The son of a phonetician, Kaluza was born at Ratibor in Germany and educated at the University of Königsberg where he served (1902–29) as a privatdocent (a largely unpaid teaching assistant). On Einstein's recommendation he was appointed in 1929 to a professorship in physics at the University of Kiel. He remained there until 1935, when he moved to a similar appointment at Göttingen University.

In Einstein's theory of general relativity, space and time are joined together into a four-dimensional space–time. In 1921, Kaluza decided to supplement Einstein's model with a fifth spatial dimension. Within this model it proved possible to derive Einstein's four-dimensional gravitational equations as well as the equations for the electromagnetic field. Thus in a world of five dimensions, gravity and electromagnetism were not distinct forces.

There were, however, two major defects in Kaluza's theory. Firstly, he could give no indication of the nature of this fifth dimension. Moreover, his theory assumed that bodies behave classically and quantum- mechanical effects were not considered. An attempt to remedy these defects was made in 1926 by Oskar Klein. This revised form, known as the Kaluza–Klein theory, has proved to be of considerable interest to string theorists such as Ed Witten.