Kapor was born in Brooklyn, New York and attended public schools in Freeport, Long Island, where he graduated from high school in 1967. He received a B.A. from Yale College in 1971 and studied psychology, linguistics, and computer science as part of an interdisciplinary major in Cybernetics. He was greatly involved with Yale's radio station, WYBC-FM, where he served as Music Director and Program Director.
He founded Lotus Development Corp. in 1982 and with Jonathan Sachs, who was responsible for technical architecture and implementation, created Lotus 1-2-3. He served as the President (later Chairman) and Chief Executive Officer of Lotus from 1982 to 1986 and as a Director until 1987. In 1983, Lotus' first year of operations, the company achieved revenues of $53,000,000 and had a successful public offering. In 1984 the company tripled in revenue to $156,000,000. The number of employees grew to over a thousand by 1985.
In 1990 with John Perry Barlow, he co-founded the Electronic Frontier Foundation, and served as its chairman until 1994. The EFF is a non-profit civil liberties organization working in the public interest to protect privacy, free expression, and access to public resources and information online, as well as to promote responsibility in new media.
Kapor is married and lives in San Francisco and the Boston area.