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 has a wire diameter of 0.5 mm or less, the copper alloy containing Ni, or Ni and Fe in an amount of 0.1% by mass or more and 1.6% by mass or less in total, and P in an amount of 0.05% by mass or more and 0.7% by mass or less, with a balance being Cu and impurities, in the copper alloy, a ratio of precipitation of P to solid solution of P being 1.1 or more.