Hertz
SI derived unit · quantity: frequency
01 · Definition
Hertz caught radio waves in his laboratory and died at thirty-six, never seeing radio itself. The unit of frequency was named after him thirty-six years after his death.
One hertz is one event per second. Formally it is simply the reciprocal second, but the hertz has a strict field of use: only periodic processes, where the event repeats at equal intervals. The heart beats at about 1 Hz, the mains in the socket oscillates at 50 Hz, the note A above middle C is 440 Hz, a processor ticks in gigahertz. The reciprocal second goes by other names too: the becquerel for radioactive decay has the same dimension, and so does angular velocity in radians per second, but these are different quantities and must not be confused.
The second to the minus one stands behind the hertz, the becquerel and the radian per second, and the dimension will not tell them apart — the difference lies in the nature of the process. ISO 80000-3 allows the hertz for periodic phenomena only, ISO 80000-10 assigns the becquerel to random decays, and angular frequency is prescribed in radians per second precisely so that the factor of two pi is not lost in the notation. Formally the radian is dimensionless and rad/s could be shortened to s⁻¹, but then rotations and oscillations would become indistinguishable on paper.
02 · Conversion
Enter a frequency and the passport returns the period and the wavelength
Frequency and period are reciprocal, so the table turns the quantity over rather than scaling it. Revolutions and beats per minute are the same cycles, merely referred to a minute.
The wavenumber in the table is not a frequency but its spectroscopic stand-in: the reciprocal centimetre says how many wavelengths fit into a centimetre, and it converts to hertz by multiplying by the speed of light. Chemists and spectroscopists use it because the number comes out convenient: the carbon–oxygen bond vibration gives 1700 reciprocal centimetres instead of fifty-one terahertz.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| Hz | hertz, the SI unit | 50 | physics, engineering, music |
| kHz | kilohertz | 0.05 | sound, long waves |
| MHz | megahertz | 5·10⁻⁵ | radio, clock rates |
| GHz | gigahertz | 5·10⁻⁸ | processors, Wi-Fi, radar |
| THz | terahertz | 5·10⁻¹¹ | infrared and visible light |
| rad/s | radian per second | 314.16 | mechanics, oscillation theory |
| c/s | cycles per second | 50 | radio engineering before the 1960s |
| kc/s | kilocycle per second | 0.05 | valve receiver dials |
| Mc/s | megacycle per second | 5·10⁻⁵ | shortwave communication |
| rpm | revolution per minute | 3000 | shafts, motors, discs |
| s | period in seconds | 0.02 | pendulums, mechanics |
| cm⁻¹ | wavenumber | 1.668·10⁻⁹ | spectroscopy, chemistry |
Frequency and period are reciprocal, so the table turns the quantity over. The radian per second differs from the hertz by a factor of two pi: the fifty hertz of the mains is 314 radians per second
03 · Orders of magnitude
from the orbit of Mars to gamma quantaOne hertz: a resting pulse, one cycle per second
04 · Measuring instruments
What frequency is measured with
It counts pulses over a reference interval and divides one by the other. The accuracy rests entirely on the internal crystal: over a one-second gate the instrument cannot know the frequency better than one count, which is why high frequencies are measured by division and low ones by timing the period.
It shows the shape of the oscillation in time: the frequency follows once the period has been counted off the sweep. The method is cruder than a counter, but the signal itself is there to see — distortion, jitter, and the fact that the oscillation is not a single one at all.
It flashes at a known frequency: when a mark on a rotating body appears frozen, the two frequencies agree. The method touches nothing and is therefore indispensable for shafts and blades, yet it deceives — the wheel also stands still at multiples, and an experienced mechanic always checks at twice the rate.
It does not measure a frequency but defines one: cooled caesium atoms are tossed through a microwave cavity and the oscillator is tuned to the resonance. Instruments of this kind keep world time, while optical standards on strontium and ytterbium are already hundreds of times better.
05 · Writing rules
Capital H, small z, and no “per second”
The symbol comes from a surname, so the first letter is capital and the second small: Hz, not HZ and not hz. The name of the unit in running text is lowercase — hertz. Prefixes are set without a space and in their proper case: kHz with a small k, MHz and GHz with a capital.
A non-breaking space separates the number from the symbol. The Russian symbol is Гц, with a capital Г and a small ц. The multiplying prefixes run up to exa: kilohertz, megahertz, gigahertz, terahertz, petahertz, exahertz; the last two turn up in optics and X-ray physics. ISO 80000-3 permits rotational frequency to be given in hertz if one revolution is taken as a cycle, but engineering prefers revolutions per minute, and the two notations should not be mixed in one document.
06 · Neighbouring units
Three units share the dimension of the reciprocal second with the hertz. What tells them apart is not the arithmetic but what exactly repeats — and whether it repeats at all.
random decays
cycles per second
angular frequency
Of the Simetrium passports sit next to the hertz second, of which it is the reciprocal, becquerel of the same dimension and another meaning, radian s as revolutions per minute for rotation, and decibel, used to describe how a signal falls off with frequency.
07 · Historical section
Cycles per second that became a surname
At Karlsruhe he built an oscillator with a spark gap and a receiving loop a few metres away. A spark jumped in the loop in step with the discharges of the oscillator: the wave had crossed the air and been caught. Hertz measured its length from the standing pattern against the laboratory wall — it came out about a metre.
For half a century radio engineering wrote cycles per second, and receiver dials carried kilocycles and megacycles. The notation was transparent but cumbersome, and it looked different in every language — no common symbol existed.
The International Electrotechnical Commission proposed naming the unit the hertz, but habit held firm: kilocycles vanished from the dials only towards the end of the sixties, after the General Conference had brought the hertz into the International System.
The astronomical definition of the second was replaced by an atomic one: the frequency of the transition in caesium-133 was declared an exact number of hertz. From that moment the hertz stopped being derived from the second in substance — if anything, it is the other way round.
Hertz thought his experiments useless
In 1887 he drew a spark in a receiving circuit from a discharge in a transmitting one and proved that the electromagnetic waves Maxwell had predicted exist. Asked what use it was, he answered that there was no practical sense in it whatever — it was merely a confirmation of the theory. Eight years later Popov and Marconi began sending signals, and by the time the unit of frequency was named after him, radio already linked continents. Today the hertz measures everything from a processor clock to the frequency of gravitational waves.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI units that neither engineering nor daily life can do without. Each gets its own sheet: definition, conversion, instruments, writing rules. In 10 languages.
SI derived units with names of their own
the hertz passport is openSI base units
in terracotta — the second, which the hertz turns overFrequency in other notations
Passport language
10 languages. The symbol Hz is international, but the mains frequency differs across them: fifty hertz in Europe and Asia, sixty in the Americas and Japan — the passport fills in the local value.