Threading and thread measuring
Acme thread measurement over wires (3-wire method)
Pitch diameter from the micrometer reading over three wires for 29 degree Acme threads (ASME B1.5), single start.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Acme pitch diameter from measurement over wires
Pitch diameter (E)
in
E = M - 4.9939 x W + 1.9334 x P = 1.0072 - 4.9939 x 0.1033 + 1.9334 x 0.2 = 0.8780 in
22.301 mm. Best wire for 5 TPI: 0.10329 in. Lead angle about 4.15 degrees (single start). Compare E to your class limits for the external thread in ASME B1.5.
Best wire and target measurement over wires
Measurement over wires (M)
in
M = E + 4.9939 x W - 1.9334 x P = 0.88 + 4.9939 x 0.1033 - 1.9334 x 0.2 = 1.0092 in
25.633 mm. Best wire: W = 0.51645 x P = 0.51645 x 0.2 = 0.10329 in.
Source: Machinery's Handbook (three-wire measurement of Acme threads); ASME B1.5 (Acme screw threads)
This is the simplified formula for single-start Acme threads with a small lead angle. The calculator shows the lead angle so you can judge it. For multi-start threads or close tolerances, apply the lead angle correction in Machinery's Handbook or ASME B1.5.
How it works
Acme pitch diameter from measurement over wires
E = M - 4.9939 x W + 1.9334 x P
| Symbol | Meaning | Unit |
|---|---|---|
| E | Pitch diameter | in |
| M | Micrometer reading over the three wires | in |
| W | Wire diameter you use | in |
| P | Pitch, 1 / TPI | in |
| 4.9939 | 1 + 1 / sin 14.5 degrees (half of the 29 degree thread angle) | |
| 1.9334 | (cot 14.5 degrees) / 2 |
Best wire size and lead angle
W = 0.51645 x P; lead angle = atan(L / (pi x E))
| Symbol | Meaning | Unit |
|---|---|---|
| 0.51645 | 1 / (2 x cos 14.5 degrees): the wire that touches the flanks at the pitch line | |
| L | Lead: equal to P on a single-start thread | in |
| lead angle | Helix angle at the pitch diameter | deg |
The constants follow from the 29 degree thread angle in the general three-wire formula. At the best wire, M = E + 0.6457 x P. Any wire from about 0.4873 x P to 0.6500 x P touches the flanks and stands above the major diameter; both limits come from the basic Acme profile in ASME B1.5, and the calculator flags a wire outside them.
Worked example: 1-5 ACME-2G (external)
1-5 ACME-2G external thread, single start, measured over 0.1033 in wires. Micrometer reading M = 1.0072 in.
- Pitch: P = 1 / 5 = 0.2000 in.
- Best wire: W = 0.51645 x 0.2000 = 0.10329 in. The 0.1033 in wire matches it.
- Wire term: 4.9939 x 0.1033 = 0.51587 in.
- Pitch term: 1.9334 x 0.2000 = 0.38668 in.
- E = 1.0072 - 0.51587 + 0.38668 = 0.8780 in (22.301 mm).
- Lead angle: atan(0.2000 / (3.1416 x 0.8780)) = 4.15 degrees.
- Basic pitch diameter: 1.0000 - 0.5 x 0.2000 = 0.9000 in.
- Class 2G allowance: 0.020 x sqrt(1.0000) = 0.0200 in, so the 2G external maximum is 0.9000 - 0.0200 = 0.8800 in.
Result: pitch diameter 0.8780 in, 0.0020 in under the 2G maximum. Check it against the class 2G external minimum in the ASME B1.5 table.
Worked example: 1/2-10 ACME-2G (external)
1/2-10 ACME-2G external thread, single start, measured over 0.0516 in wires. Micrometer reading M = 0.4983 in.
- Pitch: P = 1 / 10 = 0.1000 in.
- Best wire: W = 0.51645 x 0.1000 = 0.05165 in. The 0.0516 in wire is within 0.00005 in of it.
- Wire term: 4.9939 x 0.0516 = 0.25769 in.
- Pitch term: 1.9334 x 0.1000 = 0.19334 in.
- E = 0.4983 - 0.25769 + 0.19334 = 0.4340 in (11.022 mm).
- Lead angle: atan(0.1000 / (3.1416 x 0.4340)) = 4.20 degrees.
- Basic pitch diameter: 0.5000 - 0.5 x 0.1000 = 0.4500 in.
- Class 2G allowance: 0.020 x sqrt(0.5000) = 0.0141 in, so the 2G external maximum is 0.4500 - 0.0141 = 0.4359 in.
Result: pitch diameter 0.4340 in, 0.0019 in under the 2G maximum. Check it against the class 2G external minimum in the ASME B1.5 table.
Best wire sizes for Acme threads
| TPI | Pitch (in) | Best wire (in) | Best wire (mm) | Constant 4.9939W - 1.9334P (in) |
|---|---|---|---|---|
| 16 | 0.06250 | 0.03228 | 0.8199 | 0.04036 |
| 14 | 0.07143 | 0.03689 | 0.9370 | 0.04613 |
| 12 | 0.08333 | 0.04304 | 1.0932 | 0.05381 |
| 10 | 0.10000 | 0.05165 | 1.3118 | 0.06458 |
| 8 | 0.12500 | 0.06456 | 1.6397 | 0.08072 |
| 6 | 0.16667 | 0.08608 | 2.1863 | 0.10763 |
| 5 | 0.20000 | 0.10329 | 2.6236 | 0.12915 |
| 4 | 0.25000 | 0.12911 | 3.2795 | 0.16144 |
| 3 | 0.33333 | 0.17215 | 4.3726 | 0.21525 |
| 2.5 | 0.40000 | 0.20658 | 5.2471 | 0.25830 |
| 2 | 0.50000 | 0.25823 | 6.5589 | 0.32288 |
Computed from W = P / (2 x cos 14.5 degrees) with unrounded values, then rounded once. The constant is M - E at the best wire, lead angle ignored. Inch values to 5 decimal places, metric to 4.
Source: Machinery's Handbook (three-wire measurement of Acme threads); TPI from the ASME B1.5 general purpose series
Shop notes
- The Acme best wire (0.51645 x P) is smaller than the 60 degree best wire (0.57735 x P) at the same TPI. A 60 degree wire set is the wrong size for Acme.
- Two wires go in adjacent grooves on one side, one wire opposite, between them.
- On coarse pitches the wires can roll out of the groove. A light film of oil or a wire holder keeps them in place.
- For a 2G external thread, the maximum pitch diameter sits below basic by the allowance, 0.020 x sqrt(D) with D the nominal diameter in inches. Size to the class limits, not to basic.
- Metric trapezoidal threads use a 30 degree angle and different constants; this page does not cover them.
FAQ
What is the best wire size for a 1-5 Acme thread?
W = 0.51645 x P. For 5 TPI, P = 0.2000 in, so the best wire is 0.10329 in (2.6236 mm). A 0.1033 in wire is the size used in the worked example on this page.
Why can you not use the 60 degree 3-wire formula on an Acme thread?
The constants come from the thread angle. A 60 degree thread uses 3 and 0.86603; a 29 degree Acme thread uses 4.9939 and 1.9334. The 60 degree formula on an Acme thread gives a wrong pitch diameter.
Does the Acme 3-wire formula account for lead angle?
No. It is the simplified formula for single-start threads with a small lead angle. The 1-5 example has a lead angle of about 4.15 degrees. For multi-start threads or close tolerances, use the lead angle correction in Machinery's Handbook or ASME B1.5.
Which limits do you compare an Acme pitch diameter to?
The external thread pitch diameter limits for your class in ASME B1.5, for example class 2G (general purpose, external). For 2G the maximum pitch diameter is basic minus an allowance of 0.020 x sqrt(D): for 1-5 Acme, 0.9000 - 0.0200 = 0.8800 in. Take the minimum from the ASME B1.5 table.
Last updated