Where I live, Code requires 4 wires for 220. 2 hots, 1 ground and 1 neutral.
Ummm... What? 110V has hot, neutral, and ground. 220V has two hots and a ground - no neutral.
Further, as 220V drops the amperage the wire size required drops as well. So likely that the same size wires will work.
If the original 110V circuit is dedicated, it COULD be as simple as a new breaker on the one end and a new plug on the other end. But not enough information by the OP to tell if that is the case.
If the original 110V circuit is part of a series, then new wire will have to be run and price will also depend on distance of the run and accessibility to run new wires.
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