BIZOMAT MAKEOS · Threads
Unified Thread Limits of Size (Classes 1A–3B)
What are the limits of size for this UNC, UNF or UN thread in the chosen class?
Allowance, major, pitch and UNR minor diameter limits of an external Unified inch thread, and minor and pitch diameter limits of the mating internal thread, for classes 1A/1B, 2A/2B and 3A/3B, by the ASME B1.1 formulas.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Basic major diameter | in | Basic major diameter in inches. |
| Threads per inch | TPI | Threads per inch. |
| Thread class | choice | Tolerance class of the thread (2A/2B is the general-purpose class). |
| Length of engagement (0 = standard) | in | Length of engagement; 0 uses the smaller of 9 pitches and the basic diameter, which reproduces the published tables. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Basic major diameter
- What it is
- The basic major diameter of the UNC, UNF or UN thread, the nominal size from the thread designation, such as 0.5 for a ½-13 thread.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 10 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Give the decimal inch size, not a fraction or a screw number: ½ is 0.5, and a No. 10 screw is 0.190.
What this means: Threads per inch
- What it is
- The number of thread crests in one inch of length, the second number in the designation (13 in ½-13 UNC). The pitch is 1 ÷ n.
- Units and format
- Enter a number in TPI: threads per inch. The form accepts 0.000001 TPI to 200 TPI. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 13 TPI as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fewer threads per inch means a larger pitch, a deeper thread and wider tolerances.
- Get it right
- Threads per inch, not pitch: a 13 TPI thread has a pitch of about 0.0769 in.
What this means: Thread class
- What it is
- The tolerance class of the thread pair: 1A/1B loose, 2A/2B general purpose, 3A/3B close. A is the external (bolt) thread and B the internal (nut) thread.
- Units and format
- Choose one of 3 options from the list: 1A / 1B; 2A / 2B; 3A / 3B.
- Example
- The form opens with “2A / 2B” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- A lower class number gives wider pitch diameter tolerances; classes 1A and 2A also get an allowance.
- Get it right
- Class 3A has no allowance, so a plated or coated 3A thread may not assemble.
What this means: Length of engagement (0 = standard)
- What it is
- The axial length over which the bolt and nut threads actually engage, which sets the pitch diameter tolerance. Enter 0 to use the standard engagement the published tables are based on.
- Units and format
- Enter a number in in: inches. The form accepts 0 in to 100 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer engagement widens the pitch diameter tolerance slightly.
- Get it right
- Keep 0 unless the drawing specifies a longer or shorter engagement; a non-zero value gives limits that differ from the tables.
Method and formulas
- P = 1/n; base pitch tolerance Td2(2A) = 0.0015 D^(1/3) + 0.0015 √LE + 0.015 P^(2/3).
- Class factors on Td2: 1A × 1.5, 2A × 1, 3A × 0.75; internal = 1.3 × external of the same class. Allowance es = 0.3 × Td2(2A) for 1A and 2A, 0 for 3A.
- dmax = D − es; major tolerance Td = 0.060 P^(2/3) (1A: 0.090); d2max = dmax − 0.64951905P; d2min = d2max − Td2; UNR minor max = dmax − 1.19078493P.
- Internal: D2min = D − 0.64951905P; D2max = D2min + TD2; D1min = D − 1.08253175P. Values are rounded to 0.0001 in as in ASME B1.1.
- Example: 0.5-13 class 2A: major 0.4985 / 0.4876 in, pitch 0.4485 / 0.4435 in.
Limitations
- Maximum internal minor diameter and class 1B/3B minor tolerances follow additional rules in ASME B1.1; take them from its tables.
- Uncoated threads; coatings must fit within the allowance.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find inspection limits for any UN thread size
- Set up thread gauges and CNC thread cutting
- Check special-diameter threads not in printed tables
Who it is for
- Quality inspectors
- Machinists
- Design engineers
What you get
- Allowance
- External major, pitch and UNR minor limits
- Internal minor (minimum) and pitch limits
- Pitch diameter tolerances
Interpreting the result
- Gauge with GO/NOT GO thread gauges; use these limits to check special sizes and set-ups.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1813–1866. Topic reference; no source tables or recommended settings are reproduced.
- ASME B1.1 Unified Inch Screw Threads (UN and UNR Thread Form)
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Open the Unified Thread Limits of Size (Classes 1A–3B) calculator