Richard Alexander Fullerton Penrose was born in Carlisle, Pennsylvania, the second son of Charles and Valeria Fullerton Biddle Penrose on March 24, 1827; his elder brother was William McFunn Penrose. He was educated at the local Dickinson Grammar School and entered Dickinson College proper in 1842, graduating with the class of 1846. He went on to the medical school at the University of Pennsylvania and received his medical degree in March 1849.
Penrose was a resident at the Philadelphia Hospital between 1850 and 1853 and also opened a private practice in 1851. He was the visiting physician for the Southern Home for Children in the city and later, in 1856, helped found the Children's Hospital of Philadelphia. He was to continue as a consultant for the Philadelphia Hospital from 1855 to 1864. Meanwhile, Penrose began teaching in his specialty of the diseases of women and children both at the Philadelphia Hospital and in private lessons. His reputation as a fine teacher led to his appointment in 1863 to the professorship of obstetrics and diseases of women and children at the University of Pennsylvania; he served in this post till 1889. His attentions were distracted for a time, however, when, during the Civil War, he took up the post of Acting Assistant Surgeon in the Union Army as a doctor at the Satterlee Army Hospital in Philadelphia between 1862 and 1864. After the war, his reputation continued to grow and he was instrumental in the founding of the Gynecian Hospital in Philadelphia and the American Gynecological Society in 1876. In 1875, Dickinson College awarded him an honorary doctorate of letters.
On September 28, 1858, Penrose married Sarah Hannah Boies of Wilmington, Delaware and the couple had seven sons, including Boies Penrose, later a United Senator from Pennsylvania, and Richard A.F. Penrose, Jr., later a famous geologist. Sarah died in 1881 and, on December 26, 1908, Richard Alexander Fullerton Penrose died of pneumonia in Philadelphia. He was eighty-one years old.