A steel for induction hardening consisting of, as a chemical composition, by mass%: C: 0.40% to 0.60%; Si: 0.01% to 1.4%; Mn: 0.2% to less than 1.0%; Cr: 0.01% to less than 0.5%; Al: 0.11% to 0.17%; S: more than 0.03% to 0.07%; N: 0.0030% to 0.0075%; P: less than 0.05%; B: 0% to 0.005%; Mo: 0% to 0.2%; Ni: 0% to 1.0%; Cu: 0 % to 1.0%; Ca: 0% to 0.005%; Mg: 0% to 0.005%; Zr: 0% to 0.005%; Rem: 0% to 0.005%; Ti: 0% to 0.2%; Nb: 0% to 0.2%; V: 0% to 0.35%; Sb: 0% to 0.015%; Te: 0% to 0.2%; Pb: 0% to 0.5%; Bi: 0% to 0.5%; and the remainder consisting of Fe and impurities, wherein the chemical composition satisfies Expressions to , at a 1/4 position of a diameter of the steel, an area fraction of AlN having an equivalent circle diameter of more than 200 nm is 20% or less of an area fraction of all AlN having an equivalent circle diameter of 40 nm or more, and at the 1/4 position of the diameter of the steel, a number density of Mn sulfide-based inclusions having a maximum diameter of 0.3 μm or more and 10 μm or less is 100 pieces/mm 2 or more and 2500 pieces/mm 2 or less. 0.000330 ≤ Al × N ≤ 0.000825 4.6 ≤ Mn / S ≤ 14.0 15.5 ≤ − 1.40 × Al + 0.0175 × 214 × C + 1 / 7 × Si + 1 / 5 × Mn + 1 / 9 × Cr − 211 ≤ 25.65 where the symbols "C", "Si", "Mn", "Cr", "Al", "N", and "S" included in Expression , Expression , and Expression respectively indicate amounts of C, Si, Mn, Cr, Al, N, and S by unit mass%, wherein the area fraction of AlN is obtained from 20 or more of sample sectional photographs taken in a visual field of 1000 μm 2 at a magnification of 40,000 times according to the replica method of the transmission electron microscope by putting together a plurality of images, and the number density of the fine MnS inclusions is obtained from image analysis of 60 photographs of a polished longitudinal section of a steel bar in a visual field of 110 μm × 75 μm taken by using an optical microscope at a magnification of 1000 times. C: 0.40% to 0.60%; Si: 0.01% to 1.4%; Mn: 0.2% to less than 1.0%; Cr: 0.01% to less than 0.5%; Al: 0.11% to 0.17%; S: more than 0.03% to 0.07%; N: 0.0030% to 0.0075%; P: less than 0.05%; B: 0% to 0.005%; Mo: 0% to 0.2%; Ni: 0% to 1.0%; Cu: 0 % to 1.0%; Ca: 0% to 0.005%; Mg: 0% to 0.005%; Zr: 0% to 0.005%; Rem: 0% to 0.005%; Ti: 0% to 0.2%; Nb: 0% to 0.2%; V: 0% to 0.35%; Sb: 0% to 0.015%; Te: 0% to 0.2%; Pb: 0% to 0.5%; Bi: 0% to 0.5%; and the remainder consisting of Fe and impurities, wherein the chemical composition satisfies Expressions to , at a 1/4 position of a diameter of the steel, an area fraction of AlN having an equivalent circle diameter of more than 200 nm is 20% or less of an area fraction of all AlN having an equivalent circle diameter of 40 nm or more, and at the 1/4 position of the diameter of the steel, a number density of Mn sulfide-based inclusions having a maximum diameter of 0.3 μm or more and 10 μm or less is 100 pieces/mm 2 or more and 2500 pieces/mm 2 or less. 0.000330 ≤ Al × N ≤ 0.000825 4.6 ≤ Mn / S ≤ 14.0 15.5 ≤ − 1.40 × Al + 0.0175 × 214 × C + 1 / 7 × Si + 1 / 5 × Mn + 1 / 9 × Cr − 211 ≤ 25.65 where the symbols "C", "Si", "Mn", "Cr", "Al", "N", and "S" included in Expression , Expression , and Expression respectively indicate amounts of C, Si, Mn, Cr, Al, N, and S by unit mass%, wherein the area fraction of AlN is obtained from 20 or more of sample sectional photographs taken in a visual field of 1000 μm 2 at a magnification of 40,000 times according to the replica method of the transmission electron microscope by putting together a plurality of images, and the number density of the fine MnS inclusions is obtained from image analysis of 60 photographs of a polished longitudinal section of a steel bar in a visual field of 110 μm × 75 μm taken by using an optical microscope at a magnification of 1000 times. <EOS>