A free-cutting copper alloy comprising: higher than 77.0 mass% and lower than 81.0 mass% of Cu; higher than 3.4 mass% and lower than 4.1 mass% of Si; 0.07 mass% to 0.28 mass% of Sn; 0.06 mass% to 0.14 mass% of P; higher than 0.02 mass% and lower than 0.25 mass% of Pb; less than 0.06 mass% of Ni; optionally one or more element(s) selected from the group consisting of higher than 0.02 mass% and lower than 0.08 mass% of Sb, higher than 0.02 mass% and lower than 0.08 mass% of As, and higher than 0.02 mass% and lower than 0.30 mass% of Bi; and the balance being Zn and inevitable impurities, wherein the total amount of Fe, Mn, Co, and Cr as the inevitable impurities is lower than 0.08 mass%; when the Cu content is represented by [Cu] mass%, the Si content is represented by [Si] mass%, the Sn content is represented by [Sn] mass%, the P content is represented by mass%, and the Pb content is represented by [Pb] mass%, the relations of 1.0 ≤ f 0 = 100 × Sn / Cu + Si + 0.5 × Pb + 0.5 × P − 75.5 ≤ 3.7, 78.5 ≤ f 1 = Cu + 0.8 × Si − 8.5 × Sn + P + 0.5 × Pb ≤ 83.0, and 61.8 ≤ f 2 = Cu − 4.2 × Si − 0.5 × Sn − 2 × P ≤ 63.7 are satisfied, in constituent phases of metallographic structure, when the area ratio of α phase is represented by (α)%, the area ratio of β phase is represented by (β)%, the area ratio of γ phase is represented by (γ)%, the area ratio of κ phase is represented by (κ)%, and the area ratio of μ phase is represented by (μ) %, relative to the total area ratio of α phase, β phase, γ phase, δ phase, ε phase, ζ phase, η phase, κ phase, μ phase and χ phase, the relations of 36 ≤ κ ≤ 72, 0 ≤ γ ≤ 2.0, 0 ≤ β ≤ 0.5, 0 ≤ μ ≤ 2.0, 96.5 ≤ f 3 = α + κ, 99.4 ≤ f 4 = α + κ + γ + μ, 0 ≤ f 5 = γ + μ ≤ 3.0, and 38 ≤ f 6 = κ + 6 × γ 1 / 2 + 0.5 × μ ≤ 80 are satisfied, the length of the long side of γ phase is 50 μm or less, the length of the long side of μ phase is 25 μm or less, the amount of Sn in κ phase is 0.08 mass% to 0.45 mass%, and the amount of P in κ phase is 0.07 mass% to 0.22 mass%; and wherein the microstructural parameters are measured according to the methods disclosed in the description. higher than 77.0 mass% and lower than 81.0 mass% of Cu; higher than 3.4 mass% and lower than 4.1 mass% of Si; 0.07 mass% to 0.28 mass% of Sn; 0.06 mass% to 0.14 mass% of P; higher than 0.02 mass% and lower than 0.25 mass% of Pb; less than 0.06 mass% of Ni; optionally one or more element(s) selected from the group consisting of higher than 0.02 mass% and lower than 0.08 mass% of Sb, higher than 0.02 mass% and lower than 0.08 mass% of As, and higher than 0.02 mass% and lower than 0.30 mass% of Bi; and the balance being Zn and inevitable impurities, wherein the total amount of Fe, Mn, Co, and Cr as the inevitable impurities is lower than 0.08 mass%; when the Cu content is represented by [Cu] mass%, the Si content is represented by [Si] mass%, the Sn content is represented by [Sn] mass%, the P content is represented by mass%, and the Pb content is represented by [Pb] mass%, the relations of 1.0 ≤ f 0 = 100 × Sn / Cu + Si + 0.5 × Pb + 0.5 × P − 75.5 ≤ 3.7, 78.5 ≤ f 1 = Cu + 0.8 × Si − 8.5 × Sn + P + 0.5 × Pb ≤ 83.0, and 61.8 ≤ f 2 = Cu − 4.2 × Si − 0.5 × Sn − 2 × P ≤ 63.7 are satisfied, in constituent phases of metallographic structure, when the area ratio of α phase is represented by (α)%, the area ratio of β phase is represented by (β)%, the area ratio of γ phase is represented by (γ)%, the area ratio of κ phase is represented by (κ)%, and the area ratio of μ phase is represented by (μ) %, relative to the total area ratio of α phase, β phase, γ phase, δ phase, ε phase, ζ phase, η phase, κ phase, μ phase and χ phase, the relations of 36 ≤ κ ≤ 72, 0 ≤ γ ≤ 2.0, 0 ≤ β ≤ 0.5, 0 ≤ μ ≤ 2.0, 96.5 ≤ f 3 = α + κ, 99.4 ≤ f 4 = α + κ + γ + μ, 0 ≤ f 5 = γ + μ ≤ 3.0, and 38 ≤ f 6 = κ + 6 × γ 1 / 2 + 0.5 × μ ≤ 80 are satisfied, the length of the long side of γ phase is 50 μm or less, the length of the long side of μ phase is 25 μm or less, the amount of Sn in κ phase is 0.08 mass% to 0.45 mass%, and the amount of P in κ phase is 0.07 mass% to 0.22 mass%; and wherein the microstructural parameters are measured according to the methods disclosed in the description.