What Size Conduit for 10/3 Wire?

10/3 wire pulled as individual THHN conductors (three #10 plus one #10 ground) needs 1/2 inch EMT, or 1/2 inch Schedule 40 PVC, at the NEC 40% fill limit. The 4 conductors total 0.0844 square inches (NEC Chapter 9 Table 5); with three or more conductors the raceway may be filled to 40%, so the smallest conduit whose 40% area covers 0.0844 sq in is 1/2 inch EMT.

1/2 inch EMT. Its internal area at 40% fill exceeds the 0.0844 sq in that 10/3 (three #10 plus one #10 ground) occupies. Going one trade size down would exceed 40% and violate NEC Chapter 9 Table 1. If you are running RMC use 1/2 inch; IMC and PVC each have their own internal area, shown in the table above.

Yes. Every conductor in the raceway counts for fill, including the equipment grounding conductor (NEC Chapter 9 Table 1). That is why 10/3 is figured here as three #10 plus one #10 ground: the 4 conductors together, not just the current-carrying ones. Leaving the ground out of the count is the most common conduit-fill mistake.

If you sleeve an intact 10/3 NM cable (Romex) rather than pulling individual THHN, the fill is figured differently: a single cable is treated at the 53% one-conductor limit using the cable's actual cross-sectional area (NEC Chapter 9, Note 9), which usually needs a larger conduit than individual THHN. Most conduit runs use individual THHN conductors, which is what the 1/2 inch answer above assumes.