Rajpur is located at . It has an average elevation of 225 metres (738 feet).
India census, Rajpur had a population of 17,913. Males constitute 51% of the population and females 49%. Rajpur has an average literacy rate of 59%, lower than the national average of 59.5%: male literacy is 68%, and female literacy is 49%. In Rajpur, 17% of the population is under 6 years of age.