This free-cutting copper alloy contains more than 77.0% but less than 81.0% Cu, more than 3.4% but less than 4.1% Si, 0.07% to 0.28% Sn, 0.06% to 0.14% P, and more than 0.02% but less than 0.25% Pb, with the remainder being made up of Zn and unavoidable impurities. The composition satisfies the following relations: 1.0≤f0=100×Sn/(Cu+Si+0.5×Pb+0.5×P−75.5)≤3.7, 78.5≤f1=Cu+0.8×Si−8.5×Sn+P+0.5×Pb≤83.0, 61.8≤f2=Cu−4.2×Si−0.5×Sn−2×P≤63.7. The area ratios (%) of the constituent phases satisfy the following relations, 36≤κ≤72, 0≤γ≤2.0, 0≤β≤0.5, 0≤μ≤2.0, 96.5≤f3=α+κ, 99.4≤f4=α+κ+γ+μ, 0≤f5=γ+μ≤3.0, 38≤f6=κ+6×γ1/2+0.5×μ≤80. The long side of the γ phase does not exceed 50 μm, and the long side of the μ phase does not exceed 25 μm.