According to Rainier Ballistics, a .40-inch caliber round would be 10 millimeter caliber, when described using the metric system. As the Sportsman's Guide explains, this is an ammunition caliber common in pistols and other small arms.
As Firearms ID explains, caliber is a term used to indicate the diameter of a bullet in hundredths of an inch. The term caliber is of English origin and is primarily used by ammunition and firearm manufacturers in the United States. Firearms and ammunition of European origin use the metric system and would, for example, refer to a 30 caliber bullet as an 7.62 millimeter bullet.