Eunice Newton was born in Goshen, Connecticut, to Isaac Newton Jr. and Thirza (née Foote) Newton. This marked the beginning of her life, which would later become remarkable for its contributions to both science and women's rights.

Eunice attended the Troy Female Seminary (later the Emma Willard School) in Troy, New York, for a few terms. This institution was progressive for its time, offering courses in science and mathematics not typically available to women. Though the exact years of attendance are not fully established, it influenced her later achievements.

Eunice attended the Rensselaer School (now Rensselaer Polytechnic Institute) in Troy, New York, during a period when it allowed female students to participate in science courses. She received instruction from Amos Eaton and Ebenezer Emmons, prominent natural scientists of the day, which was incredibly important for a women at that time.

Eunice Newton married Elisha Foote, a lawyer, judge, and statistician. This union provided her with a supportive intellectual partnership and likely influenced her later scientific work. Elisha's own interest in science may have provided her with support and additional opportunity for research.