Help Battery Question

[supersize]

My battery status says im full. ill be on the phone or on facebook and it will suddenly die after like 10 minutes. The battery life is still in the 80's when it dies. when i go to turn it back on, it has the dead battery sign and its beeping red, and before i can even do anything, it dies again. If i connect it to a charger, then start it up, and pull it off the charger (all within a matter on 1 minute), its back to its regular status at 80% or whatever it was. i can talk or go on facebook again for about 10 mins, and it does the same thing over again. I upgraded to 2.2 and that diddnt help, i wiped my phone and memory card clean, that diddnt help. Now tonight, i rooted it, deleted my battery stats, let it die from a full charge (which only took 10 minutes again), then plugged it in, let it charge to 100% (only took like 5 minutes) and its still doing the same thing so re-calibrating the battery diddnt do nothing. Whats causing this? could it be a bad battery or is my phone shot?