He was educated at Sherborne, and was an undergraduate at Queens' College, Cambridge,[3] where he was tutored privately by English mathematician William Hopkins and graduated in 1834 as senior wrangler and first Smith's prizeman.

[2] Kelland's early research work, undertaken at the University of Cambridge, was influenced by mathematicians Joseph Fourier and Augustin Louis Cauchy.

His theoretical work on water waves (1840, 1844), published in Transactions of the Royal Society of Edinburgh, tried to explain aspects of the important experiments of John Scott Russell, then being carried out near Edinburgh.

He gave a geometrical Theory of Parallels outlining a version of non-Euclidean geometry.

He wrote mathematics books and edited works of mathematician John Playfair and polymath Thomas Young.