How to calculate thickness of cable based on material and current?
There are some topics you should pay attention concerning the cable thickness selection: the voltage dropout, cable heating, electro-magnetic interference, impedance matching.

The maximum allowed voltage dropout is a good parameter to calculate the cable thickness. In most situations this is the limitation factor and may define alone (without the need to calculate the other factors) the cable thickness.

\$ V_{drop} = R_{cable} \times I \$

\$ R_{cable} = \dfrac {p \times length}{CrossSectionArea}\$

Where p is the material electrical resistivity

For a round cable:

\$ R_{cable} = \dfrac {p \times length}{\pi \times radius²}\$

Joining the equations we have that the thickness should be at least:

\$ radius &gt;= \sqrt{ \dfrac {p \times length \times I}{V_{drop}\times \pi}}\$

Assuming that a voltage drop of 0.5(v) is allowed and you'll be using a 2 meters copper cable (p=1.68×10−8) for a maximum 16(A) current:

\$ radius &gt;= \sqrt{ \dfrac {1.68×10^{−8}\times 2 \times 16}{0.5 \times \pi}}\$

\$ radius = 0.59 mm \$

\$ diameter = 2 \times radius = 1.18 (minimum) \$

From this AWG table we have that a cable of AWG-thickness of 11 has a diameter of 2.3mm, that is enough for your application.

The table also states that this AWG 11 can carry over 12(A) for what they call "Maximum amps for power transmission". This is a lower number than the one we calculated, but we should pay attention that this is a general advice for any cable length, not for a specific 2 meters cable (which I supposed in this calculation).

The cable heating is a little harder to calculate. You'll need information on heat dissipation characteristics of the environment and the cable: temperature, air flow, sunlight incidence, cable thinness, cable material, insulator layer and even the cable color (black cables heat up faster but also cool faster).

In general the cable insulation has a good thermal protection (around 80 Celsius degrees) which is enough for most cases. You should pay attention only if your cable will go through some heat source. In this case a thicker cable with a better insulator can stand up better.

Unfortunately there is differences among AC and DC current for cable selection. If you're going to transport AC current, a thinner cable may limit the maximum frequency you can carry, above which the signal may start degrading due Skin Effect as @TokenMacGuy noted . Lucky this is not the case with DC.

The last topic I said that could interfere with the cable thickness selection is the impedance matching. For more precise circuits, the resistance from the cable can make a huge impact in the power transmission. This problem arises mainly when there is a huge current, more than 100 (A), or the load resistance is really low, as speakers with 8 or 4 ohms. In this case a thicker cable with a lower resistance is desirable.