Three-wire pitch diameter calculator and UN thread dimensions

All values computed at run time from ASME B1.1 formulas. Nothing is transcribed from a published table. Inch units throughout. Formulas and their limits are stated at the bottom of the page and in the source comments.

Reference tool. Not a certified measurement. Values are computed from published ASME B1.1 formulas and are provided for reference and estimation only. ASME B1.1 is the controlling document; where this page and the standard disagree, the standard governs. Verify all values against the current edition of ASME B1.1 or an equivalent controlled source before using them for inspection, acceptance, or the disposition of product. This tool does not cover coated or plated threads, UNR or UNJ forms, multiple-start threads, minor diameter limits, or gage tolerances per ASME B1.2. No warranty of any kind is made as to accuracy, completeness, or fitness for a particular purpose, and no liability is accepted for any loss or damage arising from its use. Version 1.0 · Computed from ASME B1.1 formulas · Last reviewed August 2026

Measurement over wires

Thread

Class

Wire diameter (in)

Defaults to best wire size. Type your certified wire size to override.

Measured M (in, optional)

Enter a micrometer reading to get pitch diameter and a pass/fail.

Apply lead angle correction Off by default, matching common shop practice for 60° threads. Turning it on adds 0.75 · W · tan²λ to M. The correction is shown either way so you can see its size.

UN thread dimensions, #0 through 4 in

Series

Find size

Diameter range

Size	TPI	Series	Pitch	Basic diameters			Class 2A major		Class 2A pitch dia		Class 2B pitch dia		L_E basis
Size	TPI	Series	Pitch	Major	Pitch	Minor (ref)	Max	Min	Max	Min	Min	Max	L_E basis

Minor diameter is basic reference only. Minor diameter limits are intentionally not published here. Basic minor diameter is the internal thread value, D − 1.0825318p; B1.1 does not specify minor diameter limits for UN external threads, which are controlled by the GO gage.

Formulas used

Basic form

Pitch	`p = 1 / n`
Height of sharp V	`H = p √3 / 2 = 0.8660254038 p`
Basic pitch diameter	`D₂ = D − 0.75 H = D − 0.6495190528 p`
Basic minor diameter, internal	`D₁ = D − 1.25 H = D − 1.0825317547 p`
Number size nominal diameter	`D = 0.060 + 0.013 × size number`

Tolerances and allowance

Class 2A pitch diameter tolerance	`T₂ₑ = 0.0015 ∛D + 0.0015 √Lₑ + 0.015 ∛(p²)`
Length of engagement, UNC and UNF	`Lₑ = D`
Length of engagement, UNEF	`Lₑ = 9p`
Allowance, Classes 1A and 2A	`es = 0.300 T₂ₑ` (Class 3A: zero)
PD tolerance multipliers on T₂ₑ	`1A 1.500 2A 1.000 3A 0.750 1B 1.950 2B 1.300 3B 0.975`
Major diameter tolerance, external	`1A: 0.090 ∛(p²) 2A and 3A: 0.060 ∛(p²)`

Length of engagement is not always 9 pitches. Per B1.1 para. 5.1, tolerances for UNC, UNF, UNS and the 4, 6 and 8-UN series are based on a length of engagement equal to the basic major diameter, while UNEF and the 12, 16, 20, 28 and 32-UN series are based on 9 pitches. Applying 9p to everything moves 1/4-20 UNC from 0.0037 to 0.0040 and 4-12 UN from 0.0065 to 0.0082. Every result on this page shows which basis it used.

Three-wire measurement

General form, A = half included angle	`M = E + W (1 + csc A) − (p/2) cot A`
60° thread, A = 30°	`M = E + 3W − 0.8660254038 p`
Pitch diameter from a reading	`E = M − 3W + 0.8660254038 p`
Best wire size	`W = p / (2 cos A) = 0.5773502692 p`
Lead angle at pitch diameter	`tan λ = p / (π E)`, single start
Lead angle correction, additive to M	`c = 0.75 W tan²λ`

On the lead angle correction. Published sources disagree on whether the cosine term inside the Machinery's Handbook correction takes the half angle, 30°, giving the 0.75 coefficient above, or the included angle, 60°, giving 0.433. The two readings differ by a factor of 1.732, roughly 0.00004 in on 1/2-13. This page implements the half-angle reading. Verify against your own wire certificate or lab procedure before using corrected values for acceptance. The correction is off by default and its magnitude is always displayed.

Scope and exclusions

Three-wire measurement applies to external threads only. Internal classes show pitch diameter limits with no M value; internal pitch diameter is measured with ball anvils or thread plug gages.

Not covered: minor diameter limits, UNR root geometry, UNJ threads, coated or plated gaging limits, multiple-start threads, and lengths of engagement outside the range B1.1 tabulates. Classes 1A and 1B appear only where B1.1 defines them, which is UNC in 1/4 in and larger.

The one input not derived from formula is the list of standard diameter and pitch combinations, which is a standardization decision rather than a calculable quantity. Everything else on this page, including all number-size nominal diameters, is computed.