Battement Arrondi is a classical ballet term that means “rounded battement.” This term describes a step when the toes of a dancer’s working foot move in a semi-circle in the air, at about 45 degrees starting from front to back(en dehors) or back to front (en dedans).
Commonly in ronde jambe exercises at barre, a grand battement arrondi is the same semi-circle idea but bigger, typically above 90 degrees.