Phoebe Sarah Hertha Marks was born in Portsea, Hampshire, England, to Levi Marks, a Polish Jewish watchmaker and clockmaker, and Alice Moss, a seamstress. She was the third of eight children.

Her father, Levi Marks, died, leaving the family in financial hardship. Hertha's mother struggled to support the children.

Hertha was sent to live with her aunt, Marion Hartog, who ran a school in London. This provided her with a better education than she would have received otherwise and exposed her to a more intellectual environment.

While living with her aunt, Hertha displayed a keen aptitude for mathematics and science. She also learned French and developed a strong interest in radical political thought.

Ayrton earned a scholarship to study mathematics at Girton College, Cambridge. Although she excelled in her studies, women were not awarded degrees at Cambridge at this time. She was coached by mathematician Charlotte Scott.

Ayrton passed the Cambridge Mathematical Tripos examinations, achieving a high score. However, as a woman, she was not granted a degree. She received a 'certificate of attendance' instead.

After Cambridge, Hertha sat and passed an external exam earning a Bachelor of Science degree from the University of London.

Ayrton invented a line divider, a mathematical instrument used to enlarge, reduce, and divide lines into equal parts. She patented the invention, providing her with some financial independence.