Wire:

As you already know, wire comes in many different styles and sizes. I will touch on a few design parameters that you must consider when choosing wire. The most important consideration is the amount of current that will be carried by the wire. The wire's size is indicated by gauge. The most common wire sizes used in car audio range between 4awg and 22awg. The larger the awg (American Wire Gauge) number, the smaller the wire size.

Resistance:

We already discussed resistance. Now you need to realize that all wire has resistance. This is the reason that wire has current limitations. If you remember the formulas from Ohm's law, you will remember P=I^2*R. The power dissipated in wire will be in the form of heat.

For Those Who Refuse to Fuse:

Now let's see what will happen if excess current is passed through a small conductor. We will assume that some imaginary piece of wire (we don't want to destroy a real piece of wire) has .01 ohms of resistance (e.g. a 15 foot long piece of 8 gauge wire) and that wire is connected directly to the positive terminal of the battery (without a fuse... that should scare you). Now let's say that the other end of the wire is allowed to touch to the chassis of the vehicle (which, in most vehicles, is connected to the negative terminal of the battery). The two battery terminals are basically shorted together by the wire (through the chassis). In this situation, a very large amount of current will flow through the piece of wire.

If we wanted to calculate the current flow through the wire, we would use the Ohm's law formula I=E/R. If we use the ideal automotive battery, which is rated at 12 volts, and divide it by the resistance of the wire which is approximately .01 ohms, we get a current of 1200 amps.

I = E/R
I = 12/0.01
I = 1200 amps

Then plug the current into the formula P=I^2*R. We get:

P = I²*R
P = (1200*1200)*0.01
P = 14,400 Watts

This shows that the wire would dissipate 14,400 watts of heat which would melt the wire's insulation and more than likely ignite everything that comes in contact with the wire (fuel lines, other wires, carpet, plastic, insulation). In comparison, the largest burner on your electric stove will not put out that much heat on high!

Note:

We could have simply used the formula P = E²/R but many of you are new to this stuff so I went the 'scenic route'. To prove that it comes out to the same value:

P = E²/R
P = 12²/.01
P = 14,400 Watts

Safety:

Any time that a tap is made off of a power source (battery, fuse block, distribution block...), you MUST put a fuse inline as close to the source as possible. Another thing to keep in mind is that you must insert a fuse inline anytime that the wire size is reduced, such as a tap off of the main power wire for an amplifier, head unit, equalizer... The fuse must be rated to open (blow) well before the wire starts to overheat. A secondary but very important consideration is environment. Is the temperature going to be extreme, hot or cold? Is there anything like oil, grease or solvents that will come in contact with the wire's insulation? All of these things have to be considered to build a reliable, high quality system.

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Note:

If you're using a screen resolution higher than 800x600 and have trouble reading/using the following flash calculators/demos, click on the link below each one to make it fill the frame. Use your back 'button' to return to this page. For the demo with the volume slider, click on the slider handle to lock/unlock the slider. Then move your mouse to set the value.

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Resistance in Speaker Wire:

Many people are told that they need to use very large speaker wire to prevent a noticeable loss in output. For most situations, 16g speaker wire is absolutely fine. In the following calculator, you can see just how little loss you'll have with a given wire size. Keep in mind that 1 dB is generally the minimum difference you'll be able to hear. If the loss is less than 1dB, you'll never hear it.

Quick Reference: This table shows the amount of current flow which will cause a 1/2 volt drop in a 15 foot run of cable. Many people consider 1/2 volt to be the maximum acceptable voltage loss in a system's main power wire. The 'total amp power' is the total maximum unclipped RMS power output‡ of all of the amplifiers combined. It is based on 60% efficiency (for class AB amplifiers) and a battery voltage of 13.8 volts.

‡ For all of the calculators and tables on this page, unless otherwise noted, 'max power' is the RMS power output when the amplifier is on the threshold of clipping.

Maximum Power for a Given Wire Size: If you have a power wire in your vehicle and want to know how much power you can run on it, use the following calculator. If you don't know if you have class A/B or class D amplifiers, leave the efficiency at 50%.

1. Enter the total power output of all of your amplifiers, length of the power wire, wire gauge you intend to use, battery (charging system) voltage and amplifier efficiency below.
2. It will calculate the total voltage drop you can expect in your main power wire at full power output.
3. Note: Class A/B amplifiers (most amplifiers) are generally 50-60% efficient at full power. Class D amplifiers are about 70-80% efficient at full power. Both are much less efficient at less than full power.
4. Notice how the current draw increases as the efficiency decreases (and vice versa).

Note:

If there was a warning of too few circular mils in the calculator above, the wire that you've chosen may have problems with overheating at full power. You will get this warning when you punch in the numbers for something like a short piece of 8g wire to go between the distribution block and the amplifier. Some people use a single strand of 8g wire to make the connection between the dblock and an 800 or 1000 watt amp. Even though the voltage drop in that short piece of wire may not be significant, the power dissipation may be sufficient to soften/melt the insulation. The value of 300 circular mils per amp of current is somewhat arbitrary and may lead to some arguments but it is a safe value.

Another note:

I know that a lot of people find this page when searching for wire current carrying capacity for AC circuits. The voltage drop given by this calculator is for one conductor (such as the power wire from the battery to an amplifier). For 2 conductors (such as are used for 120 volt equipment) the voltage drop would be twice the values given by the calculator.

Oxygen Free Copper:
< RANT >

As you have probably noticed, wire designated as OFC wire usually has a clear insulation and the wire is bright and shiny underneath the transparent insulator. Well... It is nice and shiny for a while but after a short time (actually from the time it is drawn), it starts to oxidize (unless the wire is kept in an oxygen free atmosphere). When copper oxidizes, it becomes a less effective conductor. This means that, in time, the wire's current carrying capabilities will become significantly reduced. The problem is made worse by having many very small conductors. This creates even more surface area which makes the oxidation process even more efficient. In my opinion, if you are designing a system of any type for long term use, I think the better choice is a 'tinned' copper wire. In this type of wire, the copper is plated with tin (maybe a lead/tin alloy) or similar conductor which will not oxidize as quickly and never as completely as the bare copper. As a side note, this has nothing to do with the copper being 'oxygen free'. It has everything to do with the fact that the wire is unprotected (untinned) and is finely stranded. I used OFC wire in this example because most OFC has many fine unprotected strands.
< /RANT >

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TECH TIP

Wire Connections and Resistance:

Whenever making connections, make sure that they are tight. If you're making crimp connections, try to pull the wire out of the connector. If you can pull the wire out of the connector, it wasn't crimped good enough. If you are inserting the wire into a terminal block, tighten the screw down tight. If there is a bad connection and a sufficient amount of current flow through the junction (wire to terminal block), the block will heat up and possibly do irreparable damage to the terminal block or the printed circuit board (if the terminal block is on your amp).

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Calculating Resistance and Cross Sectional Area

Calculating Resistance:

At some point in time, you may need to determine the resistance in a length of wire but you may not have a reference book available. This section will help you to calculate resistance for different wire sizes and lengths. To make quick calculations with an easy reference I use 10g wire as the starting point. It's resistance is approximately 1 ohm per thousand feet of wire length which makes it easy to remember. For non critical calculations, I round it to 1 ohm/1000 ft or 0.001 ohms/foot of wire. If you have a 15 foot run of 10g wire and want to determine the resistance in that run of wire (like the calculator does above), you simply multiply the resistance per foot by the length of the wire.

Resistance = .001*15

Resistance = .015 ohms

 

Different Wire Gauges:

The previous calculation is great if you're using 10g wire but what if you have a different wire gauge. Although wire resistance can be calculated using a logarithmic scale, I'm going to keep it simple here and use a simple multiplier. For each single digit change in the gauge, the resistance changes by a factor of ~1.26. This means that an 11g wire would have a resistance of approximately 1.26 ohms per thousand feet of wire (remember that we're using 10g wire as a reference and it has a resistance of 1 ohm per thousand feet). A 9g wire would have a resistance of ~.79 ohms per thousand feet (1 ohm/1.26). You can easily step through the wire sizes by continuing to multiply each consecutive value by 1.26. If you have to calculate the resistance of a wire with a significantly larger or smaller gauge (like 4g power wire), you can use the following formula:

For 4g wire:

Resistance = 1/1.26^(difference between 4g and 10g)

Resistance = 1/1.26^6

Resistance = 1/4 ohms per 1000 feet of wire

Resistance = .25 ohms per 1000 feet of wire (or 0.00025 ohms per foot)

Or for 16g wire:

Resistance = 1*1.26^(difference between 16g and 10g)

Resistance = 1*1.26^6

Resistance = 1*4 ohms per 1000 feet of wire

Resistance = 4 ohms per 1000 feet of wire (or 0.004 ohms per foot)

Or for 20g wire:

Resistance = 1*1.26^(difference between 20g and 10g)

Resistance = 1*1.26^10

Resistance = 1*10 ohms per 1000 feet of wire

Resistance = 10 ohms per 1000 feet of wire (or 0.01 ohms per foot)

 

To determine the voltage drop at the current that you expect to pass through the wire, you can use the Ohm's Law formula V=I*R. V is the voltage drop across the piece of wire. I is the current flow through the wire. R is the resistance of the length of wire. If you have 15 feet of 4g power wire and your amplifier will draw 150 amps max...

Voltage Drop = current flow * (length of wire in feet * resistance per foot)

Voltage Drop = 150 * (15*.00025)

Voltage Drop = 150 *.00375 ohms

Voltage Drop = .563 volts at 150 amps of current

 

Calculating Wire Diameter and Area:

Here in the US, we use the AWG (American Wire Gauge), circular mils and square mils. In most other parts of the world, they use mm². I'll try to touch on each of these.

Solid Wire Diameter:

This section will address the diameter of solid wire. Stranded wire has air spaces between conductors and different combinations of different gauge strands will result in different overall diameters. Keep in mind that, in the following description, we are talking about the area of the wire in a circular shape. This means that the total cross sectional area is doubled when the diameter is increased by a factor of 1.414.

OK... For a reference that's relatively easy to remember, lets use 10g wire again. It's ~0.1" in diameter. If we go up in wire size 6 sizes again (to 4g), the diameter is going to be double the 10g wire. The multiplier is ~1.123 per gauge.

Diameter = .1*1.123^(difference between 4g and 10g)

Diameter = .1*1.123^6

Diameter = .1*2.005

Diameter = approximately 0.2" in diameter

Until now we've only discussed the diameter of the wire. The cross sectional area of round wire is the one-half of the diameter (the radius) squared then multiplied by Pi (r²*3.14). For some conductors like buss bars and circuit boards, you won't have a wire gauge or diameter to use to see how much current a conductor can handle. Circular mils, square mils and mm² allow us to express the cross sectional area and therefore calculate the resistance for the conductor. It has another advantage over simply stating the diameter of a conductor in that it doesn't matter if the wire is stranded or solid. If a cross sectional area is given in in circular mils, square mils and mm², spaces between conductors are no longer a factor.

Circular Mils:

One 'mil' is one thousandth of an inch. A wire with a cross sectional area of 1 circular mil has a diameter of .001". If we need to calculate the circular mils for a 10g wire, we simply square the diameter in mils. Since the 10g wire has an approximate diameter of .1" or 100 mils, we square 100 and get 10,000 circular mils. 10g wire actually has a cross sectional area of 10,384 circular mils but for car audio appliciations, 10,000 circular mils will be close enough and easy to remember.

Note:

Various wire tables list slightly different values for circular mils and the diameter of the different wire sizes. The values here are a rough average of the various tables I've found.

Circular Mil Foot:

A circular mil foot is a piece of wire with a cross sectional area of 1 circular mil and a length of 1 foot. To calculate the resistance for a length of wire, there are a couple of things you need to know. The first, cross sectional area in circular mils, has been discussed. The second, the length, is known (15 feet in this example). And the Third is the Specific Resistivity for the conductor. The Specific Resistivity is the value of resistance for a circular mil foot of wire. For copper, the SR is 10.37. To determine the resistance for a 15 foot long piece of 10g wire we can use the following formula:

Resistance = SR*(length of wire/cross sectional area in circular mils)
Resistance = 10.37*(15 feet/10384 circular mils)
Resistance = 0.015 ohms for a 15 foot length

For 4g wire:

Resistance = SR*(length of wire/cross sectional area in circular mils)
Resistance = 10.37*(15 feet/41534 circular mils)   (4g wire has 41534 circular mils)
Resistance = 0.00375 ohms for a 15 foot length

As you can see, we got the same resistance for the 15 foot long piece of 10g wire as before (with an entirely different method). If you were using a different type of wire like silver, gold or aluminum, the specific resistance would be different. You should also know that the SR used here is for copper at or near room temperature (~70F).

Square Mils:

Square Mils are similar to circular mils in that their outer dimensions are again 1 mil but this time we're talking about the area of a square instead of a circle. This makes a square mil slightly larger than a circular mil. The conversion factor to convert from one to the other is:

1 circular mil = .7854 square mils

1 square mil = 1.273 circular mils

Square Millimeters:

In Europe and other parts of the world, they use a somewhat less confusing system to express wire cross sectional area. They express it in square millimeters(mm²). For square conductors, it is simply the height times the width of the conductor in millimeters. For round conductors, it's the radius (half the diameter) of the conductor squared then multiplied by Pi.

For example a 10g conductor with a diameter of ~2.6mm:
Area of the conductor = radius of conductor squared*Pi
Area of the conductor = R²*3.14
Area of the conductor = 1.3²*3.14
Area of the conductor = 1.69*3.14
Area of the conductor = 5.3 mm²

The following diagram shows the relationship between a piece of solid round wire and a piece of square copper stock with the same area (and therefore the same resistance for a given length).

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Square Millimeters to Circular Mils:

 

To convert from mm² to circular mils, multiply by 1973.

For 10g wire:
5.3 mm² * 1973 = 10457 circular mils

The answer we got (10457) is a little off from the actual value of 10384 circular mils for 10g wire but that's because we didn't have enough significant digits for the area of the wire. If we'd used the more accurate value of 5.26, we'd have been closer to the actual cross sectional area. Either value is close enough for this tutorial and anything related to car audio.

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Solid Wire Table:

The values in the first table are based on a value of 10,000 circular mils for 10g wire. I skewed the values slightly so you could see how the diameter and cross sectional area of one wire relates to the others. Remember that 10g wire is the reference. The second table is more accurate. The values on either table would be good enough for calculations in car audio applications.

The Following calculator will allow you to enter whole and fractional wire gauges (fractional wire gauges are used for magnet wire) between 0000 and 46 gauge. It also allows direct current input instead of having it calculated like the calculator above. After all of the material we just covered, it should be self-explanatory. Due to different rounding on the spreadsheet and the calculator, the values will differ slightly between the calculator and the table above.

Definitions:

 

PVC:

PVC is short for PolyVinyl Chloride. Different formulations make the material soft and suitable for wire insulation or hard and suitable for water and drain pipe.

Thermoplastic:

A thermoplastic is a plastic that can be softened by heat which allows it to be easily formed. Different types of thermoplastics are PVC, Polyethylene and Polypropylene.

Latex:

A light colored fluid produced by various plants and used to make latex rubber products.

Common Wire Designations:

The following designations will help you understand the properties of thhn and other wire types. Keep in mind that these are general properties. There will be exceptions to these rules. Before you use any wire in a critical situation, consult the datasheet from the wire's manufacturer.