The wire gauge you need is a function of several things.
- The acceptable voltage drop or power loss (that appears to be the
only thing considered in the website you linked). The voltage drop (and power loss) is proportional to wire length and inversely
proportional to the cross-sectional area of the wire- in other words
inversely proportional to the square of the wire diameter (assuming constant current).
- The acceptable temperature rise. This is a function of the number
of current-carrying wires bundled together, the environment (maximum ambient temperature
and air pressure or altitude, for example), the insulation type, the
wire type (some types of wire are plated to withstand higher
temperatures than bare copper without corroding).
- Regulatory requirements and other considerations- for example, the
wire may be rated for 200°C insulation, but you might not want the
wire to run that hot.
- Fusing- the fuse or circuit breaker should protect the wire in the
case of faults such as overload or short circuit.
Very short lengths of wire can depend on heat sinking through the ends (indeed, in a vacuum, that may be the main heat loss mechanism), but usually that's not taken into account.
Normally you'd run through a checklist such as the above to make sure ALL the requirements are satisfied simultaneously, so you might find that using PTFE insulated wire allows you to use AWG 18 wire, but because of the voltage drop limitation you'll have to use AWG 12 wire.
How to determine cable sizes in theory
There are well established methods for calculating the required size of cables, based on:
I²R Heating - acceptable conductor temperature before the insulation material is damaged.
For regular PVC-insulated cables, you may assume this as 75°C (V-75.)
Other temperature ratings are possible. In Australia, mains power cable is often rated to 90°C - either because it is 90°C rated PVC, or because it's 90°V rated XLPE.
For special applications, you can get 110°C or 150°C rated cable. For really special applications, you can use metal insulated metal sheathed cable 'Pyrotenax', which is literally fireproof and can be run as hot as you please.
Heat dissipation of cable - depends on the thickness of the cable's insulation, outer surface area of the cable - basically, all the things affecting the cable's "thermal resistance".
Ambient conditions. Cables in circulating air are able to dissipate heat better than those where the heat is trapped inside an enclosure.
There are reports and standards that detail the theoretical calculations of how effectively cables dissipate heat under a variety of conditions. Try ERA report 69.30 Parts III and V for details.
How to select cables in practice
In practice, cable rating information is tabulated into a usable form like the examples below, from the Nexans Olex "Handbook 2013", a catalogue of low-voltage cables. This is simply a look-up table of current-carrying capacity (amps) vs. cable size.
Note all conductor sizes are specified in mm² - conversion to AWG or kcmil is left as an exercise to the reader.
Also note this is for low voltage cables in the sense of mains power cables (240 VAC or 415V three phase) but the same principles apply to extra-low voltage wiring. For heating purposes, the amps are all that matter. Whether the amps in question are 240 VAC amps or 5 VDC amps is largely irrelevant.
For de-rating purposes, you may assume that the inside of a sealed electronics enclosure is something like "enclosed conduit in air" - this is a plastic enclosure with no air circulation.
It is also normal to apply derating factors for the external ambient air temperature. These tabulated ratings are all at 40°C ambient temperature, which is the norm for Australia. A 45°C ambient temperature might translate to a 0.91 derating factor, for example.
Yet more derating factors apply if you are running multiple cables bunched together, as the cables heat each other up.
If you want to be conservative, take the 'enclosed, in air' cable rating, and apply a further 0.65 derating factor, which should cover you for pretty much any possible derating you will experience in practice, due to ambient temperature, cooling (or lack thereof), bunching of cables, etc.
For context, 1.5mm² is the normal size for domestic 10 A extension cables. 2.5mm² is the normal size for building wire (i.e. wiring supplying wall power points.)
Further details
You might consult your local electrical code for further guidance on cable derating factors. In Australia this is AS3008.1.1 Electrical installations - selection of cables. This has tables giving derating factors for various temperatures, various bunchings of cables, and so on.
In the US it might be one of your NEC codes.
Again, these standards are intended to be applied for mains power cabling, but the same physical effects apply to all cables - heating due to 240 VAC amps is the same as 5 VDC amps. There is some minor difference due to thicker insulation on higher voltage cables, which thermally insulates the cable. The skin effect also increases effective resistance (i.e. power dissipation) at AC frequencies. Both these effects are conservative in your favour if you are considering low voltage DC cables.
Cyclic loading
You might notice the above gives no consideration to cyclic loading. If you need a wire to carry a cyclic load, try this table:
Best Answer
Voltage rating applies to the insulation, but there are subtleties.
On very low voltage (like 12V), pretty much any insulation thick enough to stick to the wire will do. On higher voltages, insulation thickness and material type really matters.
For example, the wire you link is a hookup wire for low voltage electronics. In this use case, you want thin insulation, because this makes the wire more flexible, and practical to use. This explains the very low 60V rating. It will be inadequate for your 80 volts.
If the wire is exposed (for example, it runs on the floor and people could walk on it) or if it is exposed to vibrations or chemicals, then of course this has to be taken into account too. Insulation will need to be rated for this.
In your use case, I would use simple 2-conductor lamp cord. It is cheap, readily available, inconspicuous, and robust.
EDIT:
For a 20m run it will most likely be mounted on walls or at least attached to something, so check regulations in your area for things like electrical conduits, etc.
For example, your hookup wire would only be allowed inside an enclosure. Here, as a general rule, wires with hazardous voltage are not allowed to be apparent, which means they have to be inside a conduit, for example:
If it can be touched, walked on, etc, then it has to be a cable. In the above photo, if the wires were cables instead, the T-junction could be omitted, with cables visible. In this case, the conduits would be used more as a convenient way to bunch up the cables and mount them on the wall.