Hertha Ayrton was born Phoebe Sarah Marks in Portsea, Hampshire, England, on 28 April 1854. In her youth she went by the name Sarah. She was the third child of a Polish Jewish watchmaker named Levi Marks, an immigrant from Tsarist Poland; and Alice Theresa Moss, a seamstress, the daughter of Joseph Moss, a glass merchant of Portsea. Her father died in 1861, leaving Sarah's mother with seven children and an eighth expected. Sarah then took up some of the responsibility for caring for the younger children.

At the age of nine, Sarah was invited by her aunts, who ran a school in northwest London, to live with her cousins and be educated with them. She was known to her peers and teachers as a fiery, occasionally crude personality. Her cousins introduced Ayrton to science and mathematics. By age 16, she was working as a governess, but she had not renounced her ambitions.

George Eliot supported Ayrton's application to Girton College, Cambridge. There, Ayrton studied mathematics and was coached by physicist Richard Glazebrook. She also constructed a sphygmomanometer (blood pressure meter), led the choral society, founded the Girton fire brigade, and, together with Charlotte Scott, formed a mathematical club. In 1880, Ayrton passed the Mathematical Tripos, but Cambridge did not grant her an academic degree because at the time it did not award full degrees to women. Ayrton then passed an external examination at the University of London, which awarded her a Bachelor of Science degree in 1881.

Ayrton was brought up as Jewish but was agnostic by her teens. She adopted the name "Hertha", first given as a nickname by her friend Ottilie Blind, after the eponymous heroine of a poem by Algernon Charles Swinburne that criticised organised religion.

As a teenager, Ayrton became deeply involved in the women's suffrage movement, joining the WSPU in 1907 after attending a celebration with released prisoners. In 1909 Ayrton opened the second day of the Knightsbridge "Women's Exhibition and Sale of Work in the Colours" which included new model bicycles painted in purple, white and green and raised from 50 stalls and tea etc. £5,664 for the movement. Ayrton was with the delegation that went with Emily Pankhurst to see the Prime Minister and met his private secretary instead on 18 November 1910 (Black Friday). Ayrton permitted Christabel Pankhurst to transfer sums to her bank account to avoid confiscation in 1912, and hosted Pankhurst in times of recovery from imprisonment and force feeding. One attempt to re-arrest Pankhurst on 29 April 1913 to continue her sentence was driven back by suffragettes picketing outside, but Pankhurst was eventually re-arrested outside Ayrton's home on her way to the funeral of Emily Davison (who was killed after running in front of the King's horse at the Derby).

Ayrton was a close friend of the scientist Marie Curie and gave her daughter, Irène Curie, mathematics lessons. Although Curie usually chose to withhold her name from petitions, Ayrton managed to persuade her to sign a protest against the imprisonment of suffragettes through her daughter.

It was through suffrage activism that she met Barbara Bodichon, a fellow suffragist and a co-founder of Cambridge's Girton College. Bodichon helped to make it financially possible for Ayrton to attend Girton and went on to support her financially throughout her education and career, including bequeathing her estate to Ayrton.