Born in Bristol, he was educated at Blundell's School and graduated from Trinity College, Cambridge as third wrangler in the mathematics tripos before turning to physiology. While still an undergraduate at Trinity College, he derived in 1909 what came to be known as the Langmuir equation. ). This is closely related to Michaelis-Menten kinetics. In this paper, Hill's first publication, he derived both the equilibrium form of the Langmuir equation, and also the exponential approach to equilibrium. The paper, written under the supervision of John Newport Langley, is a landmark in the history of receptor theory, because the context for the derivation was the binding of nicotine and curare to the "receptive substance" at the neuromuscular junction.
While a student he had enrolled in the Officers Training Course; he was a crack shot. In 1914, at the outbreak of World War I, Hill because the musketry officer of the Cambridgeshire Regiment. The British made no effort to make use of their Scientists. At the end of 1915, while home on leave he was asked by Horace Darwin from the Ministry of Munitions to come for a day to advise them on how to train anti-aircraft gunners. On site, Hill immediately proposed a simple two mirror method to determine airplane's heights. Transferred to Munitions, he realized that the mirrors could measure where smoke shells burst and if he fit this data with the equations describing a shell's FLIGHT they could provide accurate range tables for anti-aircraft guns. To measure and compute he assembled a team of men too old for conscription, Ralph H. Fowler (a wounded officer), and lads too young for Service including Douglas Hartree and Arthur Milne. Someone dubbed his motley group "Hill's Brigands", which they proudly adopted. Later in the war they also worked on locating enemy planes from their sound. He sped between their working sites on his beloved motorcycle. At the end of the war Major Hill issued certificates to more than one hundred Brigands. He was awarded an OBE.
Hill returned briefly to Cambridge in 1919 before taking the chair in physiology at the Victoria University of Manchester in 1920 in succession to william Stirling. Using himself as the subject —he ran every morning from 7:15 to 10:30 — he showed that running a dash relies on Energy stores which afterwards are replenished by increased oxygen consumption. Paralleling the work of German Otto Fritz Meyerhof, Hill elucidated the processes whereby mechanical work is produced in muscles. The two shared the 1922 Nobel Prize in Physiology and Medicine for this work .
In 1923 he succeeded Ernest Starling as professor of physiology at University College London, a few years later becoming a Royal Society Research professor there, where he remained until retirement in 1951. In 1933, he became with Lord Beveridge and Lord Rutherford a founder member and vice-president of the Academic Assistance Council (which in 1936 became the Society for the Protection of Science and Learning). By the start of the Second World War, the organisation had saved 900 academics (18 of whom went on to win Nobel Prizes) from Nazi persecution. He prominently displayed in his laboratory a toy figure of Adolf Hitler with saluting arm upraised, which he explained was in gratitude for all the Scientists Germany had expelled, some of whom were now working with him. Hill believed that "Laughter is the best detergent for nonsense".
In 1935 he served with Patrick Blackett and Sir Henry Tizard on the committee that gave birth to radar. He was also biological secretary of the Royal Society; william Henry Bragg was President. Both had been frustrated by the delay in putting Scientists to work in the previous war. The Royal Society collated a list of Scientists and Hill represented the Society at the Ministry of Labor. When the war came Hill led a campaign to liberate refugee Scientists who had been interned. He served as an independent Member of Parliament (MP) for Cambridge University from 1940 to 1945. In 1940 he was posted to the British Embassy in Washington to promote war research in the still neutral United States. He was authorized to swap secrets with the Americans, but this could not work: how do you place a value on another's secret? Hill saw the answer and persuaded the British to show the Americans everything they were working on (except for the atomic bomb). The mobilization of Allied scientist was one of the major successes in the war.
After the war he rebuilt his laboratory at University College and vigorously carried on research. In 1951 his advocacy was rewarded by the establishment of a Biophysics Department under his leadership. In 1952 he became head of the British Association for the Advancement of Science and Secretary General of the International Union of Scientific Organizations. He was President of the Marine Biological Association from 1955 to 1960. In 1967 he retired to Cambridge where he gradually lost the use of his legs. He died "held in the greatest affection by more than a hundred scientific descendants all over the world".
On 9 September 2015 an English Heritage Blue plaque was erected at Hill's former home, 16 Bishopswood Road, Highgate, where he had lived from 1923-1967. Since then the house had been divided into flats and owned by Highgate School, where Hill was a Governor from 1929-1960. It has now been sold, redeveloped and renamed as Hurstbourne. In Hill's time, according to his grandson Nicholas Humphrey, regular guests at the house included 18 exiled Nobel laureates, his brother-in-law, the Economist John Maynard Keynes, and friends Stephen Hawking and Sigmund Freud. After-dinner conversations in the drawing room would inevitably involve passionate debates about science or politics. “Every Sunday we would have to attend a tea party at grandpa’s house and apart from entertaining some extraordinary guests, he would devise some great games for us, such as frog racing in the garden or looking through the lens of a (dissected) sheep’s eye.” Sir Ralph Kohn FRS who proposed the Blue plaque, said: “The Nobel Prize winner A. V. Hill contributed vastly to our understanding of muscle physiology. His work has resulted in wide-ranging application in Sports Medicine. As an outstanding Humanitarian and Parliamentarian, he was uncompromising in his condemnation of the Nazi regime for its persecution of Scientists and others. A. V. Hill played a crucial role in assisting and rescuing many refugees to continue their work in this country.”