoidal threads
W = 0.51764 x P; M = d2 + 4.8637 x W - 1.8660 x P; d2 = M - 4.8637 x W + 1.8660 x P
| Symbol | Meaning | Unit |
|---|---|---|
| d | Nominal major diameter | mm |
| P | Pitch | mm |
| d2 | Pitch diameter | mm |
| W | Wire diameter; 0.51764 x P = P / (2 x cos 15°) touches the flanks at the pitch line | mm |
| M | Micrometer reading over three wires | mm |
| 4.8637 | 1 + 1 / sin 15° (half of the 30° thread angle) | |
| 1.8660 | (cot 15°) / 2 |
Basic profile, ISO 2904
d2 = D2 = d - 0.5 x P; H1 = 0.5 x P; h3 = 0.5 x P + ac; d3 = d - 2 x h3; D1 = d - P; D4 = d + 2 x ac
| Symbol | Meaning | Unit |
|---|---|---|
| H1 | Basic flank height (overlap) | mm |
| ac | Crest clearance: 0.15 mm (P 1.5), 0.25 mm (P 2 to 5), 0.5 mm (P 6 to 12), 1.0 mm (P 14 to 44) | mm |
| h3 | External thread depth | mm |
| d3 | External minor diameter | mm |
| D1 | Internal minor diameter | mm |
| D4 | Internal major diameter | mm |
Worked example: Tr20 x 4
Tr20 x 4 external thread, single start, best wires.
- Basic pitch diameter: d2 = 20 - 0.5 x 4 = 18.000 mm.
- Best wire: W = 0.51764 x 4 = 2.0706 mm, about 2.071 mm.
- Wire term: 4.8637 x 2.0706 = 10.071 mm.
- Pitch term: 1.8660 x 4 = 7.464 mm.
- M = 18.000 + 10.071 - 7.464 = 20.607 mm.
- Thread depth: h3 = 0.5 x 4 + 0.25 = 2.25 mm, so d3 = 20 - 2 x 2.25 = 15.50 mm.
Result: M = 20.607 mm (0.8113 in) over 2.071 mm wires at the basic pitch diameter of 18.000 mm.
Worked example: Tr32 x 6
Tr32 x 6 external thread, single start, best wires.
- Basic pitch diameter: d2 = 32 - 0.5 x 6 = 29.000 mm.
- Best wire: W = 0.51764 x 6 = 3.106 mm.
- M = 29.000 + 4.8637 x 3.1058 - 1.8660 x 6 = 29.000 + 15.106 - 11.196 = 32.910 mm.
- Thread depth: h3 = 0.5 x 6 + 0.5 = 3.50 mm, so d3 = 32 - 2 x 3.50 = 25.00 mm.
Result: M = 32.910 mm over 3.106 mm wires at the basic pitch diameter of 29.000 mm.
Shop notes
- The result is basic pitch diameter. Tolerance classes, for example 7e (external) and 7H (internal), come from ISO 2903.
- The formula ignores lead angle and assumes a single-start thread.
- Use the wire size you own. The formula works for any wire that touches the flanks; the best wire touches at the pitch line.
- A trapezoidal thread is 30° included. Acme wires and constants (29°) give the wrong answer here.
FAQ
What wire size do you use for Tr20 x 4?
Best wire 2.071 mm (0.51764 x 4). Any wire that touches the flanks works in the formula; enter the size you own.
What should Tr20 x 4 measure over wires?
20.607 mm at the basic pitch diameter of 18.000 mm, with 2.071 mm best wires.
Can you use Acme wire constants on a trapezoidal thread?
No. Acme is 29° (4.9939 and 1.9334); metric trapezoidal is 30° (4.8637 and 1.8660). Swapping them gives a wrong pitch diameter.
What do you compare the trapezoidal pitch diameter to?
The basic d2 is d - 0.5 x P: 18.000 mm for Tr20 x 4. Limits come from the tolerance class in ISO 2903, for example 7e for an external thread and 7H for an internal thread.
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