Emma Constance Stone was born on the 4th of December in 1856 to father William Stone and Mother Betsy née Haydon. When Constance was three, Her mother gave birth to Grace Clara Stone, Constance's new sister. Soon after the birth of her sister, her brother was born. Clara took her place as middle child when William Stone took her place.
In 1872, Constance left her home at Hobart Town and moved with her family to Melbourne. When she was old enough, she was educated chiefly by her mother who was a former governess. They relied on the income of her fathers job as a builder after her mother retired to stay at home with the kids.
Constance had had an early interest in anatomy, but could not study medicine at Melbourne university since they do not admit woman into the medical coarse, so in 1884 she went overseas to Women's Medical College of Pennsylvania in the United States. After a 3-year degree, she went to Trinity College Tornonto and graduated M.D.,CH.M with first-class honours from the college.