Unified Thread Limits Calculator

Unified Thread Limits Calculator (2A/2B)

ASME B1.1 class 2A external and 2B internal limits from diameter and TPI: allowance, major and pitch diameter limits, minor diameter limits — the formula behind the tables.

Machining 4 inputs 9 results

Inputs

View results

Nominal major diameter (D)

Threads per inch (TPI)

TPI

Length of engagement

Results

Default result

Edit inputs

2A allowance(es)

0.0011in

0.3 × the 2A PD tolerance — the deliberate clearance class 2A external threads give up (2B starts at basic).

Also computed

2A major dia max(d_max)0.2489in

What the blank or thread OD is turned/rolled to.

2A major dia min(d_min)0.2408in

2A pitch dia max(d2_max)0.2164in

GO limit for the external thread — wires or the ring gauge check this.

2A pitch dia min(d2_min)0.2127in

2A PD tolerance 0.0037 in.

2B pitch dia min(D2_min)0.2175in

Basic pitch diameter — the internal GO limit.

2B pitch dia max(D2_max)0.2224in

2B PD tolerance 0.0049 in (1.3 × the 2A tolerance).

Method notes 4 notes

ASME B1.1 formula method, classes 2A/2B: Td2(2A) = 0.0015·∛D + 0.0015·√LE + 0.015·∛P², allowance = 0.3·Td2(2A), major tolerance 0.060·∛P², Td2(2B) = 1.3·Td2(2A), minor tolerance 0.25P − 0.4P². Values rounded per the standard (tolerances/PD to 0.0001 in, minor limits to 0.001 in) — output matches the published tables.
Classes 1A/3A/1B/3B, UNJ (ASME B1.15) and small number-size special cases are out of scope here; the standard’s own tables govern. UNR differs from UN only in external root radius — these PD/major limits apply to both.
2A maximum major/PD sit one allowance below basic — that clearance is what lets plated or hot assemblies still go together; class 3 fits delete it.
Gauging practice (GO/NOGO, wire methods) is ASME B1.2; the minimum 2B minor is the tap-drill floor, and the thread tap drill size calculator picks the drill.

Every ASME B1.1 limit descends from one formula: Td2(2A) = 0.0015·∛D + 0.0015·√LE + 0.015·∛P² (tables use LE = D), with allowance = 0.3·Td2, the 2B pitch tolerance = 1.3·Td2, major tolerance 0.060·∛P² and 2B minor tolerance 0.25P − 0.4P². For 1/4-20 that yields the familiar row — 2A PD 0.2164/0.2127, major 0.2489/0.2408, 2B PD 0.2175/0.2224, minor 0.196–0.207 — and this calculator reproduces the published tables exactly while also covering UNS pitches, odd diameters and real engagement lengths the tables skip.

How to use this calculator

Enter diameter and TPI. Any combination — UNC, UNF, UNEF or a special UNS pitch. Number sizes: D = 0.060 + 0.013 × the number.
Keep the table basis or set LE. Published tables assume engagement equal to the diameter; a longer real engagement legitimately widens the PD tolerance.
Read the limits. External 2A: allowance, major and PD limits (what wires and ring gauges check). Internal 2B: PD and minor limits (the tap-drill band).
Gauge per B1.2. These are design limits; acceptance gauging practice is its own standard.

How it works

Every number in the B1.1 limit tables descends from one tolerance formula, scaled by class:

Td2(2A) = 0.0015·∛D + 0.0015·√LE + 0.015·∛P² · es = 0.3·Td2 · Td2(2B) = 1.3·Td2

External 2A limits stack down from basic (allowance, then tolerance); internal 2B limits stack up from basic. The minor-diameter band this produces is exactly what the tap drill size calculator aims a drill into, the thread pitch chart carries the standard series, and measuring the result over wires is the same three-wire logic gears use over pins.

Worked example

Verified against the live calculator

1/4-20 UNC at the table basis (LE = D = 0.25 in), P = 0.05:

Td2 = 0.0037 · es = 0.0011 · 2A PD: 0.2164/0.2127 · 2B PD: 0.2175/0.2224 · 2B minor: 0.196–0.207

The external max major lands at 0.2489 (basic 0.2500 minus the allowance) and the min at 0.2408. Every one of these digits matches the published table row — the calculator exists for the sizes the tables skip: special UNS pitches, large diameters, and the honest tolerance for engagements longer than one diameter.

Frequently asked questions

What are the pitch diameter limits for a 1/4-20 2A thread?

Max 0.2164 in, min 0.2127 in. The basic pitch diameter is 0.2175; class 2A subtracts an allowance of 0.0011 (0.3 × the PD tolerance) for the max, then the tolerance of 0.0037 for the min — all from the B1.1 formulas this calculator runs.

How are unified thread tolerances calculated?

From one master formula: the class 2A pitch-diameter tolerance is 0.0015·∛D + 0.0015·√LE + 0.015·∛P², with the tables built at LE = D. Everything else is derived — allowance = 0.3 × it, the 2B tolerance is 1.3 × it, the 2A major tolerance is 0.060·∛P², and the 2B minor tolerance is 0.25P − 0.4P².

What is the difference between 2A and 3A threads?

The allowance, mainly: class 2A external threads sit one allowance (0.3 × Td2) below basic size, guaranteeing clearance even at maximum material — which is what lets plating, coating and hot assembly still work. Class 3A deletes the allowance and tightens the tolerance to 0.75 × for precision fits.

What minor diameter does a 2B tapped hole need?

Between the basic minor diameter (D − 1.0825P) and that plus 0.25P − 0.4P². For 1/4-20 that is 0.196–0.207 in — the reason the #7 drill (0.201) is the standard tap drill: it lands comfortably inside the band at about 75% thread.

Method & assumptions

ASME B1.1 formula method for classes 2A and 2B only, verified 2026-06-10 against two independent formula references and a third published table; the implementation reproduces the published 1/4-20, 3/8-16, 1/2-13 and 10-32 rows exactly, including the standard's rounding (tolerances and PD limits to 0.0001 in, minor limits to 0.001 in).
Classes 1A/3A/1B/3B, UNJ (ASME B1.15), and the special small number-size adjustments are out of scope — the standard's tables govern there.
UNR differs from UN only in the external root radius; the major and pitch diameter limits here apply to both forms.
Design limits, not gauging: GO/NOGO and wire-measurement acceptance practice is ASME B1.2.