A covered electrical wire comprises a conductor and an insulating covering layer provided outside the conductor, the conductor being a stranded wire composed of a plurality of copper alloy wires composed of a copper alloy and twisted together, and having a wire diameter of 0.5 mm or less, the copper alloy containing Fe in an amount of 0.1% by mass or more and 1.6% by mass or less, P in an amount of 0.05% by mass or more and 0.7% by mass or less, and one or more elements selected from Ni, Al, Cr and Co in an amount of 0.01% by mass or more and 0.7% by mass or less in total, with a balance being Cu and impurities.