Maximum range for 777-300ER with a full passenger payload weight of 77,600lbs (361 pax), or ZFW of 447,600lbs. is 7,720nm or (8,878sm).
That range plan assumes standard day temp, zero wind, standard reserves plus allowance. Takeoff weight of 759,600lbs.
Boeing website quotes 7,880nm or (9,062sm), with slightly different assumptions on passenger payload weight.
Now of course this plan has nothing to do with how airlines actually operate the aircraft. In the real world there is wind, weather, route modifications, different seating arrangements, and cargo on board the aircraft. Operators optimize their aircraft to extract the best payload/range/revenue solution possible. In practice it seems that segments of 5,900-6,300nm are at the peak of the curve balancing all three of those factors. This comes out to a nominal payload capability of 115,000-135,000lbs, giving operators great flexibility on what they can put on the plane to make money.
SIA's A345's carry 170pax and are getting around 40,000-50,000lb payloads on the, nominally, 8,300nm (9,545sm) SIN