## The Copper Wire Gauge for Electrical Technology

An explanation of the A WG wire gauge system, with some handy tricks for converting between gauge and size.

By Antonio L. Eguizabal, VE7FIF

### Introduction

Insulated copper wire is used extensively in electrical and electronics applications. In amateur radio use, it is predominant. Copper is a metal with excellent thermal, electrical, mechanical and physical characteristics; unequaled in its cost-benefit properties. Hence its widespread use throughout the world of electrotech-nology. Most amateur radio circuits use insulated circular-cross-section (round) copper wire. Presently, in Canada, the US and other countries, the round copper wire is based on the American Wire Gauge (AWG) system. In this article, the basis for this gauge

151 West Osborne Road North Vancouver, BC V7N 2P9 Canada is presented, together with some of its interesting properties.

Sizing of Round Copper Wire

Circular-cross-section, bare copper wire can be sized in several ways. For smaller conductors (up to No. 4/0 or

0000 AWG) it follows the American Wire Gauge.1 For larger conductors, the tendency is to use the cross-section area expressed in circular mils (the area corresponding to a circle of 0.001 inches, or 1 mil, in diameter). The AWG system uses inches and feet and has no direct equivalent in the metric system.

The metric world usually sizes round copper conductors by their cross-section area in square millimeters (mm2) and sometimes uses a system based on the diameter in milli-

### 1 Notes appear on page 23.

meters for small wires.2 In the UK, round copper wire follows the Standard Wire Gauge (SWG)3, which is similar to the AWG but is not always exactly equivalent, as shown in the wire tables of Note 2. To make matters more confusing, other systems are used for other materials, such as the Steel Wire Gauge, the Birmingham Wire Gauge, the Old English Wire Gauge, the old Paris Gauge, and so on. For a history of wire gauges, the reader can consult Note 4.

### The AWG System

The American Wire Gauge was invented by J. R. Brown in 1857 and is also known as the Brown and Sharp gauge. It is the prevalent wire gauge in North America and other countries for solid, round, bare copper wire of diameter less than 0.46 inches. Its use is a defacto standard for Canada and the US, being specified for electrical wiring using copper wire as regulated by the Canadian Electrical Code and the National Electrical Code in the United States.5-6

Together with other gauges such as the ones already mentioned, the AWG system has the property that its sizes represent approximately the successive steps in the process of wire drawing (pulling through a hard steel die of known diameter).

Its numbers are retrogressive—a larger number denoting a smaller wire—corresponding to the successive drawing operations. For example, No. 0 AWG could be the first pass and No. 1 AWG the second pass through a smaller diameter die. Actually, the AWG system starts at No. 0000 (or 4/0 AWG) and stops at No. 50 AWG. The gauge numbers obey a mathematical relation and are not arbitrarily chosen as it may appear at first glance.

The basis of the AWG is a mathematical law. I briefly mentioned the relation in a previous article, which is repeated here for completeness.7 The gauge is specified by two diameters and the law that a given number of intermediate diameters are formed by a geometrical progression. Thus, the diameter of No. 0000 or 4/0 AWG is defined as 0.4600 inches and the diameter of No. 36 AWG is 0.005 inches (see Notes 1 and 2). There are 38 sizes between these two, hence the ratio of any diameter to the next diameter of a larger size is given by:

V 0.0050 4

This is called the progression constant of the AWG system. It can be verified with a calculator by taking the logarithm (any base will do) of 92, dividing by 39 and then taking the anti-log (same base) of the quotient. A good calculator will display as many digits as shown here—or more. My HP-41CV shows 1.122 932 197 when FIX is set at the maximum of 9 digits.

This number has some interesting properties:

a) The square of the progression constant is (1.1229322)2=1.2610.

b)The sixth power, that is the ratio of any diameter to the diameter of the sixth greater number is: (1.1229322)6=2.0050.

c) The fact that b) is so close to the number 2, is the basis of numerous useful relations and computation short cuts.

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