Boys was the eighth child of the Revd Charles Boys, Anglican vicar of Wing, Rutland. He was educated at Marlborough College and the Royal School of Mines, where he learned physics from Frederick Guthrie and taught himself higher mathematics while completing a degree in mining and metallurgy. As a student at the School of Mines he invented a mechanical device (which he called the "integraph") for plotting the integral of a function. He worked briefly in the coal industry before accepting Guthrie's offer of a position as "demonstrator."
Boys achieved recognition as a scientist for his invention of the fused quartz fibre torsion balance, which allowed him to measure extremely small forces. He used his invention to build a radiomicrometer capable of responding to the light of a single candle more than one mile away, and used that device for astronomical observations. In 1895 he published a measurement of the gravitational constant G that improved upon the accuracy achieved by Cavendish.
Boys' work on calorimetry was used by the government to price natural gas by energy content rather than volume. He also worked on high-speed photography and conducted public lectures on the properties of soap films, which were gathered into the book Soap Bubbles: Their Colours and the Forces Which Mould Them, a classic of scientific popularization which remains in print today. The first edition of Soap Bubbles appeared in 1890, and the second in 1911. The book deeply impressed French writer Alfred Jarry, who in 1898 wrote the absurdist novel Exploits and Opinions of Dr. Faustroll, pataphysician, in which the title character, who was born at the age of 63 and sails in a sieve, is described as a friend of C.V. Boys (see also Pataphysics).
Boys was a professor at the Royal College of Science in South Kensington from 1889 to 1897, as well as an examiner at the University of London. In 1899 he presented the Royal Institution Christmas Lectures. He was elected to the Royal Society in 1888 and knighted in 1935. He was awarded the Royal Medal in 1896 and the Rumford Medal in 1924.
He married Marion Amelia Pollock in 1892. She caused a scandal by having an affair with the Cambridge mathematician Andrew Forsyth, as a result of which Forsyth was forced to resign his chair. Marion divorced Boys in 1910 and married Forsyth.