Kumar Bhattacharyya was born in Bangalore, the elder son of Sudhir Kumar Bhattacharyya (1909-1987) and Hemanalini Chakraborty. Of Bengali origin, the Bhattacharyyas were a zamindari family from Dhaka District (then in the Bengal Presidency of British India and now in Bangladesh). At the time, his father, a distinguished professor of physical chemistry and subsequently Fellow of the Indian National Science Academy, was a professor at the Indian Institute of Science in Bangalore, where Bhattacharyya spent the first 12 years of his life. In 1952, upon his father's appointment as head of the chemistry department at the new Indian Institute of Technology, Kharagpur, the family moved to Kharagpur.