Roy was the first of two children of Kali Nath Roy and Suniti Bala Roy. His father, Kali Nath Roy was a freedom fighter and the Chief Editor of the newspaper The Tribune, then publishing from Lahore. During the massacre of the Indians at the hands of the British in the infamous incident at Jallianwala Bagh in April 1919, The Tribune published a news report titled "Prayer at the Jama Masjid", on April 6, 1919. For this "offence" Kali Nath Roy was sentenced to rigorous imprisonment for two years along with a fine of one thousand rupees.
In 1931, when Roy joined the Department of Applied Mathematics at the University of Calcutta as a research associate, he used computing facilities at the newly established Indian Statistical Institute, which was founded by Professor P. C. Mahalanobis. Roy along with several talented young scholars including J. M. Sengupta, H. C. Sinha, Raj Chandra Bose, K. R. Nair, K. Kishen and C. R. Rao, joined to form an active group of statisticians under Mahalanobis. Roy was one of the very early students of Mahalanobis, who initiated some of the early works in Statistics. He was well known for his pioneering contribution to multivariate statistical analysis, mainly that of the Jacobians of complicated transformations for various exact distributions, rectangular coordinates and the Bartlett decomposition. His dissertation included the Post master's work at the Indian Statistical Institute where he worked under Mahalanobis.
It was Bose who first went to the United States as a visiting professor at Columbia University and then joined the University of North Carolina at Chapel Hill in 1947. Roy followed suit by later joining him at the University of North Carolina at Chapel Hill in the spring of 1950, after initially travelling to the United States to take up a Visiting Professorship of Statistics at Columbia University in New York in the spring of 1949. In between this Roy returned to India and became Head of the Department of Statistics at the University of Calcutta during the academic year 1949–50. Roy joined Bose as full Professor of Statistics in the Statistics Department at the University of North Carolina at Chapel Hill. S. N. Roy had 15 doctorate students there from 1950 till 1963. To commemorate his Birth Centenary an International Conference on "Multivariate Statistical Methods in the 21st Century: The Legacy of Prof. S.N. Roy" was held at Kolkata, India during December 28–29, 2006. The Journal of Statistical Planning and Inference published a special Issue for celebrating the Centennial of Birth of S. N. Roy.
S. N. Roy is presently being survived by son Subir Roy who is an MD, Obstetrician & Gynecologist, Reproductive Endocrinologist at the LAC+USC Medical Center, LA, and daughter Sunanda R. McGarvey who works at the National Center of Public Health Informatics, CDC in Washington, DC.