The court's ruling will determine the fine the oil company must pay for the accident, The (New Orleans) Times Picayune reported Monday.
In opening arguments, the federal government said 4.2 million barrels went into the gulf during the 2010 incident. BP maintained the number was closer to 2.45 million barrels.
The court's findings could result in fines ranging from $2.7 billion to $18 billion.
Steve O'Rourke, a lawyer for the federal government, told the court BP would try to convince the court the government's estimates were politically driven.
"Between BP's own experts, there's a 25 percent difference," he said.
He charged the amount of oil that spewed into the Gulf of Mexico during the spill was the equal of 16 Exxon Valdez tankers, a reference to a ship that spilled oil in Alaska in 1989.
In his opening statement, BP lawyer Mike Brock argued better estimates could be determined by measuring the contents of the oil reservoir before and after the spill.
"This information is relied on in the industry to help make predictions about the well, assuming that it's successfully drilled," Brock said. "These are not figures that BP has come up with after the fact."
This phase of the trial is expected to take three weeks. Earlier phases looked at the causes of the blowout and how it could have been prevented and BP's efforts to stop the spill after it started.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Megyn Kelly: Santa Claus and Jesus are both white men