Capalik was born in Sarajevo, the capital of Bosnia and Herzegovina and then part of Yugoslavia. His Bosnian Croat father and Bosnian Serb mother owned and operated casinos, which would be destroyed in the war. The family left the city on April 4, 1992 and sought refuge in the Netherlands, where Kristian's grandmother lived. Later in the year, Kristian and his brother Alen, who was also a tennis player, immigrated to the United States. Alen went to Philadelphia and Kristian was accepted into the Palmer Tennis Academy in Tampa.