Power matriculated as a pensioner of Christ's College, Cambridge in 1641 and graduated B.A. in 1644. He became a regular correspondent of Sir Thomas Browne, who had lived in Halifax 1633-1635 on scientific subjects. He graduated M.A. in 1648, and M.D. in 1655 (1654?). It appears that he practised his profession at Halifax for some time, but he eventually removed to New Hall, near Elland. Power was elected and admitted a fellow of the Royal Society 1 July 1663, he and Sir Justinian Isham being the first elected members.
He died at New Hall on 23 December 1668, and was buried in the church of All Saints, Wakefield, with a brass plate to his memory, with a Latin inscription, on the floor in the middle chancel.
His only published work is 'Experimental Philosophy'. Its three books deal respectively with microscopy and corpuscularian theory; the experiments of Torricelli; and the vacuum, and refutations proposed for the works of the Jesuit Jacobus Grandamicus (Jacques Grandami, 1588–1672).
In a series of experiments with his friend, Richard Towneley, Power discovered the relationship between the pressure and volume of a gas that later became known as Boyle's law. This relationship was outlined in "Experimental Philosophy." However, many may argue nevertheless that Boyle, after discussing the theory with Towneley and reading a pre-publication manuscript of "Experimental Philosophy" cited the hypothesis as the sole work of Richard Towneley. Boyle's mention of the theory preceded the publication of "Experimental Philosophy" by one year, which, combined with Boyle's promotion of the idea and his significant status as an aristocratic scientist, ensured the theory would be known as "Boyle's Law." Boyle attributed Towneley as the sole researcher, ensuring that Power's contributions were all but lost to history. 
- "Power, Henry (PWR641H)". A Cambridge Alumni Database. University of Cambridge.
- "Power, Henry". Dictionary of National Biography. London: Smith, Elder & Co. 1885–1900.
- "Experimental Philosophy, in three Books". London. 1664. doi:10.1179/amb.1922.214.171.124. ISBN 978-1240810734. OCLC 872500329.
(actually published in 1663)
- Andrew Pyle (editor), Dictionary of Seventeenth Century British Philosophers (2000), article on Power, pp. 667-670.
- Webster, Charles (1965). "The Discovery of Boyle's Law, and the Concept of the Elasticity of Air in the Seventeenth Century". Archive for History of Exact Sciences. Springer-Verlag. 2 (6): 441–502. doi:10.1007/BF00324880. ISSN 1432-0657. OCLC 39966759.