Cavendish inherited two fortunes that were so large that Jean Baptiste Biot called him "the richest of all the savants and the most knowledgeable of the rich". At his death, Cavendish was the largest depositor in the Bank of England. He was a shy man who was uncomfortable in society and avoided it when he could. He could speak to only one person at a time, and only if the person were known to him and male. He conversed little, always dressed in an old-fashioned suit, and developed no known deep personal attachments outside his family. Cavendish was taciturn and solitary and regarded by many as eccentric. He communicated with his female servants only by notes. By one account, Cavendish had a back staircase added to his house to avoid encountering his housekeeper, because he was especially shy of women. The contemporary accounts of his personality have led some modern commentators, such as Oliver Sacks, to speculate that he was autistic.
His only social outlet was the Royal Society Club, whose members dined together before weekly meetings. Cavendish seldom missed these meetings, and was profoundly respected by his contemporaries. However, his shyness made conversation difficult; guests were advised to wander close to him and then speak as if "into vacancy. If their remarks were scientifically worthy, they might receive a mumbled reply". Cavendish was more likely not to reply at all. Cavendishs religious views were also considered eccentric for his time. He was considered to be agnostic. As his biographer, George Wilson, comments, "As to Cavendishs religion, he was nothing at all."
The arrangement of his residence reserved only a fraction of space for personal comfort as his library was detached, the upper rooms and lawn were for astronomical observation and his drawing room was a laboratory with a forge in an adjoining room. He also enjoyed collecting fine furniture, exemplified by his purchase of a set of "ten inlaid satinwood chairs with matching cabriole legged sofa".
Because of his asocial and secretive behaviour, Cavendish often avoided publishing his work, and much of his findings were not told even to his fellow scientists. In the late nineteenth century, long after his death, James Clerk Maxwell looked through Cavendishs papers and found observations and results for which others had been given credit. Examples of what was included in Cavendishs discoveries or anticipations were Richters law of reciprocal proportions, Ohms law, Daltons law of partial pressures, principles of electrical conductivity (including Coulombs law), and Charles's Law of gases. A manuscript "Heat", tentatively dated between 1783 and 1790, describes a "mechanical theory of heat". Hitherto unknown, the manuscript was analysed in the early 21st century. Historian of science Russell McCormmach proposed that "Heat" is the only 18th-century work prefiguring thermodynamics. Theoretical physicist Dietrich Belitz concluded that in this work Cavendish "got the nature of heat essentially right".
As Cavendish performed his famous density of the Earth experiment in an outbuilding in the garden of his Clapham Common estate, his neighbours would point out the building and tell their children that it was where the world was weighed. In honour of Henry Cavendishs achievements and due to an endowment granted by Henrys relative William Cavendish, 7th Duke of Devonshire, the University of Cambridges physics laboratory was named the Cavendish Laboratory by Maxwell, the first Cavendish Professor of Physics and an admirer of Cavendishs work.