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### UN External Screw Threads Formulas and Calculator

ANSI Hardware Design Guide and Charts

Unified Inch Screw Threads Calculator for UN Threads

Inch Size UN External Screw Threads Formulas and Calculator per. ASME B1.1

The formulas below are for inch screw threads are based on those listed in ASME B1.1, Unified Inch Screw Threads.

For internal threads see:

Screw Threads Calculator for Internal Unified Inch Screw

Formulas Used:

Note that calculated values may be slightly different than table reference
data due to math rounding differences.

Maximum external major diameter

Eq. 1

d_{max.} = d_{bsc} − es

Eq. 2

where

d_{bsc} = Basic major diameter

es = Allowance

- Classes 1A and 2A, es = 0.300 & Class 2A pitch diameter tolerance
- Class 3A, es = no allowance

*Major Diameter Tolerance*

(1 ) Class 1A = 0.090 P^{2/3}

(2) Classes 2A and 3A = 0.060 P^{2/3}

The tolerance for Class 2A coarse and the 8-thread series threads of unfinished,
hot-rolled material is0.0903P^{2/3}.

This does not apply to standard
fasteners with rolled threads.

Minimum dia major diameter

Eq. 3

dmin. = dmax. − Td

where

Class 1A Td = 0.090 P^{2/3}

Classes 2A and 3A Td = 0.060 P^{2/3}

The tolerance for Class 2A coarse and the 8-thread series threads of unfinished,
hot-rolled material is0.0903P^{2/3}. This does not apply to standard
fasteners with rolled threads.

Maximum external pitch diameter

Eq. 4

d_{2}max. = dmax. − 2h_{as}

where

dmax = Maximum external major diameter

2h_{as} = 0.64951905P

Minimum external pitch diameter

Eq. 5

d_{2}min. = d_{2}max.
− Td_{2}

where

d_{2} = 0.0015 (d bsc)^{1/3} + 0.0015 LE^{1/2}
0.015 (P^{2})^{1/3}

Maximum external UNR minor diameter

Eq. 6

d_{3}max. = dmax. − 2h_{s}

where

2h_{s} = 1 .19078493P

dmax. = Maximum external major diameter

Maximum external UN minor diameter

Eq. 7

d_{1}max. = dmax. − 2h_{s}

where

2h_{s} = 1 .08253175P

dmax. = Maximum external major diameter

LE = length of engagement

P = thread pitch = 1/n

n = number of
threads per inch

Notes

External Thread

(a) Maximum Major Diameter (External Threads)

(1 ) For
Classes 1A and 2A, d = basic major diameter, Dbsc, minus allowance.

(2) For
Class 3A, d = basic major diameter, Dbsc.

(b) Minimum Major Diameter (External Threads). For all classes, equals maximum major diameter, minus major diameter tolerance for respective class of thread.

(c) Maximum Pitch Diameter (External Threads)

(1 ) For Classes 1A and 2A,
d_{2} =basic pitch diameter D_{2}bsc, minus allowance.

(2)
For Class 3A, d_{2} = basic pitch diameter D_{2}bsc.

(d) Minimum Pitch Diameter (External Threads). For all classes, equals maximum pitch diameter, minus pitch diameter tolerance for respective class of thread.

(e) Maximum Minor Diameter (External Threads). In dimensioning UN series external threads, the minor diameter is not specified. In practice, the minor diameter is satisfactory when accepted by a standard GO thread gage in accordance with ASME B1.2. When it is desirable to obtain minor diameter values for reference purposes and for UNR threads, they can be calculated as follows:

(1 ) For UN series threads, the formulas are:

(a) for Classes 1A and 2A, d_{1}
= basic minor diameter D_{1}bsc, minus allowance

(b) for Class 3A, d1
= basic minor diameter D_{1}bsc

(2) For UNR series threads, the
formulas are:

(a) for Classes 1A and 2A, d3 p basic minor diameter D_{1}bsc,
minus allowance, minus H/8

(b) or Class 3A, d_{3} = basic minor
diameter D_{1}bsc, minus H/8

(f) Minimum Minor Diameter (External Threads). When it is desirable for design purposes to calculate the minimum diameter, it can be obtained for all classes by the formula: minimum pitch diameter minus 0.64951905P.

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