Rolled steel bar or rolled wire material for cold-forged component

A rolled steel bar or rolled wire material for use in a cold-forged component and having a prescribed chemical composition, wherein Y1 and Y2 represented by Y1=(Mn)×(Cr) and Y2=0.134×(D/25.4-(0.50×√(C)))/(0.50×√(C)) satisfy Y1>Y2, the tensile strength thereof is 750 MPa or less, the internal structure thereof is a ferrite/pearlite structure, and the ferrite fraction constitutes 40% or more of the internal structure.