Rudolf Hermann Arndt Kohlrausch (November 6, 1809 in Göttingen – March 8, 1858 in Erlangen) was a German physicist.

He was a native of Göttingen, the son of the Royal Hanovarian director general of schools Friedrich Kohlrausch. He was a high-school teacher of mathematics and physics successively at Lüneburg, Rinteln, Kassel and Marburg. In 1853 he became an associate professor at the University of Marburg, and four years later, a full professor of physics at the University of Erlangen.^[1]

In 1854 Kohlrausch introduced the relaxation phenomena, and used the stretched exponential function to explain relaxation effects of a discharging Leyden jar (capacitor).^[2][3] In an 1855 experiment (published 1857) with Wilhelm Weber (1804–1891), he demonstrated that the ratio of electrostatic to electromagnetic units produced a number similar to the value of the speed of light,^[4] a constant which they named ${\displaystyle c}$. Kirchhoff recognized that the ratio is equal to ${\displaystyle {\sqrt {2}}}$ the speed of light.^[5] This finding was instrumental towards Maxwell's conjecture that light is an electromagnetic wave.

He was the father of physicist Friedrich Kohlrausch.

• Elektrodynamische Maaßbestimmungen : insbesondere Zurückführung der Stromintensitäts-Messungen auf mechanisches Maass (with Wilhelm Weber) 1857. "Electrodynamic Measurements, Especially Attributing Mechanical Units to Measures of Current Intensity". German text. English translation

• Kohlrausch function