A number of his computations aimed at determining the surfaces and volumes of different types of bodies and constitute, in fact, the processes of integral calculus, as developed later. In astronomy he was one of the early reformers of Ptolemaic views. He analyzed several problems related to the movements of sun and moon and wrote treatises on sun-dials.
Only a few of Thabit's works are preserved in their original form.
The medieval astronomical theory of the trepidation of the equinoxes is often attributed to Thabit. But it had already been described by Theon of Alexandria in his comments of the Handy Tables of Ptolemaeus. According to Copernicus Thabit determined the length of the sidereal year as 365 days, 6 hours, 9 minutes and 12 seconds (an error of 2 seconds). Copernicus based his claim on the Latin text attributed to Thabit. Thabit published his observations of the Sun.
In mathematics, Thabit discovered an equation for determining the amicable numbers. He also wrote on the theory of numbers, and extended their use to describe the ratios between geometrical quantities, a step which the Greeks never took. Another important contribution Thabit made to geometry was his generalization of the Pythagorean theorem, which he extended from special right triangles to all triangles in general, along with a general proof.
In physics, Thabit rejected the Peripatetic and Aristotelian notions of a "natural place" for each element. He instead proposed a theory of motion in which both the upward and downward motions are caused by weight, and that the order of the universe is a result of two competing attractions : one of these being "between the sublunar and celestial elements", and the other being "between all parts of each element separately".