Umov was born on February 4 (N.S.) (January 23 (O.S.)), 1846 in Simbirsk (nowadays Ulyanovsk) in the family of a military doctor. Umov graduated from the Physics and Mathematics department of Moscow State University in 1867 and became a Professor of Physics in 1875. He studied theoretical physics by reading works of Gabriel Lamé, Clebsch and Clausius, that made a significant impact on the originality of his later ideas in physics.

Umov became the head of the Physics department of Moscow State University (MSU) after Aleksandr Stoletov died in 1896. Together with Pyotr Lebedev, Umov actively participated in founding the Physical Institute at the MSU.

Umov organized several educational societies. He was the president of the Moscow Society of Nature Explorers for 17 years. He was among the first Russian scientists who acknowledged the importance of the theory of relativity. In 1911, he along with a group of leading professors left Moscow University in protest of reactionary actions by the government. Umov died on January 15, 1915 in Moscow.

Umov was the first to introduce in physics such basic concepts as speed and direction of movement of energy, which are now associated with Umov-Poynting vector, and density of energy in a given point of space. During his work in Odessa in 1873 - 1874, Umov published the first papers containing the major ideas of energy movement. In his first works of this period, Umov considered potential energy as kinetic energy of some environments "imperceptible for us". From this hypothesis, he draw a conclusion: it is always possible to specify a place where the energy is in. Therefore, it is natural to raise the question about movement of energy. In his following works, Umov did not bind himself to this hypothesis about the nature of potential energy, but was guided by the principle of energy conservation only. After formulating the concept of density and movement of energy, he formulated differential equations for energy movement in elastic media and fluids. The fundamental "Encyklopǎdie der mathematischen Wissenschaften” states: "N. Umov yet in 1874 had solved a problem of the movement of energy in liquid and elastic media in completely generalized view. However, the intense attention to this view has been attracted only after Poynting has presented a stream of electromagnetic energy based on Maxwell equations" 10 years after Umov's publications.

He was the first scientist to indicate the interrelation between mass and energy proposing the formula E = kmc² with 0,5 =< k =< 1 as early as in 1873.

In 1875, Umov had solved a general problem of distribution of electric currents in conducting surfaces of any kind. In 1888 - 1891 he investigated experimentally the diffusion in water solutions, the polarization of light in opaque media, and discovered the effect of chromatic depolarization of light.

In the 1900s, he conducted a thorough analysis of many Gauss formulae regarding terrestrial magnetism, which allowed to define secular changes of the Earth's magnetic field.