IEEE Standard 835, IEEE Standard Power Cable Ampacity Tables
IEEE Standard 848, Procedure for the Determination of the Ampacity Derating of Fire Protected Cables
ICEA P-54-440, NEMA Pub. No. WC 51 - Ampacities of Cables in Open-Top Trays.
The National Electrical Code [NEC] requires their own cable sizing for premises wiring.
Refer to the NEC rules to determine building wiring, as this page relates to electronic equipment wiring.
For reference, the ampacity of copper wire at 300C for common wire sizes
14 AWG may carry a maximum of 20 Amps in free air, or 15 Amps as part of a 3 conductor cable.
12 AWG may carry a maximum of 25 Amps in free air, or 20 Amps as part of a 3 conductor cable.
10 AWG may carry a maximum of 40 Amps in free air, or 30 Amps as part of a 3 conductor cable.
8 AWG may carry a maximum of 70 Amps in free air, or 50 Amps as part of a 3 conductor cable.
The wire fusing [melting] current is based on the material the wire is made of, the diameter of the wire and the melting point of the the material.
The wire fusing current of a wire is provided in tables as constant current or as [a larger] current for some given amount of time.
I found this formula used on a few different sites [un-verified]; I=Ad(3/2) @ d is in inches, A is a constant: A = 10,244 for Copper. A = 7,585 for Aluminum.
I have listed a number of values for fusing current in the table above, for selected AWG sizes.