A product of Arezzo's youth system, Calori made his professional debut in 1985 with Serie C team Montevarchi, where he spent four season. After two seasons with Pisa, in 1991 Calori joined Udinese, where he spent eight seasons, all as a regular, gaining reputation of a powerful, strong centre back. In 1999 Calori, then aged 33, signed for Perugia, and gained space in the headlines as he scored the winning goal in a 1–0 win to Juventus in the final league week, a goal that unexpectedly let Juventus lose the Serie A title to Lazio. He retired in 2004, after spells with Brescia and Venezia.
Following his retirement as a player, Calori initially stayed at Venezia, joining the managing staff that worked alongside head coach Julio César Ribas in the arancioneroverdi's 2004–2005 season, initially as team manager, and then as assistant coach. In 2005 he became joint coach of Serie B side Triestina, alongside Adriano Buffoni, only to be sacked a few weeks later. In 2006 he was then appointed at the helm of Serie C1 team Sambenedettese, a spell which proved to be unsuccessful as he was sacked on October 2006.
On March 10, 2008 he was unveiled as new Avellino coach, replacing Guido Carboni. He left his post on June, after having failed to save his team from relegation.
On February 2009 he was unveiled as new head coach of Lega Pro Prima Divisione club Portosummaga, replacing Manuele Domenicali. He guided Portosummaga to win the Lega Pro Prima Divisione title in 2009–10, and automatic promotion to Serie B for his club, in a historical first time in the Italian second division for his club. On July 2, 2010 he was unveiled as new head coach of Serie B club Padova. Despite a good first half of season, Calori was dismissed by Padova on 15 March 2011 following a string of negative results.