Penrose was born at Bracebridge, Lincolnshire, the third son of Rev. John Penrose who was vicar there, and his wife Elizabeth Cartwright. His mother was the daughter of Edmund Cartwright and was a teacher and author of children's books under the name Mrs Markham. He was educated at Bedford Modern School, Bedford School, Winchester College and Magdalene College, Cambridge. He rowed for Cambridge in the Boat Race in the 1840, 1841 and 1842 races.
Penrose studied architecture under Edward Blore from 1835 to 1838, and studied abroad under the Cambridge designation of "travelling bachelor" from 1842 to 1845. In 1843 in Rome Penrose noticed a problem with the pitch of the roof of pediment of the Pantheon, and subsequent research confirmed that the angle had been changed from its original design. He studied the classical monuments in Greece taking and recording detailed measurements. He was one of the first people to discover the entasis of the Parthenon and to show the deliberate curvature of the steps and entablature. The Society of Dilettanti were interested in his discoveries and sent him back to Greece to confirm them.
In 1848, Penrose became a FRIBA. He became surveyor of St Paul's Cathedral in 1852, and it was there that he did his main work. His designs included the choir-school, the choir seats and the marble pulpit and stairs. He designed the memorial to Lord Napier of Magdala and the Wellington tomb in the Crypt and arranged the relocation of the Wellington monument. He was also responsible for rearranging the West entrance steps and for exposing the remains of the old cathedral in the churchyard. It was as a result of a dispute with the Dean and Chapter that he became an astronomer.
Penrose became a Fellow of Magdalene in 1884. He designed the entrance gate of Magdalene College and the Chapel Court of St John's in Cambridge. From 1886 to 1887 and from 1890 to 1891 he was Director of the British School at Athens which he designed.
He was president of the RIBA from 1894 to 1896. He was appointed architect and antiquary to the Royal Academy in 1898. He authored the entry on Sir Christopher Wren in the Dictionary of National Biography.
Penrose had married Harriette Gibbes in 1856, the daughter of Francis Gibbes, a surgeon of Harewood. His daughter Emily was the second of five children and eldest of their four daughters and became Principal of Somerville College, Oxford, Royal Holloway College, London and Bedford College, London.
- Penrose, F.C., (communicated by Joseph Norman Lockyer), The Orientation of Greek Temples, Nature, v.48, n.1228, May 11, 1893, pp. 42–43
- An Investigation of the Principles of Athenian Architecture, or, The Results of a Recent Survey Conducted chiefly with Reference to the Optical Refinements Exhibited in the Construction of the Ancient Buildings at Athens, edited by the Society of Dilettanti, London 1851
- 2nd edition: An investigation of the principles of Athenian architecture, or, the results of a survey conducted chiefly with reference to the optical refinements exhibited in the construction of the ancient buildings at Athens, London 1888 (document server of Heidelberg University)
- A work predicting eclipses
-  Oxford Dictionary of National Biography
- "Penrose, Francis Cranmer" from the Dictionary of National Biography, 1912 supplement at Wikisource
- "Penrose, Francis Cranmer (PNRS838FC)". A Cambridge Alumni Database. University of Cambridge.
- Dictionary of Art Historians - Francis C. Penrose
- Royal Academy Collections
- St Paul's Cathedral - F C Penrose project
- British School at Athens - Art and Architecture
- Works by Francis Cranmer Penrose at Wikisource