How many amps can 16 gauge wire carry?

16 AWG copper wire is not used for house circuits. As a cord it is rated 13 A, and as fixture or control wire it may be protected at no more than 10 A.

16 AWG wire ampacity

16 AWG copper and aluminum ampacity at 60, 75 and 90 °C, up to three current-carrying wires at 30 °C (86 °F) ambient and the rating as an extension cord
RatingCopperAluminum
60 °C, NM-B—not made
75 °C—not made
90 °C18 Anot made
As a cord13 A—
01020Ampacity, ARating60 °C, NM-B75 °C90 °C90 °C, Copper: 1818
16 AWG ampacity by temperature rating.

16 AWG copper may be protected by a breaker of no more than 10 A, whatever its ampacity column says.

16 AWG wire size and resistance

16 AWG bare conductor size and copper resistance at operating temperature. The diameter is the nominal AWG value; stranded wire of the same size is slightly larger.
Diameter, AWG nominal0.0508 in. / 1.29 mm
Area2,580 cmil / 1.31 mm²
Copper resistance5.000 Ω per 1,000 ft

What 16 AWG wire is used for