Born Francesco Cavalieri (in Latin, Cavalerius) in Milan was known for Cavalieri's principle, which states that the volumes of two objects are equal if the areas of their corresponding cross-sections are in all cases equal. Two cross-sections correspond if they are intersections of the body with planes equidistant from a chosen base plane. The principle was originally discovered by the 3rd century Chinese mathematician Liu Hui in his commentary on The Nine Chapters on the Mathematical Art. Cavalieri developed a "method of the indivisibles," which he used to determine areas and volumes. It was a significant step on the way to modern infinitesimal calculus.

Cavalieri took the name Bonaventura when he entered the Jesuati (not Jesuit) order. He studied theology in the monastery of San Gerolamo in Milan and geometry at the University of Pisa. He published eleven books, his first being published in 1632. He worked on the problems of optics and motion. His astronomical and astrological work remained marginal to these main interests, though his last book, Trattato della ruota planetaria perpetua (1646), was dedicated to the former. He was introduced to Galileo through academic and ecclesiastical contacts. Cavalieri would write at least 112 letters to Galileo. Galileo said of Cavalieri, "few, if any, since Archimedes, have delved as far and as deep into the science of geometry."

Cavalieri also constructed a hydraulic pump for his monastery and published tables of logarithms, emphasizing their practical use in the fields of astronomy and geography. He died at Bologna. The lunar crater Cavalerius is named for the Latin name of Bonaventura Cavalieri.