Check your arithmetic. The intermediate results seem to be incorrect, mostly by errors in placement of the decimal point. The calculation of the cross-sectional area of the wire, for example, looks to be about 1000 times the actual value.
Area = pi * (((0.0159 /12)) / 2) ^ 2 = 1.37886E-06.
As has been mentioned, the resistivity of copper that you're using has units of ohm-meter, while your lengths are in units of feet. You need to convert the resistivity to ohm-feet.
This quest has the aroma of an academic assignment. Is this homework?
I the real world, you also need to take termination resistance into account, especially over short distances (where the resistance of the cable itself may be less significant than the terminations).
If you've ever seen a wire that was burned-up from excess current, it's usually burned (or more-burned) at the terminations/connectors.
And most of the time when considering wire gauge, it's the heat we're concerned with rather than the voltage drop.
P.S.
Don't forget it's usually a round-trip... If you are running a toaster or hair dryer at the end of a 100-foot extension cord, you've got 200 feet of wire.