I am installing a 100 amp service in my pole barn. It is 250 feet from the house panel. What size wire and conduit do I need to bury for that distance?
Thank you

I would recommend using #4/0 aluminum 4 wire URD cable, which is a widely used and available product. This is rated to be direct buried, but sleeve it with 3 " PVC conduit in rocky soil and/or under truck traffic, or the entire length for extra protection and ease of changing it in the future if necessary.

Special attention will be needed at both ends as the terminals of 100 Amp breakers and terminals of 100 amp panelboards will not accept a wire this size. Simplest method would be to change over to #2 aluminum in a junction box close to both ends.