Longtime Red Wing Williams was sent to the Chicago Blackhawks, who Detroit will visit on Tuesday night.
In turn, the Blackhawks shipped defenseman Lasse Kukkonen and a third-round draft pick to the Philadelphia Flyers, who then sent Calder to Detroit.
Calder is playing out a one-year deal he signed with Chicago last summer, before the Blackhawks traded him to Philadelphia for Michal Handzus. He has nine goals and 12 assists for 21 points in 59 games.
"He's had a tough season, but he's a proven NHL player," Detroit head coach Mike Babcock said on Monday night. "He works, works and works and he'll make us a harder team to play against."
Williams is in the first year of a two-year deal he signed with the Red Wings in July. He has 11 goals and 15 assists for 26 points in 58 games.