# Unified Screw Threads (UNC/UNF/UNEF): Charts & Formulas

## 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)
0.06 0.073 0.086 0.099 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

Pitch:

• 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. 3=Tight fit, 2=Medium fit, and 1=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

Internal /
External
Nominal
Diameter
Direction
#8-32 UNC UNC undefined 0.164" 32 0.03125" 0.03125" undefined 1 Right hand
1/4 -28 UNF-2A UNF External 0.25" 28 0.0357" 0.0357" 2A 1 Right hand
3/4-20 UNEF-3B UNEF Internal 0.75" 20 0.05" 0.05" 3B 1 Right hand
1-12 UN-1A
Constant Pitch
12 TPI
External 1" 12 0.0833" 0.0833" 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" 0.0357" 2A 1 Left hand

## Possible Combinations (Diameter/Pitch)

The charts below 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 range 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 - Internal Thread
D3 Major diameter, rounded root, internal thread
d Major (Basic) diameter of external thread
d1 Minor Diameter - External Thread
d2 Pitch Diameter - External Thread
d3 MMajor diameter, rounded root, internal thread
n Number of threds per Inch (TPI)
P Pitch (Distance)
Height Parameters
H Height of fundamental triangle
Length Parameters
LE Length of Engagment
Allowance, Deviation, and Tolerances
TD1 Tolerance - D1
TD2 Tolerance - D2
Td Tolerance - d
Td2 Tolerance - d2
Crest / Root Parameters
Fcs Crest width - External Thread
Frs Root width - External Thread
Fcs Crest width - Internal Thread
Fcs Root width - Internal Thread

### 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

All dimensions are in inches. To view the Metric translation, click the Thread Link
Click icon to show Additional columns

Click icon to show Full Thread Data

#### UNF Series Basic Dimensions chart

All dimensions are in inches. To view the Metric translation, click the Thread Link
Click icon to show Additional columns

Click icon to show Full Thread Data