WASHINGTON — In a major test of how to interpret the Fourth Amendment in the digital age, the Supreme Court on Tuesday will consider two cases about whether the police need warrants to search the cellphones of the people they arrest.

“The implications of these cases are huge,” said Orin S. Kerr, a law professor at George Washington University, noting that about 12 million people are arrested every year, often for minor offenses, and that about 90 percent of Americans have cellphones.

The justices will have to decide how to apply an 18th-century phrase — the Fourth Amendment’s prohibition of “unreasonable searches and seizures” — to devices that can contain 100 times more information than is in the Library of Congress’s 72,000-page collection of James Madison’s papers.

The courts have long allowed warrantless searches in connection with arrests, saying they are justified by the need to protect police officers and to prevent the destruction of evidence. The Justice Department, in its Supreme Court briefs, said the old rule should apply to the new devices.