Ball-end mill and insert

A ball-end mill comprising, in a tip end portion of an end mill body, arcuate cutting edges each extending from a tip end to a peripherally outermost point along a curve in an S shape when viewed from the front side, spirally-shaped, peripheral cutting edges each smoothly connected to each arcuate cutting edge, and a convex rake face of each arcuate cutting edge protruding forward in a rotation direction;

• each of said arcuate cutting edges having a radial rake angle meeting the condition of β<α≦γ, wherein α is a radial rake angle at a radial angle of 5°, β is a radial rake angle at a radial angle of 90°, and γ is a radial rake angle at a rotationally most projecting point of said arcuate cutting edge;
• the radial rake angle of said arcuate cutting edge having the maximum value between said tip end and said rotationally most projecting point and in a radial angle range of 12-40°;
• and
• said radial rake angle changing along such a smooth curve that said radial rake angle gets gradually smaller in a range from a point of said maximum value to said peripherally outermost point via said rotationally most projecting point.