A firearm may have a plurality of power-consuming accessories that can be attached to the weapon. In order to reduce the weight of these power-consuming accessories, as well as the proliferation of their batteries, the Weapon Accessory Power Distribution System provides a common power source to power the power-consuming accessories attached to the weapon. One or more powered rails are provided to encircle the barrel of the weapon, to provide a point of mechanical and electrical interconnection for the power-consuming accessories to provide quick connect mounting and dismounting of the power-consuming accessory, absent the use of connectors with their tethering cables, which are susceptible to entanglement. The Weapon Accessory Rail Contacts provide the mechanism to electrically interconnect the power-consuming accessory with the powered rail.