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Faxon Firearms does not state the minimum handguard ID needed for use with the Faxon Firearms Big Gunner Style Barrel. I recommend contacting Faxon Firearms for that information.
The minimum diameter for the inside of your handguard will be more dependent on the gas block you choose than the barrel since the gas block will be the largest diameter item that the handguard has to cover. For instance, when paired with our .875" diameter gas block you would need a handguard with an inner diameter of at least 1.100" as well as a channel along the top for the gas tube and it's housing on the gas block. Larger gas blocks may require a larger inside diameter. Fortunately, due to the nature of the DPMS Gen 1/LR-308 design, most compatible handguards will have an ID greater then 1.1" so you should not have issue fitting one over this barrel.