Kohlrausch was born at Rinteln, the son of R. H. A. Kohlrausch, a famous physicist who served as professor at the University of Erlangen. Friedrich studied at Erlangen and then at Göttingen, where he gained his PhD in 1863. He held a series of professorial appointments at Göttingen, Frankfurt, Darmstadt, Würzburg, Strasbourg, and Berlin and was elected to the Academy of Sciences in Berlin in 1895.

Kohlrausch is remembered for his work on the electrical conductivity of solutions. He was able to measure the electrical resistance of electrolytes (substances that, by transferring ions, conduct electricity in solutions) by introducing an alternating current to prevent polarization of the electrodes. In this way he recorded the conductivity of electrolytes at various solute concentrations and discovered that conductivity increases with increased dilution. This finding led to the formulation of Kohlrausch's law of the independent migration of ions.