Heaviside was born at 55 Kings Street (now Plender Street) in London's Camden Town. He was short and red-  headed, and suffered from scarlet fever when young, which left him with a hearing impairment. He was a good student (e.g. placed fifth out of five hundred students in 1865). Heaviside's uncle Sir Charles Wheatstone (1802 – 1875) was the original co-inventor of the telegraph in the mid 1830s, and was an internationally celebrated expert in telegraphy and electromagnetism. Wheatstone was married to Heaviside's aunt in London and took a strong interest in his nephew's education.

Heaviside left school at age 16 to study at home in the subjects of telegraphy and electromagnetism. He continued full time study at home until age 18. Then – in the only paid employment he ever had – he took a job as a telegraph operator with the Great Northern Telegraph Company working first in Denmark and then in Newcastle - upon - Tyne, and was soon made a chief operator. It is likely that his uncle Sir Charles was instrumental in getting Heaviside the telegraph operator position. Heaviside continued to study while working, and at age 21 and 22 he published some research related to electric circuits and telegraphy. In 1874 at age 24 he quit his job and returned to studying full time on his own at his parents' home in London. He remained single throughout his life.

In 1873 Heaviside had encountered James Clerk Maxwell's newly published, and today famous, two volume Treatise on Electricity and Magnetism. In his old age Heaviside recalled:

Doing full time research from home, he helped develop transmission line theory (also known as the "telegrapher's equations"). Heaviside showed mathematically that uniformly distributed inductance in a telegraph line would diminish both attenuation and distortion, and that, if the inductance were great enough and the insulation resistance not too high, the circuit would be distortionless while currents of all frequencies would have equal speeds of propagation. Heaviside's equations helped further the implementation of the telegraph.

In 1880, Heaviside researched the skin effect in telegraph transmission lines. That same year he patented, in England, the coaxial cable. In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as quaternions) to its modern vector terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations. The four re-formulated Maxwell's equations describe the nature of static and moving electric charges and magnetic dipoles, and the relationship between the two, namely electromagnetic induction.

Between 1880 and 1887, Heaviside developed the operational calculus (involving the D notation for the differential operator, which he is credited with creating), a method of solving differential equations by transforming them into ordinary algebraic equations which caused a great deal of controversy when first introduced, owing to the lack of rigor in his derivation of it. He famously said, "Mathematics is an experimental science, and definitions do not come first, but later on." He was replying to criticism over his use of operators that were not clearly defined. On another occasion he stated somewhat more defensively, "I do not refuse my dinner simply because I do not understand the process of digestion."

In 1887, Heaviside proposed that induction coils (inductors) should be added to telephone and telegraph lines to increase their self - induction and correct the distortion which they suffered. For political reasons, this was not done. The importance of Heaviside's work remained undiscovered for some time after publication in The Electrician, and so its rights lay in the public domain. AT&T later employed one of its own scientists, George A. Campbell, and an external investigator Michael I. Pupin to determine whether Heaviside's work was incomplete or incorrect. Campbell and Pupin extended Heaviside's work, and AT&T filed for patents covering not only their research, but also the technical method of constructing the coils previously invented by Heaviside. AT&T later offered Heaviside money in exchange for his rights; it is possible that the Bell engineers' respect for Heaviside influenced this offer. However, Heaviside refused the offer, declining to accept any money unless the company were to give him full recognition. Heaviside was chronically poor, making his refusal of the offer even more striking.

In two papers of 1888 and 1889, Heaviside calculated the deformations of electric and magnetic fields surrounding a moving charge, as well as the effects of it entering a denser medium. This included a prediction of what is now known as Cherenkov radiation, and inspired his friend George FitzGerald to suggest what now is known as the Lorentz - Fitzgerald contraction.

In the late 1880s and early 1890s, Heaviside worked on the concept of electromagnetic mass. Heaviside treated this as material mass, capable of producing the same effects. Wilhelm Wien later verified Heaviside's expression (for low velocities).

In 1891 the British Royal Society recognized Heaviside's contributions to the mathematical description of electromagnetic phenomena by naming him a Fellow of the Royal Society, and the following year devoting more than fifty pages of the Philosophical Transactions of the Society to his vector methods and electromagnetic theory. In 1905 Heaviside was given an honorary doctorate by the University of Göttingen.

In 1902, Heaviside proposed the existence of the Kennelly - Heaviside Layer of the ionosphere which bears his name. Heaviside's proposal included means by which radio signals are transmitted around the Earth's curvature. The existence of the ionosphere was confirmed in 1923. The predictions by Heaviside, combined with Planck's radiation theory, probably discouraged further attempts to detect radio waves from the Sun and other astronomical objects. For whatever reason, there seem to have been no attempts for 30 years, until Jansky's development of radio astronomy in 1932.

In later years his behavior became quite eccentric. Though he had been an active cyclist in his youth, his health seriously declined in his sixth decade. During this time Heaviside would sign letters with the initials "W.O.R.M." after his name. Heaviside also reportedly started painting his fingernails pink and had granite blocks moved into his house for furniture. In 1922, he became the first recipient of the Faraday Medal, which was established that year.

Heaviside died at Torquay in Devon, and is buried in Paignton cemetery. Most of his recognition was gained posthumously.

Heaviside did much to develop and advocate vector methods and the vector calculus. Maxwell's formulation of electromagnetism consisted of 20 equations in 20 variables. Heaviside employed the curl and divergence operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (B, E, J, and ρ), the form by which they have been known ever since. He invented the Heaviside step function and employed it to model the current in an electric circuit. He invented the operator method for solving linear differential equations, which resembles current Laplace transform methods (inverse Laplace transform, also known as the "Bromwich integral"). The UK mathematician Thomas John I'Anson Bromwich later devised a rigorous mathematical justification for Heaviside's operator method.

Heaviside advanced the idea that the Earth's uppermost atmosphere contained an ionized layer known as the ionosphere; in this regard, he predicted the existence of what later was dubbed the Kennelly - Heaviside Layer. He developed the transmission line theory (also known as the "telegrapher's equations"). He also independently discovered the Poynting vector.

Heaviside coined the following terms of art in electromagnetic theory: admittance (December 1887); conductance (September 1885); electret for the electric analogue of a permanent magnet, or, in other words, any substance that exhibits a quasi - permanent electric polarization (e.g. ferroelectric); impedance (July 1886); inductance (February 1886); permeability (September 1885); permittance (later susceptance; June 1887); reluctance (May 1888).

Hertz was born in Hamburg, Germany, into a prosperous and cultured Hanseatic family. His father, Gustav Ferdinand Hertz, was a writer and later a senator. His mother was the former Anna Elisabeth Pfefferkorn. His paternal grandfather David Wolff Hertz (1757 - 1822), fourth son of Benjamin Wolff Hertz, moved to Hamburg in 1793 where he made his living as a jeweller. He and his wife Schöne Hertz (1760 - 1834) were buried in the former Jewish cemetery in Ottensen. Their first son Wolff Hertz (1790 - 1859), was chairman of the Jewish community. His brother Hertz Hertz (1797 - 1862) was a respected businessman. He was married to Betty Oppenheim, the daughter of the banker Salomon Oppenheim, from Cologne. Hertz Hertz converted from Judaism to Christianity and took the name Heinrich David Hertz.

While studying at the Gelehrtenschule des Johanneums in Hamburg, he showed an aptitude for sciences as well as languages, learning Arabic and Sanskrit. He studied sciences and engineering in the German cities of Dresden, Munich and Berlin, where he studied under Gustav R. Kirchhoff and Hermann von Helmholtz.

In 1880, Hertz obtained his PhD from the University of Berlin; and remained for post doctoral study under Hermann von Helmholtz.

In 1883, Hertz took a post as a lecturer in theoretical physics at the University of Kiel.

In 1885, Hertz became a full professor at the University of Karlsruhe where he discovered electromagnetic waves.

The most dramatic prediction of Maxwell's theory of electromagnetism, published in 1865, was the existence of electromagnetic waves moving at the speed of light, and the conclusion that light itself was just such a wave. This challenged experimentalists to generate and detect electromagnetic radiation using some form of electrical apparatus.

The first clearly successful attempt was made by Heinrich Hertz in 1886. For his radio wave transmitter he used a high voltage induction coil, a condenser (capacitor, Leyden jar) and a spark gap - whose poles on either side are formed by spheres of 2 cm radius - to cause a spark discharge between the spark gap’s poles oscillating at a frequency determined by the values of the capacitor and the induction coil.

To prove there really was radiation emitted, it had to be detected. Hertz used a piece of copper wire, 1 mm thick, bent into a circle of a diameter of 7.5 cm, with a small brass sphere on one end, and the other end of the wire was pointed, with the point near the sphere. He bought a screw mechanism so that the point could be moved very close to the sphere in a controlled fashion. This "receiver" was designed so that current oscillating back and forth in the wire would have a natural period close to that of the "transmitter" described above. The presence of oscillating charge in the receiver would be signaled by sparks across the (tiny) gap between the point and the sphere (typically, this gap was hundredths of a millimeter).

In more advanced experiments, Hertz measured the velocity of electromagnetic radiation and found it to be the same as the light’s velocity. He also showed that the nature of radio waves’ reflection and refraction was the same as those of light, and established beyond any doubt that light is a form of electromagnetic radiation obeying the Maxwell equations.

Hertz's experiments would soon trigger the invention of the wireless telegraph, radio, and later television. In recognition of his work, the unit of frequency - one cycle per second - is named the "hertz".

He always had a deep interest in meteorology probably derived from his contacts with Wilhelm von Bezold (who was Hertz's professor in a laboratory course at the Munich Polytechnic in the summer of 1878). Hertz, however, did not contribute much to the field himself except some early articles as an assistant to Helmholtz in Berlin, including research on the evaporation of liquids, a new kind of hygrometer, and a graphical means of determining the properties of moist air when subjected to adiabatic changes.

In 1886 – 1889, Hertz published two articles on what was to become known as the field of contact mechanics. Hertz is well known for his contributions to the field of electrodynamics; however, most papers that look into the fundamental nature of contact cite his two papers as a source for some important ideas. Joseph Valentin Boussinesq published some critically important observations on Hertz's work, nevertheless establishing this work on contact mechanics to be of immense importance. His work basically summarizes how two axi - symmetric objects placed in contact will behave under loading, he obtained results based upon the classical theory of elasticity and continuum mechanics. The most significant failure of his theory was the neglect of any nature of adhesion between the two solids, which proves to be important as the materials composing the solids start to assume high elasticity. It was natural to neglect adhesion in that age as there were no experimental methods of testing for it.

To develop his theory Hertz used his observation of elliptical Newton's rings formed upon placing a glass sphere upon a lens as the basis of assuming that the pressure exerted by the sphere follows an elliptical distribution. He used the formation of Newton's rings again while validating his theory with experiments in calculating the displacement which the sphere has into the lens. K. L. Johnson, K. Kendall and A. D. Roberts (JKR) used this theory as a basis while calculating the theoretical displacement or indentation depth in the presence of adhesion in their landmark article "Surface energy and contact of elastic solids" published in 1971 in the Proceedings of the Royal Society (A324, 1558, 301-313). Hertz's theory is recovered from their formulation if the adhesion of the materials is assumed to be zero. Similar to this theory, however using different assumptions, B. V. Derjaguin, V. M. Muller and Y. P. Toporov published another theory in 1975, which came to be known as the DMT theory in the research community, which also recovered Hertz's formulations under the assumption of zero adhesion. This DMT theory proved to be rather premature and needed several revisions before it came to be accepted as another material contact theory in addition to the JKR theory. Both the DMT and the JKR theories form the basis of contact mechanics upon which all transition contact models are based and used in material parameter prediction in Nano - indentation and Atomic Force Microscopy. So Hertz's research from his days as a lecturer, preceding his great work on electromagnetism, which he himself considered with his characteristic soberness to be trivial, has come down to the age of nanotechnology.

In 1886, Hertz developed the Hertz antenna receiver. This is a set of terminals which is not electrically grounded for its operation. He also developed a transmitting type of dipole antenna, which was a center - fed driven element for transmitting UHF radio waves. These antennas are the simplest practical antennas from a theoretical point of view.

In 1887, Hertz experimented with radio waves in his laboratory. These actions followed Michelson's 1881 experiment (precursor to the 1887 Michelson - Morley experiment) which did not detect the existence of aether drift, Hertz altered the Maxwell's equations to take this view into account for electromagnetism. Hertz used a Ruhmkorff coil - driven spark gap and one meter wire pair as a radiator. Capacity spheres were present at the ends for circuit resonance adjustments. His receiver, a precursor to the dipole antenna, was a simple half - wave dipole antenna for shortwaves. Hertz published his work in a book titled: Electric waves: being researches on the propagation of electric action with finite velocity through space.

Through experimentation, he proved that transverse free space electromagnetic waves can travel over some distance. This had been predicted by James Clerk Maxwell and Michael Faraday. With his apparatus configuration, the electric and magnetic fields would radiate away from the wires as transverse waves. Hertz had positioned the oscillator about 12 meters from a zinc reflecting plate to produce standing waves. Each wave was about 4 meters. Using the ring detector, he recorded how the magnitude and wave's component direction vary. Hertz measured Maxwell's waves and demonstrated that the velocity of radio waves was equal to the velocity of light. The electric field intensity and polarity was also measured by Hertz.

The Hertzian cone was first described by Hertz as a type of wave - front propagation through various media. His experiments expanded the field of electromagnetic transmission and his apparatus was developed further by others in the radio. Hertz also found that radio waves could be transmitted through different types of materials, and were reflected by others, leading in the distant future to radar.

Hertz helped establish the photoelectric effect (which was later explained by Albert Einstein) when he noticed that a charged object loses its charge more readily when illuminated by ultraviolet light. In 1887, he made observations of the photoelectric effect and of the production and reception of electromagnetic (EM) waves, published in the journal Annalen der Physik. His receiver consisted of a coil with a spark gap, whereupon a spark would be seen upon detection of EM waves. He placed the apparatus in a darkened box to see the spark better. He observed that the maximum spark length was reduced when in the box. A glass panel placed between the source of EM waves and the receiver absorbed ultraviolet radiation that assisted the electrons in jumping across the gap.

When removed, the spark length would increase. He observed no decrease in spark length when he substituted quartz for glass, as quartz does not absorb UV radiation. Hertz concluded his months of investigation and reported the results obtained. He did not further pursue investigation of this effect, nor did he make any attempt at explaining how the observed phenomenon was brought about.

Hertz did not realize the practical importance of his experiments. He stated that,

"It's of no use whatsoever [...] this is just an experiment that proves Maestro Maxwell was right - we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there."

Asked about the ramifications of his discoveries, Hertz replied,

"Nothing, I guess."

His discoveries would later be more fully understood by others and be part of the new "wireless age". In bulk, Hertz' experiments explain reflection, refraction, polarization, interference, and velocity of electric waves.

In 1892, Hertz began experimenting and demonstrated that cathode rays could penetrate very thin metal foil (such as aluminium). Philipp Lenard, a student of Heinrich Hertz, further researched this "ray effect". He developed a version of the cathode tube and studied the penetration by X-rays of various materials. Philipp Lenard, though, did not realize that he was producing X-rays. Hermann von Helmholtz formulated mathematical equations for X-rays. He postulated a dispersion theory before Röntgen made his discovery and announcement. It was formed on the basis of the electromagnetic theory of light. However, he did not work with actual X-rays.

In 1892, an infection was diagnosed (after a bout of severe migraines) and Hertz underwent some operations to correct the illness. He died of Wegener's granulomatosis at the age of 36 in Bonn, Germany in 1894, and was buried in Ohlsdorf, Hamburg at the Jewish cemetery.

Hertz's wife, Elizabeth Hertz (maiden name: Elizabeth Doll), did not remarry. Heinrich Hertz left two daughters, Joanna and Mathilde. Subsequently, all three women left Germany in the 1930s to England, after the rise of Adolf Hitler. Charles Susskind interviewed Mathilde Hertz in the 1960s and he later published a book on Heinrich Hertz. Heinrich Hertz's daughters never married and he does not have any descendants, according to the book by Susskind.

His nephew Gustav Ludwig Hertz was a Nobel Prize winner, and Gustav's son Carl Hellmuth Hertz invented medical ultrasonography.

The SI unit hertz (Hz) was established in his honor by the IEC in 1930 for frequency, a measurement of the number of times that a repeated event occurs per second (also called "cycles per sec" (cps)). It was adopted by the CGPM (Conférence générale des poids et mesures) in 1964.

In 1969 (East Germany), there was cast a Heinrich Hertz memorial medal. The IEEE Heinrich Hertz Medal, established in 1987, is "for outstanding achievements in Hertzian waves [...] presented annually to an individual for achievements which are theoretical or experimental in nature".

A crater that lies on the far side of the Moon, just behind the eastern limb, is named in his honor. The Hertz market for radioelectronics products in Nizhny Novgorod, Russia, is named after him. The Heinrich - Hertz - Turm radio telecommunication tower in Hamburg is named after the city's famous son.

Hertz is honored by Japan with a membership in the Order of the Sacred Treasure, which has multiple layers of honor for prominent people, including scientists. Heinrich Hertz was honored by a number of countries around the world in their postage issues and in Post World War II times has appeared on various German stamp issues as well.

Although Hertz would not have considered himself Jewish, his "Jewish" portrait was removed by the Nazis from its prominent position of honor in Hamburg's City Hall (Rathaus) because of his partly "Jewish ancestry." Hertz was a Lutheran; and although his father’s family had been Jewish, his father had converted to Catholicism before marrying. The painting has since been returned to public display.