Ramachandra Rao was born in an aristocratic Thanjavur Marathi Deshastha Brahmin family in 1871.

From 1910 to 1914, Rao served as District Collector of Nellore and in the Indian Public Services Commission from 4 to 20 January 1914.

Ramachandra Rao was a keen mathematician and astronomer and served as President of the Indian Mathematical Society.

[1] He assisted mathematician Srinivasa Ramanujan when he was jobless and got him a clerk's job at the Madras Port Trust.

In the Tamil biographical film Ramanujan (2014), actor Sarath Babu played the character Diwan Bahadur R. Ramachandra Rao ICS.