Pockels was born in Venice, Austrian Empire, in 1862. At the time, Venice was under Austrian rule, and Pockels' father served in the Austrian Army. When he fell sick, the family moved in 1871 to Brunswick, which was part of the nascent German Empire. There, Pockels attended the Municipal High School for Girls. Agnes was interested in chemistry  as a child. However, women were not allowed to enter universities to study. Pockels stated that "I had a passionate interest in natural science, especially physics, and would have liked to study.“ (Agnes Pockels, as translated by Giles from Autobiographical Notes in W. Ostwald, 1932.)
As a child, Pockels was interested in science, especially physics. In those days, women in Germany had no access to universities. Pockels studied science at home while caring for her parents. Pockels' younger brother Friedrich Carl Alwin Pockels studied physics at the University of Göttingen, completing his degree there. Friedrich shared textbooks from the university with Agnes Pockels in order to help her study from home. He later shared academic literature with Agnes Pockels to advance her studies.