Threading and thread measuring
3-wire thread measuring for 60 degree threads
Enter pitch, wire size and the micrometer reading over the wires to get pitch diameter for Unified inch and ISO metric external threads.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Pitch diameter from measurement over wires
Pitch diameter (E)
in
E = M - 3 x W + 0.86603 x P = 0.5145 - 3 x 0.0444 + 0.86603 x 0.076923 = 0.4479 in
11.377 mm. Best wire for 13 TPI: 0.04441 in (1.128 mm). Compare E to the class 2A limits in ASME B1.1 (external).
Best wire and target measurement over wires
Measurement over wires (M)
in
M = E + 3 x W - 0.86603 x P = 0.45 + 3 x 0.0444 - 0.86603 x 0.076923 = 0.5166 in
13.121 mm. Best wire: W = 0.57735 x P = 0.57735 x 0.076923 = 0.04441 in.
Source: Machinery's Handbook (measuring screw threads by the three-wire method); ASME B1.1 (Unified inch screw threads); ISO 965 (ISO general purpose metric screw threads, tolerances)
The result is pitch diameter, not major diameter. Compare it to the class 2A limits in ASME B1.1 (external inch threads) or the 6g limits in ISO 965 (external metric threads). Internal threads are not measured with wires; use a plug gauge.
How it works
Pitch diameter from measurement over wires
E = M - 3 x W + 0.86603 x P
| Symbol | Meaning | Unit |
|---|---|---|
| E | Pitch diameter | in or mm |
| M | Micrometer reading over the three wires | in or mm |
| W | Wire diameter (the size you use, not the nominal best size) | in or mm |
| P | Pitch: 1 / TPI for inch threads, or the metric pitch | in or mm |
Best wire size and target reading
W = 0.57735 x P; M = E + 3 x W - 0.86603 x P
| Symbol | Meaning |
|---|---|
| 0.57735 | 1 / (2 x cos 30 degrees): the wire that touches the flanks at the pitch line |
| 0.86603 | (cot 30 degrees) / 2, from the 60 degree thread angle |
| 3 | 1 + 1 / sin 30 degrees, from the 60 degree thread angle |
These are the three-wire formulas from Machinery's Handbook with the lead angle ignored. The best wire touches the flanks at the pitch diameter, so small errors in thread angle have the least effect on the reading. At the best wire, M = E + 0.86603 x P.
Any wire from about 0.5052 x P to 1.0104 x P works in the formula. Below that range the wires sit under the major diameter and the micrometer lands on the thread crests. Above it the wires ride on the crest corners instead of the flanks. Both limits come from the basic 60 degree profile in ASME B1.1; the calculator flags a wire outside them.
Worked example: 1/2-13 UNC-2A (external)
1/2-13 UNC-2A external thread, measured over 0.0444 in wires. Micrometer reading M = 0.5145 in.
- Pitch: P = 1 / 13 = 0.076923 in.
- Best wire: W = 0.57735 x 0.076923 = 0.04441 in. The 0.0444 in wire is within 0.00002 in of it.
- Three wires: 3 x 0.0444 = 0.1332 in.
- Thread angle term: 0.86603 x 0.076923 = 0.06662 in.
- E = 0.5145 - 0.1332 + 0.06662 = 0.4479 in (11.377 mm).
Result: pitch diameter 0.4479 in. Check it against the 1/2-13 UNC class 2A pitch diameter limits in ASME B1.1.
Worked example: M10 x 1.5-6g (external)
M10 x 1.5-6g external thread, measured over 0.866 mm wires. Micrometer reading M = 10.280 mm.
- Best wire: W = 0.57735 x 1.5 = 0.8660 mm, so 0.866 mm wires are the best size.
- Three wires: 3 x 0.866 = 2.598 mm.
- Thread angle term: 0.86603 x 1.5 = 1.2990 mm.
- E = 10.280 - 2.598 + 1.2990 = 8.981 mm (0.3536 in).
Result: pitch diameter 8.981 mm. Check it against the M10 x 1.5 class 6g pitch diameter limits in ISO 965.
Best wire sizes for 60 degree threads
| TPI | Pitch (in) | Best wire (in) | Best wire (mm) | Constant 3W - 0.86603P (in) |
|---|---|---|---|---|
| 4 | 0.25000 | 0.14434 | 3.6662 | 0.21651 |
| 4.5 | 0.22222 | 0.12830 | 3.2588 | 0.19245 |
| 5 | 0.20000 | 0.11547 | 2.9329 | 0.17321 |
| 6 | 0.16667 | 0.09623 | 2.4441 | 0.14434 |
| 7 | 0.14286 | 0.08248 | 2.0950 | 0.12372 |
| 8 | 0.12500 | 0.07217 | 1.8331 | 0.10825 |
| 9 | 0.11111 | 0.06415 | 1.6294 | 0.09623 |
| 10 | 0.10000 | 0.05774 | 1.4665 | 0.08660 |
| 11 | 0.09091 | 0.05249 | 1.3332 | 0.07873 |
| 12 | 0.08333 | 0.04811 | 1.2221 | 0.07217 |
| 13 | 0.07692 | 0.04441 | 1.1281 | 0.06662 |
| 14 | 0.07143 | 0.04124 | 1.0475 | 0.06186 |
| 16 | 0.06250 | 0.03608 | 0.9165 | 0.05413 |
| 18 | 0.05556 | 0.03208 | 0.8147 | 0.04811 |
| 20 | 0.05000 | 0.02887 | 0.7332 | 0.04330 |
| 24 | 0.04167 | 0.02406 | 0.6110 | 0.03608 |
| 28 | 0.03571 | 0.02062 | 0.5237 | 0.03093 |
| 32 | 0.03125 | 0.01804 | 0.4583 | 0.02706 |
| 36 | 0.02778 | 0.01604 | 0.4074 | 0.02406 |
| 40 | 0.02500 | 0.01443 | 0.3666 | 0.02165 |
| 44 | 0.02273 | 0.01312 | 0.3333 | 0.01968 |
| 48 | 0.02083 | 0.01203 | 0.3055 | 0.01804 |
| 56 | 0.01786 | 0.01031 | 0.2619 | 0.01546 |
| 64 | 0.01563 | 0.00902 | 0.2291 | 0.01353 |
| 72 | 0.01389 | 0.00802 | 0.2037 | 0.01203 |
| 80 | 0.01250 | 0.00722 | 0.1833 | 0.01083 |
Computed from W = P / (2 x cos 30 degrees) with unrounded values, then rounded once. The constant is M - E at the best wire: add it to the target pitch diameter to get the reading over wires. Inch values to 5 decimal places, metric to 4.
Source: Machinery's Handbook (three-wire method); pitches from ASME B1.1 UNC and UNF series
| Pitch (mm) | Best wire (mm) | Best wire (in) | Constant 3W - 0.86603P (mm) |
|---|---|---|---|
| 0.5 | 0.2887 | 0.01137 | 0.4330 |
| 0.6 | 0.3464 | 0.01364 | 0.5196 |
| 0.7 | 0.4041 | 0.01591 | 0.6062 |
| 0.75 | 0.4330 | 0.01705 | 0.6495 |
| 0.8 | 0.4619 | 0.01818 | 0.6928 |
| 1 | 0.5774 | 0.02273 | 0.8660 |
| 1.25 | 0.7217 | 0.02841 | 1.0825 |
| 1.5 | 0.8660 | 0.03410 | 1.2990 |
| 1.75 | 1.0104 | 0.03978 | 1.5155 |
| 2 | 1.1547 | 0.04546 | 1.7321 |
| 2.5 | 1.4434 | 0.05683 | 2.1651 |
| 3 | 1.7321 | 0.06819 | 2.5981 |
| 3.5 | 2.0207 | 0.07956 | 3.0311 |
| 4 | 2.3094 | 0.09092 | 3.4641 |
| 4.5 | 2.5981 | 0.10229 | 3.8971 |
| 5 | 2.8868 | 0.11365 | 4.3301 |
| 5.5 | 3.1754 | 0.12502 | 4.7631 |
| 6 | 3.4641 | 0.13638 | 5.1962 |
Computed from W = P / (2 x cos 30 degrees) with unrounded values, then rounded once. The constant is M - E at the best wire.
Source: Machinery's Handbook (three-wire method); pitches from ISO 261 coarse and fine series
How to read the table
Find the pitch, then read the best wire size. If your wire set has a size close to it, use that size in the calculator; the formula takes the wire in your hand. With the best wire, the reading over wires is the target pitch diameter plus the constant in the last column.
Shop notes
- Clean the wires, the thread and the micrometer faces. A chip under one wire reads as oversize pitch diameter.
- Two wires go in adjacent grooves on one side, one wire opposite, between them.
- Use light, consistent micrometer pressure. Heavy pressure presses the wires into the flanks and reads small.
- Take readings at two or three places along the thread and around it to catch taper and out-of-round.
- Class 2A has an allowance, so its maximum pitch diameter sits below basic. Do not size a 2A thread to the basic pitch diameter.
FAQ
What wire size do you use to measure a 1/2-13 thread?
The best wire is 0.57735 x P. For 13 TPI, P = 1/13 = 0.076923 in, so the best wire is 0.04441 in (1.128 mm). A 0.0444 in wire is close enough; enter the size you use.
Which limits do you compare the pitch diameter to?
For an external inch thread, the class 2A pitch diameter limits in ASME B1.1. For an external metric thread, the 6g limits in ISO 965. Internal thread limits (2B, 6H) give the wrong numbers for a male thread, and internal threads are checked with a plug gauge, not wires.
Can you measure a thread with two wires instead of three?
Three wires is the standard method, and the formula on this page assumes three: two in adjacent grooves on one side, one on the other. With one wire per side the micrometer faces can tilt with the helix.
How fine a micrometer do you need for 3-wire measuring?
A micrometer that reads 0.0001 in, or 0.001 mm on a metric micrometer, is the practical minimum. The reading goes straight into the pitch diameter, and every 0.0001 in of micrometer error is 0.0001 in of pitch diameter error.
Does the 3-wire formula account for lead angle?
No. M = E + 3 x W - 0.86603 x P ignores the helix angle. For standard single-start 60 degree threads the effect is small; Machinery's Handbook gives a lead angle correction for fine work and multi-start threads.
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