His family was of relatively low social status. His father Gebhard Dietrich Gauss (1744-1808) worked variously as a butcher, bricklayer, gardener, and treasurer of a death-benefit fund. Gauss characterized his father as honourable and respected, but rough and dominating at home. He was experienced in writing and calculating, whereas his second wife Dorothea, Carl Friedrich's mother, was nearly illiterate. He had one elder brother from his father's first marriage.

Gauss was a child prodigy in mathematics.