The son of a clergyman, Boys was born in Wing in the eastern English county of Rutland and educated at the Royal School of Mines, London. He later taught at the Royal College of Science, South Kensington. Boys left the College in 1897 to take up the appointment of Metropolitan gas referee, a post that he held until 1939 when the job was abolished. The post was something of a sinecure, and required Boys to do little more than supervise the work of his assistants and to monitor methods used to test the quality of the gas the Board supplied to its customers. Boys also found time to establish himself as an expert witness, appearing in numerous patent and other technical disputes.

Boys is best known for his determination of the gravitational constant in 1897. The measurement was first made by Henry Cavendish in 1797 and was expressed in terms of the Earth's density. Newton had proposed a density between five and six in 1687; Cavendish found experimentally a density of 5.448.

Whereas Cavendish had used a six-foot beam in his torsion rod experiment, Boys opted for a mere nine inches. The decrease in size was made possible by using some exceedingly fine quartz fibers in the torsion balance. Boys drew these fine filaments by attaching the end of an arrow to a piece of molten quartz and firing it with a crossbow. As a result uniform temperatures were easier to maintain, and convection current disturbances were minimized. Boys calculated on the basis of his measurements that two 1 gram point masses 1 centimeter apart would attract each other with a force of 6.657 6 × 10^–8 dyne, and consequently the density of the Earth would be 5.527 gm/cm³, figures which compare well with the modern figure of 6.670 × 10^–8 dyne, and 5.517 gm/cm³.

There are a number of other instruments linked to Boys. Amongst these are an integraph (1881) for mechanical integration, a radiomicrometer (1890) for measuring stellar radiation, a rotating lens camera (1900) for photographing the flight of a bullet, and, in his capacity as gas referee, an improved calorimeter to measure the calorific value of gas (1905).