The youngest of six sons and two daughters, Stratton was born at Edgbaston in Birmingham, to Stephen Samuel Stratton, a music critic and historian, and Mary Jane Marrian. He remembered Dvorak and Ebenezer Prout visiting his father. In 1891, he received a scholarship to King Edward's Grammar School in Five Ways, Birmingham, advanced to Mason College in 1897 and won an entrance scholarship to Gonville and Caius College, Cambridge, in 1900, entering the university in October 1901. He took a London BA in Greek, Latin and maths in 1903, and graduated in 1904 with the distinction of Third Wrangler in Part I of the Mathematical Tripos. He was placed in Class I, Division II of the second part of the Tripos the following year, also receiving the Tyson Medal in astronomy and an Isaac Newton Studentship. In 1906 he won a Smith's Prize and was elected a Fellow of his college, which he remained until his death.
Military service
In 1901, Statton had joined the Caius Company of the Cambridge University Rifle Volunteers, which became the Cambridge University Officers Training Corps in 1908. Partly instrumental in forming the Communications Company as a cadet corporal, he was commissioned a second lieutenant in the Territorial Army on 17 August 1910. A provisional captain in the unit when war erupted in 1914, he was commissioned a temporary captain in the Corps of Royal Engineers on 8 September 1914. As a temporary major, he became Officer Commanding of the 20th Divisional Signal Company, Royal Engineers, and took his company to France in the summer of 1915 to join the BEF. He was awarded a DSO in 1917 and promoted to acting lieutenant-colonel on 22 July, becoming Assistant Director Signals of the 19th Corps BEF under Lt-Gen. Watts. He was praised by his fellow officers for his efficiency and perpetual cheerfulness, managing to remain alert even after days without sleep, and was mentioned in despatches five times. On 29 January 1919, Stratton was appointed a knight of the Légion d'honneur of France. Upon returning to Cambridge in 1919 with the rank of major, he re-formed the signals section of the Officers Training Corps, and commanded it until 1928. For his military service, he was appointed an Officer of the Order of the British Empire, Military Division in the 1929 King's Birthday Honours list. In 1921, Stratton became the University representative for the Cambridgeshire Territorial Army Association, serving as its president from 1934 to 1940. Although nearly 60 when war erupted again in 1939, Stratton eagerly volunteered to return to active service. After persuading the War Office, he was given command of an Officer Cadet Training Unit. However, he was soon reassigned to the Royal Corps of Signals and given a special-duties role concerned with radio security. As a result, Stratton spent the war travelling extensively across the British Empire and also to the United States. Having exceeded the age limit for retirement, he relinquished his commission in the Territorial Army on 20 October 1945, retaining the rank of brevet lieutenant-colonel.
Scientific career
After a few years as mathematical lecturer at Cambridge he became Assistant Director of the Solar Physics Observatory from 1913 to 1919, then Tutor at Caius College from 1919 to 1928 and finally Professor of Astrophysics and Director of the Solar Physics Observatory from 1928 to 1947. He also wrote the main historical account of the Cambridge Observatories. He was president of the Royal Astronomical Society in 1933–35. In 1947 he was elected a Fellow of the Royal Society.
Stratton held interest in parapsychology. He was the President of the Society for Psychical Research in 1953–1955. Stratton died in Cambridge in 1960, aged 78. He never married.