C.R. Rao was born as the eighth child in a large family of six brothers and four sisters, raised by his parents, C.D. Naidu and Lakshmikantamma. Following tradition, he was named Radhakrishna after God Krishna, the eighth child in mythology. He married Bhargavi, an accomplished scholar with master’s degrees in History from Banaras Hindu University and Psychology from the University of Illinois, USA, along with a Bachelor's degree in Teacher’s Training. She worked as a professor of psychology at Jadavpur University, Kolkata, contributing significantly to the field of education.
Their daughter, Tejaswini, earned a Ph.D. in Nutrition from Pennsylvania State University and now serves as a Professor in the Dietetics and Nutrition department at SUNY College, Buffalo. She is also a talented Bharatanatyam and Kuchipudi dancer and directs the Natya dance school. Their son, Veerendra, pursued a career in electrical engineering and computer science, running a computer consultancy in Pittsburgh. He is the father of two sons, Amar and Rohith.