## Overview

The Unified Thread Standard (UTS) defines a 60° thread form in Inch dimensions as described in the ASME B1.1 standard. It is the North American equivalent of the ISO metric thread system. The UTS serves as the leading standard for bolts, nuts, and a wide variety of other threaded fasteners used in the USA and Canada. However, in recent years the metric thread standard is becoming more common.
The standard defines diameter and pitch combinations along with allowances, tolerances, and designations. It has the same 60° profile as the ISO metric screw thread, but the basic dimensions of each UTS thread were chosen as an inch fraction rather than a millimeter value.

## Designation

Basic designation syntax:

Diameter:

• From 1/4″ and above the diameters are given in inch fractions. For example 1/4″, 3/4″, 1 1/4″.
• Below 1/4″ the diameters are given by a series of numbers from #0 to #12. Each “number” describes an arbitrary diameter as shown in the below table.
• It is also allowed to denote the diameters with a decimal value. For example 0.250 (1/4″), 0.4375 (7/16″), etc.

#### Standard Diameter numbers below 1/4″

Diameter
Number
#0 #1 #2 #3 #4 #5 #6 #8 #10 #12
Diameter
(Inch)
0.006 0.0073 0.0086 0.0099 0.112 0.125 0.138 0.164 0.19 0.216
Diameter
(mm)
1.524 1.8542 2.1844 2.5146 2.8448 3.175 3.5052 4.1656 4.8260 5.4864
• By default, the pitch is given in TPI. For example, 1/4-20 means a thread with a pitch of 20 TPI (1/20=0.05″).
• It is also allowed to denote the pitch by distance. For example, 1/4-0.05P means a thread with a pitch of 0.05″ (same as 20 TPI).

Series:

• In most cases, the series will be UNC, UNF, or UNEF (Coarse, Fine, or Extra fine pitch).
• ASTM B1.1, also defines several constant pitch series. These are denoted by ##-UN. For example, 12-UN or 8-UN. The pitch remains the same for the whole diameter range in these series. However, they are much less popular.

Class:

• The class is defined by a two-character code.
• The first character is a digit between 1 and 3. 1=Tight fit, 2=Medium fit, and 3=Loose fit.
• The second character is a letter. A=External thread and B=Internal thread.
• For a detailed explanation of classes, read the dedicated section below.

• Number of Starts: By default, all threads have a single start. Thus the lead equals the pitch. For a multiple-start thread, the lead is also indicated. For example: 3/4– 0.0625P0.1875L UNF denotes a 3/4″ UNF thread with 3 starts. (0.1875/0.0625=3)

#### Designation Examples of Unified Threads

Designation Series
Internal or
External
Nominal
Daimeter
Number
of Starts
Direction
#8-32 UNC UNC Undefined 0.164" 32 0.03125"
Same as
Pitch
Undefined 1 Right Hand
1/4 -28 UNF-2A UNF External 0.25" 28 0.0357"
Same as
Pitch
2A 1 Right Hand
3/4-20 UNEF-3B UNEF Internal 0.75" 20 0.05"
Same as
Pitch
3B 1 Right Hand
1-12 UN-1A
Constant Pitch
12 TPI
External 1" 12 0.0833"
Same as
Pitch
1A 1 Right Hand
3/4– 0.0625P – 0.1875L UNF-2A UNF External 0.75" 16 0.0625" 0.1875" 2A 3 Right Hand
1/4 -28 UNF-2A-LH UNF External 0.25" 28 0.0357"
Same as
Pitch
2A 1 Left Hand

## Possible Combinations (Diameter/Pitch)

The below charts show all the possible thread combinations that are defined in ASTM B1.1

• UNC– Unified Inch Coarse Thread Series
• UNF – Unified Inch Fine Thread Series
• UNEF – Unified Inch Extra Fine Thread Series
• ##-UN – Unified Inch Constant PitchThread Series
• Click to get the Full Thread Data-Sheet for a specific combination

## Basic Thread Dimensions (UNC, UNF & UNEF)

The basic dimensions are nominal dimensions of a unified thread profile without allowance and tolerances (The thread class defines that). They are based on standard ASTM B1.1. The basic dimensions can be used for design. However, for manufacturing and machining, you need the allowable rage of each dimension. This data can be found in the standard or in the Limits and Dimensions section below. All the basic dimensions are derived from simple formulas based on the thread’s nominal diameter and pitch.

### Symbols

#### List of symbols used in charts and formulas of Unified Inch Threads

Symbol Explanation
Basic Parameters - Diameters and Pitch
D Major (Basic) diameter of internal thread
D1
D2 Pitch diameter of internal thread
D3 Major diameter, rounded root, internal thread
d Major (Basic) diameter of external thread
d1 Minor diameter of external thread
d2 Pitch diameter of external thread
d3 Major diameter, rounded root, internal thread
n Number of threds per Inch (TPI)
P Pitch (Distance)
Height Parameters
H Height of fundamental triangle
Length Parameters
Lts Length of complete external thread
Ltn Length of complete internal thread
Allowance, Deviation, and Tolerances
TD1 Tolerance for D1
TD2 Tolerance for D2
Td Tolerance for d
Td2 Tolerance for d2
Root / Creast Parameters
Fcs Flat crest width of external thread
Frs Flat root width of external thread
Fcs Flat crest width of internal thread
Fcs Flat root width of internal thread

The below video provides a short explanation of the threading terms

### Formulas for basic dimensions

$$\large d=\text{Basic Diameter}$$
$$\large P=\frac{1}{TPI}$$
$$\large H=\frac{\sqrt{3}}{2}\times{P} = 0.866025404\times{P}$$
$$\large h_s=\frac{5}{8}\times{H}$$
$$\large h_{as}=\frac{3}{8}\times{H}$$
$$\large d_2=d-{2}\times{h_{as}}$$
$$\large d_1=d-{2}\times{h_s}$$
$$\large F_{cs}=\frac{P}{8}$$
$$\large F_{rs}=\frac{P}{4}$$

$$\large D=\text{Basic Diameter}$$
$$\large P=\frac{1}{TPI}$$
$$\large H=\frac{\sqrt{3}}{2}\times{P} = 0.866025404\times{P}$$
$$\large h_n=\frac{5}{8}\times{H}$$
$$\large h_{an}=\frac{1}{4}\times{H}$$
$$\large D_1=D-{2}\times{h_n}$$
$$\large D_2=D1+{2}\times{h_{an}}$$
$$\large F_{rn}=\frac{P}{8}$$
$$\large F_{cn}=\frac{P}{4}$$

### Unified Inch Threads Dimensions Charts

#### UNC Series Basic Dimensions chart

Click the Thread Link to get the Full Thread Data for all classes in Inch and Metric units.

• All dimensions are in inches. To view Metric translation click the Thread Link

#### UNF Series Basic Dimensions chart

Click the Thread Link to get the Full Thread Data for all classes in Inch and Metric units.

• All dimensions are in inches. To view Metric translation click the Thread Link

#### UNEF Series Basic Dimensions chart

Click the Thread Link to get the Full Thread Data for all classes in Inch and Metric units.

• All dimensions are in inches. To view Metric translation click the Thread Link

#### UN Constant Pitch Series Basic Dimensions chart

Click the Thread Link to get the Full Thread Data for all classes in Inch and Metric units.

• All dimensions are in inches. To view Metric translation click the Thread Link

## limits of Thread Dimensions (UNC, UNF & UNEF)

To manufacture or measure a thread, one has to know the maximum and minimum permissible values of the basic dimensions. These values are calculated according to the thread class (See below). To understand classes, you first need to understand the terms Allowance (Sometimes referred to as deviation) and Tolerances.

Definition of terms:

• Allowance (Deviation): The minimum permissible distance between the basic and actual profile.
• Tolerance: The width of the tolerance field of a diameter on the actual thread profile. (Pitch, Major & Minor diameters)
• A small allowance means that the assembly of a male and female thread will be harder, but after assembly, there will be less freedom of movement.
• A large allowance means that the assembly of a male and female thread will be easier, but after assembly, there will be more freedom of movement.
• The allowance size does not influence a thread’s production difficulty or price.
• A wide tolerance is easier and cheaper to produce but yields a larger spread between threads.
• A narrow tolerance is challenging to produce and more expensive but yields a smaller spread between threads.

• The class is defined by a two-character code.
• The first character defines is a digit between 1 and 3. 1=Loose fit, 2=Medium fit, and 3=Tight fit.
• The second character is a letter. A=External thread and B=Internal thread.
• In the Unified Inch thread system, only classes 1A & 2A have an allowance. The allowance for the two classes is the same.
• The other 4 classes have an allowance of Zero.
• All the internal thread profiles (B classes) have no allowance.
• Classes 1A & 1B: These classes are suitable for applications where a liberal tolerance and allowance are required to permit easy assembly. The maximum diameters of Class 1A threads are smaller than the basic diameter by the allowance amount. The minimum diameters of Class 1B threads are equal to the basic diameters and consequently afford no allowance at maximum material condition.
• Classes 2A & 2B: Classes 2A (external) and 2B (internal) are the default classes used for commercial production of Nut, Bols, and otehr threaded fasteners. They are the default class unless otherwise specified. they have the same allowance as classes 1A/1B. However, they have a narrower tolerance field. The difficulty of assembly is the same, but the spread between different parts in a production batch is smaller.
• Classes 3A & 3B: These classes are suitable for applications where tight fit and accuracy of thread elements are essential. The maximum diameters of Class 3A threads and the minimum diameters of Class 3B threads are the same (Both have zero allowance). The accuracy is high, but the assembly is difficult.
• Combinations of Classes: The engineer can select any valid class for the male and female threads to achieve his design goals. The valid classes are defined in ASTM B1.1 as follows:
• Classes 2A, 2A, 3B, and 3B are always valid.
• Classes 1A & 1B are valid only for UNC threads with a nominal diameter equal to or larger than 1/4″.

The allowance es should be calculated for external threads with classes 1A and 2A. The allowance of both classes is the same and equals 0.3 times the pitch diameter tolerance of class 2A. It is the function of 3 parameters.

$$\large es = 0.3 \times \left [ 0.0015 \times \sqrt[3]{D} + 0.0015 \times \sqrt{LE} + 0.0015 \times \sqrt[3]{P^{2}} \right ]$$

\begin{array} \large \,es& = 0.3 \times\,[\,0.0015 \times \sqrt[3]{D} &\\ & +\,0.0015 \times \sqrt{LE}&\\ & + 0.0015 \times \sqrt[3]{P^{2}}\,] \end{array}
• The result should be rounded to 6 decimal places.
• ASTM B1.1 lists in a long chart the allowance for each thread size. However, the results of this formula are 100% accurate, and there is no need to browse the chart.
• You can use our Advanced Threading Calculator to obtain the allowance according to a thread description or use the mini-calculator below.

The tolerances TD for internal threads and Td for external threads are derived from the class. The tolerances can be calculated according to the below formulas.

• Td – Tolerance for External Major Diameter
• Td2 – Tolerance for External Pitch Diameter
• TD1 – Tolerance for Internal Minor Diameter
• TD2 – Tolerance for Internal Pitch Diameter
• T Base Tolerance (The tolerance of CLASS 2A pitch diameter is the base tolerance from which other tolerances are derived)
• D – Basic thread diameter.
• PPitch (1/TPI).
• LELength of engagement. (If unknown, the default is 5 * P)
• All input parameters and results are in Inches.

Base Tolerance Formula

$$\large T = 0.0015 \times \sqrt[3]{D} + 0.0015 \times \sqrt{LE} + 0.0015 \times \sqrt[3]{P^{2}}$$

\begin{array} \large \,T& = \,0.0015 \times \sqrt[3]{D} &\\ & +\,0.0015 \times \sqrt{LE}&\\ & + 0.0015 \times \sqrt[3]{P^{2}} \end{array}

(Classes 1A,2A & 3A)

$$\large T_{d(1A)} = 0.3 \times T$$

$$\large T_{d2(1A)} = 1.5 \times T$$

$$\large T_{d(2A)} = 0.06 \times \sqrt[3]{P}$$

$$\large T_{d2(2A)} = T$$

$$\large T_{d(3A)} = 0.06 \times \sqrt[3]{P}$$

$$\large T_{d2(3A)} = 0.75 \times T$$

(Classes 1B,2B & 3B)

$$\large T_{d1(1B)} = 0.25 \times P\,-\,0.4 \times P^{2}$$

$$\large T_{d2(1B)} = 1.95 \times T$$

$$\large T_{d1(2B)} = 0.25 \times P\,-\,0.4 \times P^{2}$$

$$\large T_{d2(2B)} = 1.30 \times T$$

$$\begin{array}{ll} \large T_{d1(3B)}=&0.05 \times \sqrt[3]{P} + &\\ &0.003 \times \frac{P}{D}\,-\,0.002 \end{array}$$

$$\large T_{d2(3B)} = 0.975 \times T$$

The above formulas can be used in most cases. However, ASTM B1.1 lists various scenarios where other formulas or quirky rounding rules apply. Use our Advanced Threading Calculator to get exact results for any thread.

Usage notes for the above formulas:

• The result should be rounded to 6 decimal places.
• Formulas for internal threads are valid only for thread diameters above 1/4″, a pitch between 4 and 80 TPI, and engagement lengths up to 1.5 X D.
• In some cases, ASTM B1.1 dictates special rounding rules.
• You can use the Threading Calculator, which automatically considers all the above rules.

Once the Td, TD, & es values are known, the final limits can be calculated according to the below formulas.

#### Formulas for Limits of a Metric External Thread

$$\large d_{max}=d-{es}$$
$$\large d_{min}=d_{max}-T_d$$
$$\large d_{2max} = d2 – es$$
$$\large d_{2min}=d_{2max}-T_{d2}$$

#### Formulas for Limits of a Metric InternalThread

$$\large D_{1min}=D$$
$$\large D_{1max}=D_{1min}+T_{D1}$$
$$\large D_{2minx} = D_2$$
$$\large D_{2max}=D_{2min}+ T_{D2}$$
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