Unified Thread Class 2A/2B vs 3A/3B Tolerance Calculator (ASME B1.1)
Under ASME B1.1, Unified external threads use suffix A (1A, 2A, 3A) and internal threads use suffix B (1B, 2B, 3B). Class 2A includes a mandatory 30% clearance allowance (es = 0.300 × TD_2) to prevent galling and accommodate electroplating, whereas Class 3A has zero allowance (es = 0.0000") and a 25% tighter pitch diameter tolerance (0.750 × TD_2(2A)).
ASME B1.1 Unified Thread Class 1A/2A/3A & 1B/2B/3B Tolerance Calculator
Compute exact Pitch Diameter tolerance (TD_2 / Td_2), external plating allowance (es), and Pitch/Major/Minor diameter limits per ASME B1.1.
How ASME B1.1 Calculates Pitch Diameter Tolerance (TD_2) and Allowance (es)
Every Unified National Coarse (UNC), Fine (UNF), Extra-Fine (UNEF), and Constant-Pitch (8-UN, 12-UN, 16-UN) screw thread in North American aerospace, automotive, and defense manufacturing is governed by ASME Geometric & Mechanical Standards (ASME B1.1) and NIST (National Institute of Standards and Technology) Handbook H28. Rather than relying on arbitrary lookup tables, ASME B1.1 derives every pitch diameter tolerance from a single foundational 3-term mathematical equation—the Class 2A External Pitch Diameter Tolerance (TD_2(2A))—as a function of basic major diameter D, length of engagement L_e, and thread pitch P = 1 / TPI (all in inches):
TD_2(2A) = 0.0015 × ∛D + 0.0015 × √L_e + 0.015 × P^(2/3)
Every other external and internal thread class is an exact mathematical multiplier of this Class 2A baseline, as documented in Machinery's Handbook (Industrial Press) and NASA Fastener & Mechanical Design Manual (NASA RP-1228):
For external bolt and stud threads (1A / 2A / 3A), Class 1A applies a tolerance of 1.500 × TD_2(2A), Class 2A uses 1.000 × TD_2(2A), and precision Class 3A tightens the pitch diameter tolerance band to 0.750 × TD_2(2A). Both Class 1A and Class 2A subtract a mandatory fundamental allowance of es = 0.300 × TD_2(2A) from the basic pitch diameter so the maximum material limit sits safely below basic size, whereas Class 3A has zero allowance (es = 0.0000") for tight metal-to-metal seating.
For internal tapped nuts and blind holes (1B / 2B / 3B), ASME B1.1 grants a 30% wider pitch diameter tolerance than the corresponding external class to account for tap wear and substrate springback: Class 1B = 1.950 × TD_2(2A), Class 2B = 1.300 × TD_2(2A), and Class 3B = 0.975 × TD_2(2A). All three internal classes have zero fundamental deviation (EI = 0.0000"), meaning their minimum pitch diameter always equals the exact Basic Pitch Diameter D_2 = D - 0.649519 × P.
| Thread Size (UNC / UNF) | Basic Pitch Dia (d_2 = D - 0.6495P) | Class 2A Allowance (es) | Class 2A Pitch Dia Limits | Class 3A Pitch Dia Limits (0 Allowance) | Class 2B Pitch Dia Limits | Class 3B Pitch Dia Limits |
|---|---|---|---|---|---|---|
| #10-24 UNC (0.1900") | 4.138 mm (0.1629") | 0.025 mm (0.0010") | 0.1586" to 0.1619" | 0.1604" to 0.1629" | 0.1629" to 0.1672" | 0.1629" to 0.1661" |
| #10-32 UNF (0.1900") | 4.310 mm (0.1697") | 0.023 mm (0.0009") | 0.1658" to 0.1688" | 0.1674" to 0.1697" | 0.1697" to 0.1736" | 0.1697" to 0.1726" |
| 1/4"-20 UNC (0.2500") | 5.525 mm (0.2175") | 0.028 mm (0.0011") | 0.2127" to 0.2164" | 0.2147" to 0.2175" | 0.2175" to 0.2224" | 0.2175" to 0.2211" |
| 1/4"-28 UNF (0.2500") | 5.761 mm (0.2268") | 0.025 mm (0.0010") | 0.2225" to 0.2258" | 0.2243" to 0.2268" | 0.2268" to 0.2311" | 0.2268" to 0.2300" |
| 5/16"-18 UNC (0.3125") | 7.021 mm (0.2764") | 0.030 mm (0.0012") | 0.2712" to 0.2752" | 0.2734" to 0.2764" | 0.2764" to 0.2817" | 0.2764" to 0.2803" |
| 3/8"-16 UNC (0.3750") | 8.494 mm (0.3344") | 0.033 mm (0.0013") | 0.3287" to 0.3331" | 0.3311" to 0.3344" | 0.3344" to 0.3401" | 0.3344" to 0.3387" |
| 1/2"-13 UNC (0.5000") | 11.430 mm (0.4500") | 0.038 mm (0.0015") | 0.4435" to 0.4485" | 0.4463" to 0.4500" | 0.4500" to 0.4565" | 0.4500" to 0.4548" |
| 1/2"-20 UNF (0.5000") | 11.875 mm (0.4675") | 0.033 mm (0.0013") | 0.4619" to 0.4662" | 0.4643" to 0.4675" | 0.4675" to 0.4731" | 0.4675" to 0.4717" |
| 3/4"-10 UNC (0.7500") | 17.399 mm (0.6850") | 0.046 mm (0.0018") | 0.6773" to 0.6832" | 0.6806" to 0.6850" | 0.6850" to 0.6927" | 0.6850" to 0.6907" |
Electroplating & Anodizing Rule: Why Class 2A Accommodates Coating Without Undercutting
When a commercial zinc, cadmium, or nickel electroplating of radial thickness t is applied to a 60° screw thread, trigonometry dictates that the effective pitch diameter increases by 4 × t (because coating builds on both opposing 30° flanks on both sides of the bolt diameter: 2 × t / sin(30°) = 4 × t!). Under ASME B1.1 Section 7, the built-in Class 2A allowance (es) may be consumed by electroplating so that plated Class 2A parts can pass a Basic Class 3A GO ring gage without pre-plating undercutting, provided the coating thickness does not exceed es / 4 (or es / 6 for uneven barrel plating). Conversely, because Class 3A has zero allowance (es = 0), any Class 3A thread that will be plated or hard-anodized must be machined undersize before coating!
| ASME B1.1 Thread Class | Internal / External | Pitch Dia Tolerance Multiplier | Fundamental Allowance (es / EI) | Plating & Coating Clearance Rule | Typical Engineering Application |
|---|---|---|---|---|---|
| Class 1A | External Bolt / Stud | 1.500 × TD_2(2A) | es = 0.300 × TD_2(2A) | Generous clearance for dirty field assembly | Ordnance, field construction bolts, hot-dip galvanized |
| Class 2A | External Bolt / Screw | 1.000 × TD_2(2A) (Baseline) | es = 0.300 × TD_2(2A) | Accommodates electroplating up to 1/6 of es | 90% of commercial cap screws, hex bolts, general CNC |
| Class 3A | External Precision Screw | 0.750 × TD_2(2A) | es = 0.0000" (Zero Allowance) | Must pre-undercut before plating | Socket head cap screws (SHCS), aerospace, medical |
| Class 1B | Internal Tapped Nut | 1.950 × TD_2(2A) | EI = 0.0000" (Basic Pitch Dia) | Matches 1A external threads | Heavy industrial nuts requiring rapid assembly |
| Class 2B | Internal Tapped Hole | 1.300 × TD_2(2A) | EI = 0.0000" (Basic Pitch Dia) | Standard GH3 / H3 tap limit | Standard CNC tapped holes in steel, aluminum, cast iron |
| Class 3B | Internal Precision Hole | 0.975 × TD_2(2A) | EI = 0.0000" (Basic Pitch Dia) | Requires GH2 / H2 precision ground tap | Aerospace locknuts, zero-backlash instrument threads |
Selecting GH-Limit Taps (H2, H3, H5) and Measuring Pitch Diameter Over 3 Wires
To hold Class 2B vs Class 3B internal pitch diameter limits on the shop floor, you must select the proper ground-thread H-Limit Tap (where each H number adds +0.0005" above basic pitch diameter). Standard commercial taps for 1/4"-20 through 1/2"-13 Class 2B holes are typically H3 (+0.0010" to +0.0015" over basic), whereas tight Class 3B aerospace holes require a precision H1 or H2 tap so the new tap does not cut oversize above the 3B NO-GO plug gage limit. Inspect your external 2A/3A pitch diameter directly on the lathe using our Three-Wire Thread Measurement Calculator, program your CNC threading passes on our Fanuc G76 Threading Cycle Calculator, verify tap drill percentage of thread on our Thread Engagement Tap Drill Calculator, and compute assembly preload torque on our Bolt Torque & Clamp Load Calculator.