Benjamin Bramer was fostered by his sister and her husband Bürgi after the death of his father. Bürgi tutored Bramer in mathematics and Bramer became interested in combining mathematics with architecture. He went with Bürgi to Prague when he was 16 years old and remained there for about five years.
Bramer directed constructions of fortifications and castles within the district of Hesse-Kassel north of Bavaria. He was appointed master builder to the court in Marburg in 1612. In 1629 he directed the construction of fortifications of Marburg castle and fortifications of the town. He also directed the construction of a fortress at Rheinfels (1625) and fortifications in Kassel (1630-1634). In 1635 Bramer was appointed master builder of the fortress of Ziegenhain.
His first publication was on the calculation of sines. He also published on the vacuum, holding similar views to Galileo. He followed Alberti (1435), Dürer (1525) and Bürgi (1604) when in 1630 he constructed a device that enabled one to draw accurate geometric perspective. The instrument had been described in a 1617 publication. Bramer designed several other mathematical instruments.