Free-cutting steel and manufacturing method thereof

A free-cutting steel comprising:

• a composition of, in % by mass,
• 0.15% or less of C,
• 0.5% or more and 2.0% or less of Mn,
• 0.200% or more and 0.650% or less of S,
• more than 0.01% and 0.05% or less of O,
• 0.05% or more and 2.00% or less of Cr,
• 0.02% or more and less than 0.10% of Pb,
• 0.005% or more and 0.015% or less of N,
• with an A value defined by a following formula (1) satisfying 4.0 or more and 20.0 or less, and
• a remainder being Fe and unavoidable impurities;
• and
• a microstructure with 1000 or more sulfide particles with an equivalent circle diameter of less than 1 μm per mm2, 500 or more sulfide particles with an equivalent circle diameter of 1 μm or more and 5 μm or less per mm2, and 1000 or more Pb particles with an equivalent circle diameter of 1 μm or less per mm2,
• wherein
• A value=(Mn+5Cr)/S (1)
• here, symbols of elements in the formula (1) indicate contents, in % by mass, of the elements.