Axel Fredrik Cronstedt was born on 23 December 1722 on the estate of Ströpsta, in Sudermania.
His father, Gabriel Olderman Cronstedt (1670–1757), was a military engineer.
His mother, Maria Elizabeth Adlersberg, was Gabriel Cronstedt's second wife.
Beginning in 1738, Axel Cronstedt  was an unregistered student at   the University of Uppsala, hearing lectures with Johan Gottschalk Wallerius (1709–1785), professor  of  chemistry,  and astronomer Anders  Celsius (1701–1744). At Uppsala, he became a friend of Sven Rinman, discoverer  of Rinman's green. 
In  1743, during an unstable period politically,   Cronstedt left Uppsala to act as his father's secretary on a military tour of inspection. This tour strengthened his interest in mines and mineralogy.
Cronstedt entered the School of Mines where his instructors included geologist Daniel Tilas (1712-1772). On Tilas' recommendation, Cronstedt went on mining tours in the summers of 1744 and 1745. In 1746, he surveyed copper mines.
From 1746 to 1748 Cronstedt took classes with George Brandt, the discoverer of cobalt, at the royal mining laboratory in  Stockholm, the Laboratorium Chemicum. There he studied chemical analysis and smelting.
Between 1748, when he completed his studies, and 1758, Cronstedt held a variety of positions. In 1756, he was disappointed to be passed over for a position at the Bureau of Mines, but in 1758, he became a superintendent of mining operations for the mining districts of Öster and Västerbergslagen.
In 1760 Cronstedt married Gertrud Charlotta     Söderhielm (1728–1769). In 1761, he moved to  the estate of Nisshytte,  north  of Riddarhyttan.  He died there on 19 August 1765.