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### Screw Threads Calculator for Internal Unified Inch Screw

ANSI Hardware Design Guide and Charts

Unified Inch Screw Threads Calculator for UN Threads

UN Internal 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.

Formulas Used:

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

Minimum internal minor diameter

Eq. 1

D_{1}min. = Dbsc - 2h_{n}

Eq. 2

2h_{n} = 1.08253175P

where

Dbsc = Basic major diameter

2h_{n} = double height of internal
thread

P = 1/n

n = threads per inch

Eq. 3

D_{1}max. = D_{1}min. + TD_{1}

Eq. 4

TD_{1} = 0.25P - 0.4P^{2}

where

D_{1} max. = Maximum internal minor diameter

D_{1} min. =
Minimum internal minor diameter

TD_{1} = internal minor diameter
tolerance

Eq. 5

D_{2} min. = Dbsc − h_{b}

Eq. 6

h_{b} = 0.64951905P

where

D_{2}min. = Minimum internal pitch diameter

D bsc = Basic major
diameter

h_{b} = twice the external thread addendum

Eq. 7

D_{2}max. = D_{2} min. + TD_{2}

Eq 8.

TD_{2} = 1 .300 Td_{2}

Eq. 9

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

where

D_{2} max. = Maximum internal pitch diameter

D_{2} min. =
Minimum internal pitch diameter

TD_{2} = internal pitch diameter
tolerance

LE = length of engagement

P = thread pitch

Eq 10

D min. = D bsc

where

Dmin. = Minimum internal major diameter

Dbsc = Basic major diameter

Notes

(a) Maximum Major Diameter (Internal Threads ). In dimensioning internal threads, the maximum major diameter is not specified, being established by the crest of an unworn tool. In practice, the major diameter of an internal thread is satisfactory when accepted by a gage or gaging method that represents the maximum material condition of an external thread that has no allowance.

(b) Minimum Major Diameter (Internal Threads), Dbsc. For all classes, equals basic diameter Dbsc.

(c) Minimum Pitch Diameter. For all classes, D_{2}bsc equals basic pitch
diameter D_{2} minimum.

(d) Maximum Pitch Diameter (Internal Threads). For all classes, equals
minimum pitch diameter D_{2}bsc, plus pitch diameter tolerance for respective
class of thread

(e) Minimum Minor Diameter (Internal Threads). For all classes, D_{1}bsc equals
minimum pitch diameter D_{2} minimum minus 0.43301122P, then rounded off to the
nearest 0.001 in. for sizes 0.138 in. and larger. For Class 3B, a cipher is
added to yield four decimal places.

(f) Maximum Minor Diameter (Internal Threads) . All classes are calculated before rounding, then rounded for Classes 1B and 2B to the nearest 0.001 in. for sizes 0.138 in. and larger. Class 3B values are rounded to four decimal places.

Plating considerations

Standard internal threads provide no allowance for coating thickness. To determine before coating gaging limits for a coated thread, increase

(a) the minimum pitch diameter by 4 times the maximum coating thickness, if specified, or by 6 times the minimum or nominal coating thickness, if not specified.

(b) the maximum pitch diameter by 4 times the minimum or nominal coating thickness.

(c) the minimum minor diameter by 2 times the maximum coating thickness, if specified, or by 3 times the minimum or nominal coating thickness, if not specified.

(d) the maximum minor diameter by 2 times the minimum or nominal coating thickness.

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