Wire

Wire is a single electrical conductor that may or may not be insulated by a jacket. See Cable for multiple conductors housed within a single jacket.

Sizing

AWG

American Wire Gauge is the standard system for wire sizing in North America. Wire sizes are logarithmically stepped, with a larger gauge signifying a smaller cross section. The formula for calculating diameter of a wire for standard and metric units is as follows, where $d_{n}$ is the wire diameter and $n$ is the wire gauge. Note that this is the diameter of a bare solid-core wire—stranded wire will have the same cross-sectional area, but a larger overall diameter.

$d_{n}=0.005~\mathrm {inch} \times 92^{\frac {36-n}{39}}=0.127~\mathrm {mm} \times 92^{\frac {36-n}{39}}$

Metric

The wire cross section is often given in square millimeters (mm^2). This can be converted to/from AWG for example using this tool (that gives you a lot more bonus information as well), or the table above.

Choosing Wire Gauge

Ampacity

Theoretically, any wire can carry any amount of current, as long as the voltage drop across the wire does not drop the voltage to an unusable level. However if the wire is too small it could heat up to an insane temperature and burn your car to a crisp. Ampacity is the maximum current you can safely pass through the wire. A larger gauge wire will be able to carry more current, but will be heavier.

If the datasheet for the wire you're using lists an ampacity, that makes your job easy. If it doesn't, you can use a wire sizing standard like one of the ones in the Standards section of this page.

Voltage Drop

Voltage drop is the reduction in voltage in a circuit from the source to the load. Since all wires have resistance, there will always be a difference in voltage from one end of a wire to another if current is flowing through it. If the voltage drops too low, electrical devices may not function properly. Since a larger gauge wire will have a smaller resistance per foot, going to a larger gauge wire decreases the voltage drop.

This is easily calculated with the formula $V=IR$, where $V$ is the change in voltage, $I$ is the current running through the wire, and $R$ is the resistance of the wire. When choosing wire gauges, it might be a good idea to choose a fixed percentage voltage drop (say, 5%), and then choose all your wire gauges based on that.

Temperature Ratings

As mentioned above, wires have temperature ratings. How hot a wire gets depends on the type and width of insulation, the wire gauge, whether the wire is in a bundle or by itself, and whether the wire is in free stream air or not. Annoyingly, this is really hard to quantify, so use your best judgement. Consider flexible heat shielding for wiring that gets too close to hot parts of the car (e.g., the exhaust).

Construction

Conductor

Material

Wire conductors are almost always made out of either copper or aluminum. Aluminum has 61% the conductivity of copper, but it has 30% the weight - meaning a bare aluminum wire has half the weight of a bare copper wire with the same resistance. Aluminum wire is also generally cheaper. However, aluminum has a higher coefficient of thermal expansion than copper, and thus expands more under heat. This means it can "creep," resulting in loose connections. Aluminum can also rust, and the resulting layer of Aluminum Oxide could impede the flow of electricity. Aluminum is also a softer metal, and is thus more prone to nicks.

Solid vs. Stranded Wire

Solid conductors are made of one single strand of copper or aluminum, whereas stranded wire is made of many strands of copper or aluminum. Stranded wire is less durable, but its greater flexibility means that solid wire is hardly ever used in automotive applications.

Electrical Characteristics

Voltage Rating

Wire manufacturers will specify a voltage rating, which is the maximum voltage you can apply to the wire. If the voltage rating is exceeded, the insulation could break down and cause a short circuit or a fire. The most common voltage rating seems to be 600V, but if you're working with high voltages this is worth double checking.

Resistance

The resistance of a wire is used to determine the voltage drop across a wire and the heat it outputs (see above). It is often specified in datasheets as ohms per 1000 feet (or the metric equivalent) since the resistance will be larger for longer wires.

Standards

SAE AS50881

SAE AS50881 is the current SAE standard for wiring in aerospace vehicles. The method described in this standard compensates for the number of wires in a wire bundle, what size they are, and how many are carrying current. The older version of this standard is MIL-W-5088.

MIL-STD-975

This is NASA's standard for the selection of standard electronic parts. In Appendix A, Section 3.16, they give a method of finding a wire's ampacity, calibrating for wire temperature rating and the number of wires in a wire bundle. Because it's NASA's wiring standard, it assumes a vacuum, with no heat dissipation due to conduction or convection, so it might be conservative for FSAE use.

IEC 60287

Under this standard, you calculate the wire size based on thermal characteristics of the wire. For Formula SAE use, probably the most useful equations are those marked "in free air", as there are many equations that are for use in underground applications. With the methods described in this standard, you can also calculate the ampacity of multi–wire cables, or even shielded cables, based on the exact materials the cable is made out of.

National Electrical Code

The United States has a National Electrical Code (NEC) which gives a wire sizing table. You might see it quoted online, but it is designed for house wiring, which is generally embedded in the walls and not in free air. As a result, this source might be conservative depending on your application.