Argelander’s father, Johann Gottlieb Argelander, was a wealthy merchant from Finland; his mother, Dorothea Wilhelmine Grünlingen, was German.
Friedrich Wilhelm August Argelander was born on March 22, 1799, in Memel in the Kingdom of Prussia (now Klaipėda in Lithuania), the son of a father of Finnish descent, Johann Gottfried Argelander, and German (Prussian) mother, Wilhelmina Dorothea Grünhagen.
The boy grew up in the easternmost corner of Prussia, and the Napoleonic Wars brought him into close contact with the major political events of his day. After the defeat of Prussia in the campaign of 1806, Queen Louise and her sons fled from Berlin to Memel. The crown prince, who later became Friedrich Wilhelm IV, and Prince Friedrich lived in the Argelander home, and young Argelander formed a lasting friendship with both of them.