Nikhil Ranjan Sen was born on 23 May 1894 in Dhaka, the youngest of their four sons and four daughters of Kalimohan Sen and his wife Vidhumukhi Devi. He attended Dhaka Collegiate School, where his classmate was the famous scientist Meghnad Saha. He then went to complete his school education at Rajshahi Collegiate School. In 1909, he obtained a scholarship with his third position in order of merit for the entrance examination of Calcutta University. After passing the intermediate examination in 1911, he studied honors mathematics in Presidency College in Calcutta, where he had Saha and Satyendranath Bose as classmates. Bose, Saha, and Sen got the three highest spots in the 1913 honors examination in Calcutta University. They went on to become postgraduate students in Presidency College. Sen topped the 1916 Mixed Mathematics examination, a year after Bose and Saha topped the same exam.