[1] Born in the town of Soltau, Hanover, the son of local teacher Georg Heinrich Wöhler, he showed early mathematical ability and won a scholarship to study at the Higher Vocational College of Hannover from 1835, under the direction of Karl Karmarsch.

In 1843, after a brief stay in Hannover, he started to receive instruction in locomotive driving in Belgium, returning as an engineer on the Hanover-Brunswick line of the Royal Hanoverian State Railways.

The recognition of his keen administration and technical leadership resulted in his appointment as director of the newly formed Imperial Railways in Alsace-Lorraine in 1874, based at the board's headquarters in Straßburg, a post he held until his retirement in 1889.

Wöhler started his axle investigations by research into the theory of elasticity and was led, in 1855, to a method for predicting the deflection of lattice beams that anticipated the work of Émile Clapeyron.

Wöhler showed clearly that fatigue occurs by crack growth from surface defects until the product can no longer support the applied load.