**In this article, BoatHowTo expert ****Nigel Calder**** explores the rich history of sizing conductors - and why we have such unintuitive measures such as the AWG (American Wire Gauge) system. Throughout history, politics often trumped science.**

This article was initially published in the NMEA's Marine Electronics Journal

Conductor sizing is critical to the performance and safety of electrical systems. Undersized conductors create excessive resistance which results in **voltage losses** from one end of the conductor to the other (voltage drop) and, in extreme cases, temperatures high enough to melt insulation and **start fires** (most notably if the circuit does not have adequate overcurrent protection - circuit breakers and fuses).

In the boat world we have various tables that help us determine an appropriate conductor size for any application. In the USA the best known are the tables developed by the **American Boat and Yacht Council (ABYC)** and found in the** E-11 standard **(*AC and DC Electrical Systems on Boats*). In Europe, we have the tables developed by the **International Organization for Standardization (ISO)** and found in the **13297 standard** (*Small Craft – Electrical Systems – Alternating and Direct Current Installations*).

And of course, for the lazy ones among us, there are the BoatHowTo Wire Size Calculators which make determining the right size of conductors very easy.

A quick perusal of the standards will reveal conductor sizing that is variously referenced in terms of *American Wire Gauge (AWG)*, *diameter*, *Circular Mils (CM)*, and *cross sectional area (CSA)*, with additional references to *Society of Engineers (SAE)* sizing. Imperial (inches) and metric (millimeters) units are both used. It can be confusing, especially given that some of these sizing methodologies are counter intuitive, notably the AWG and SAE systems in which the smaller a conductor the larger its ‘gauge’ number.

Let’s unpick these various sizing methods, starting with American Wire Gauge.

## AWG - The American Wire Gauge System

To create a conductor of a given diameter, a larger rod is drawn through a ‘*die*’ with a conical mouth that tapers down to an exit hole of a given size. If the process of thinning and elongating the rod is too aggressive, the rod will break: i.e. there is only so much of a diameter reduction that can be achieved by drawing the rod through a single die. For smaller diameter conductors the **rod must be drawn through a succession of ever smaller dies**.

Before the introduction of machinery, the thinning and elongation was done by hand, pulling the rod through a *draw plate* containing the various tapered holes. **There is evidence that this technique was used to make gold ornaments in ancient times**; wire as fine as 32 gauge in modern terms has been found in Roman jewelry. The draw plate technique was described in detail in the Medieval era.

Through trial and error it was found that **an approximate 11% reduction in rod diameter** when passing through each successive die allows for a margin to protect against breakage. Over time, manufacturers developed sets of similar (but by no means identical) dies for making different wire sizes, accompanied by a ‘gauge plate’ used to show customers the available diameters.

In the various gauge systems, a gauge number (e.g. 18) describes the number of dies through which the conductor has been pulled in order to reduce it down to a given diameter.

In the 1830’s a British mechanical engineer developed an instrument capable of measuring diameters to a millionth of an inch. These new instruments created the possibility for standardizing gauges. In the UK this resulted in the **British Standard Wire Gauge** (SWG, still in use in the UK and in some of its former colonies).

In the USA the resulting **American Wire Gauge (AWG)** is based on a set of dies developed in 1855 by the Brown and Sharpe company (AWG is also sometimes known as B&S). The **Society of Automotive Engineers (SAE)** has its own set of die sizes which, for a given gauge number,** typically result in a somewhat smaller conductor diameter than in the AWG system**. I have been unable to determine the historical origins of this system.

### Where Zeroes Ought to Count

In the early days **the original rod (i.e. before passing through any dies) was specified as #1**. Ideally this would be the starting point for any system but by the time things began to be standardized there were mechanisms - first water power and then steam power - that enabled ever larger rods to be drawn through dies, resulting in sizes larger than #1. These were accommodated by going first to zero (‘0’) and from there stacking zeros for each increase in diameter – e.g. 0000. These multiple zero sizes can also be described as 1/0, 2/0, 3/0, 4/0 etc., **with the zero pronounced as ‘ought’** – e.g. 00 or 2/0 is pronounced ‘two ought’. In the AWG system there are 40 gradations from 4/0 down to #36, with 4/0 being 0.46 inches in diameter and #36 being 0.005 inches in diameter. The British system begins at 7/0, with a diameter of 0.5 inches, and runs down to #50, with a diameter of 0.001 inches.

If, using the AWG system, you divide 0.005” (the smallest conductor size) into 0.46” (the largest conductor size) you get 92 – i.e. the ratio of the smallest wire gauge to the largest is 1:92. There are 39 steps (changes in die size) between 4/0 and 36 gauge conductors. Based on these numbers, the AWG standard (now ASTM B258-02) defines the ratio between successive sizes to be the 39^{th} root of 92, or 1.1229318. Moving up in conductor size you multiply a given diameter by this to find the next gauge size diameter. Going the other way, any given gauge diameter is multiplied by the reciprocal (0.890526) to find the next lower diameter.

I was pretty good at high school math, but this is nuts! Why do we have to make simple things so complicated?

There are a couple of useful rules of thumb that came out of this:

- For every three ‘step’ changes (e.g. #16 to #13) the
*cross-sectional area*of a conductor doubles or halves (depending on which way you go). Put another way, two 16 gauge conductors have about the same cross-sectional area (and hence amp-carrying capability) as a single 13 gauge conductor (if you can find a 13 gauge conductor; standard sizes tend to go in even numbers until we get to large conductors). - If the
*diameter*of a conductor is doubled or halved, the gauge number will change by 6 (e.g. #10 is about twice the diameter of #16), with a quadruple impact on the cross sectional area and as such resistance and ampacity.

### Stranded Conductors

Because of the air spaces between strands, and because the gauge size is based on the copper in the conductor, stranded conductors of a given gauge size always have a larger diameter than solid conductors, with the increase depending on the number of strands.

Stranded wires are specified with three numbers:

- The gauge size of the conductor (how much copper is in it)
- The number of strands
- The gauge size of a strand.

For example, a 16 AWG 26/30 stranded conductor is a 16 AWG conductor with 26 strands of 30 AWG wire.

The ABYC has three classes of stranding, Type 1, 2 and 3, with Type 1 being solid conductors, Type 2 limited stranding, and Type 3 fine stranding. The ISO has two classes, Type A and B, which correlate with the ABYC’s Type 2 and 3. This is one of the few areas where the standards are more-or-less identical.

There are a dozen or more ways of making stranded conductors depending on the lay of the strands (one catalog I looked at had 16 different variations of stranded conductors for most conductor sizes). Neither the ABYC nor ISO take a position on this although the minimum stranding requirements do effectively result in specific construction methods which vary with the size of the conductor.

Phew! Let’s try something a little simpler. Or maybe not…

## Cross-Sectional Area of Conductors

Given that the amp carrying capability of a conductor, its ‘ampacity’, is directly related to its cross sectional area, a more useful way to specify conductor sizes would seem to be a system based on **cross-sectional area**. The formula for this is the one we learned in high school, where and r² is the radius (half the diameter) multiplied by itself. Let’s say we have a 1/0 AWG conductor which, by definition, has a diameter of 0.3249 inches. The radius is half the diameter, i.e. inches. If we multiply this by itself, we get 0.02639 square inches. If we now multiply by we get square inches. We can see immediately that these are not easy numbers with which to work!

### Square Mills...

The first step to simplifying things is to convert diameters into thousands of an inch, or ‘mils’, rather than inches. Our starting point diameter, multiplied by 1,000, becomes 324.9 mils and our ending point area becomes 82,940 square mils (note that because we have squared the radius this ending point number is 1,000 x 1,000 = 1,000,000 times higher than our CSA in square inches). So far so good, but now we do something else that’s also a bit nutty!

### ... are not Circular Mills

Somewhere in the historical process I guess the assumption was made that electricians were not competent to determine a radius from a diameter (i.e. divide by 2) and to then square the radius and apply to it. The conventional formula for cross sectional area was ditched and instead the diameter is simply squared (multiplied by itself) to arrive at something known as ‘circular mils’. In our case the 1/0 diameter of 324.9 mils multiplied by itself becomes 105,560 circular mils. The practical effect of this is to arrive at 4 circular mils for every 3.14 square mils – i.e. **wire sizing in circular mils always modestly exaggerates the CSA (by ~13%)**.

### How About Metric Instead?

As early as the 1600’s a French clergyman proposed a universal system of measurement **based on the decimal system** (multiples of 10). We owe its adoption to the French Revolution of 1789 and a 1790 request from the National Assembly to the French Academy of Sciences. **The core unit was to be a measurement of distance equal to one ten millionth of the distance from the north pole to the equator on the line of longitude running through Paris.** This was defined as a *metre* (*meter* in the U.S.; from the Greek word for *measure*). All other measures of volume and weight were to be derived from the metre.

It took years to measure a long enough arc (from Barcelona to Dunkirk) to determine the length of a meter, and there were errors in the measurement of the earth’s circumference (the surveyors did not understand the flattening of the poles), but to this day the length they came up with is the length of a meter. **The metric system was officially adopted by the French government in 1795.** It had its ups and downs, and was at one point banned by Napoleon, but gradually won widespread recognition, becoming the basis for the **International System of Units (SI units)** now used by much of the world. The British considered metrifying wire sizing in the late 1800’s but decided not to, at least in part because the system was developed by the French!

## Square Millimeters Cross-Sectional Area

One of the benefits of measuring in meters is the meter is already subdivided into 1,000 millimeters so we don’t need to go through the mils exercise (multiplying inches by 1,000) to arrive at easily grasped numbers. An AWG 6 conductor, for example, with a diameter of 0.162 inches (162 mils) has a diameter of 4.11 mm.

**In the metric wire sizing system, the diameter is divided by 2 to find the radius and the full formula is applied to arrive at the CSA.** If we want to derive an exact equivalence between AWG and metric conductor sizes, we have to go back to the defining conductor diameters in the AWG standard, which are not published in most conductor sizing tables (including those in ABYC E-11 and ISO 13297), convert these to millimeters, divide by 2 to get the radius, and then apply the formula. This gives us the CSA of the AWG conductor in mm². In the case of our AWG 6 conductor with a diameter of 4.11mm, the radius is 2.055 mm which, if squared and multiplied by , becomes 13.27mm². Unlike the AWG circular mils number, this is the actual CSA of the conductor.

Unfortunately, if we go through this exercise of converting AWG conductor sizes to metric we discover there is neither a good match with many standard metric conductor sizes, nor any kind of a universal ‘factor’ we can apply to correct for this. **We discover that for many tables in which metric equivalences are given for ABYC conductor sizes, the CSA can vary by as much as 21%.** In general, but not always, in these tables the metric conductors have more copper, in which case the metric cable has a greater ampacity, but for some commonly published correlations the metric conductor has up to 9% less copper, which could, for example, make a substantial negative difference to system performance if a system is being designed to accept up to a 10% voltage drop.

## Sizing Busbars

A recent addition to the ABYC’s E-11 standard, describing a mechanism for sizing custom busbars, tacitly recognizes that the metric system of calculating an accurate CSA makes more sense for sizing conductors. The process described in Appendix 3 of E-11 starts by calculating the cross-sectional area of the busbar in square millimeters (mm² = length x height in mm for rectangular busbars). Adjustments are then made for any fastener holes in the conducting path with the final ampacity determined by several factors we have not addressed here such as the lowest temperature rating of the insulation of attached conductors and whether or not these conductors pass through an engine room.

The sizing process gets complicated for busbars with a CSA that exceeds 107mm² (ABYC 4/0). There is a somewhat convoluted process to enable the existing ABYC ampacity tables to be used in order to calculate a busbar’s ampacity.

These various conductor and busbar sizing complications are a result of the fact that, from a historical perspective, standardization is a recent phenomenon and all too often it proceeded by canonizing a local convention as opposed to developing an optimized methodology. For example, British scientists were well aware when the British Standard Wire Gauge was set in stone that the metric approach made more sense, but not for the first or last time, politics trumped science!

Very interesting read Nigel.

I am interested in the brief note on busbars.

I am looking to install a 3kw inverter on a 12V system to run 19,000BTU air conditioner plus hot water heater.

What is the best material to use for a marine application, not in the engine room and able to carry something like 150 – 200 amps with a surge draw say 3-4 times that?

There would be 6 fasteners holes in the Busbar.

Many thanks and I really enjoy your stuff!

John

Here is a reply from Nigel who can’t log in right now:

John,

All busbars in marine applications should be copper, preferably tin plated for corrosion resistance.

The ABYC sizing procedure, which was added as an appendix to the latest draft of E-11, uses the following method to estimate the maximum allowable capacity for copper busbars:

1. Calculate the cross-section of the busbars in mm2. If the busbar has holes in the conducting path, subtract half the value of the hole diameter from the width of the busbar.

2. The temperature rating of the busbar corresponds to the lowest temperature rating of conductor insulation, of all conductors attached to the bar; and if the busbar is inside or outside the engine space.

3. The ampacity tables are used to determine the ampacity of a conductor with that cross-sectional area and that insulation temperature rating, in or outside an engine compartment.

Of course, you want to go in the other direction, from amps to CSA! In your case, you can ignore the inrush loads as these are very short term. You need to determine the highest running load and then you can use the BoatHowTo wire size calculator to determine the minimum cross-sectional area (CSA) in mm2 and work backwards from there (e.g., put in a busbar depth, and from this derive the width, and then adjust for any holes).

If, for example, we assume your 3,000W inverter is running at full load on a 12V system the nominal input amps are 3,000/12 = 250A. We should build in an inefficiency factor for the inverter – let’s say 80% efficiency – which gets us to 250/0.8 = 312.5A. Let’s assume an engine room, and we will be conservative on attached conductor temperature insulation and assume 90C. We assume a single conductor (no bundling). In this case we don’t care about voltage drop (we just want to determine ampacity) so we reduce the circuit length in the BoatHowTo wire sizer until we see that the wire sizing at the bottom of the calculator is determined on ampacity and not voltage drop. The wire size calculator gives us a minimum CSA of 107.21mm2 which will then need to be adjusted for any holes.

Nigel

Thanks very much Nigel for your comprehensive reply. Makes a lot of sense and is easy to calculate.

Didn’t t think of the inefficiency factor !!

Great work you guys.

John

In this article ” The Crazy World Of Conductor Sizing-The Origins of the AWG System” under the section “Square Millimeter Cross Sectional Area” in the first paragraph, it states that the diameter of an AWG 6 conductor is .162(162 mils) and had a diameter of 4.11 mm diameter. Did you pull that 4.11 from the attached chart, or is there a mathematical formula to get from .162 to 4.11mm?

Thank you for this article.

Best regards,

Ted Austin

Ted,

Given that there is a mathematical relationship between the different gauge sizes on the AWG side (see below), I would think there must be a mathematical relationship with the mm sizing but this is way beyond my pay grade to work out! I’ll bet Jan can figure this out!!

Nigel

Hi Ted,

The factor to calculate between mils and mm is 39.37. So 162 mils times 39,37 equals 4,1148 mm.

Best

Jan