| Nanohertz (nHz) | Millihertz (mHz) |
|---|---|
| 1 Nanohertz | 0.000001 mHz |
| 2 Nanohertz | 0.000002 mHz |
| 3 Nanohertz | 0.000003 mHz |
| 4 Nanohertz | 0.000004 mHz |
| 5 Nanohertz | 0.000005 mHz |
| 10 Nanohertz | 0.00001 mHz |
| 20 Nanohertz | 0.00002 mHz |
| 25 Nanohertz | 0.000025 mHz |
| 50 Nanohertz | 0.00005 mHz |
| 100 Nanohertz | 0.0001 mHz |
| Reference | Nanohertz (nHz) | Millihertz (mHz) |
|---|---|---|
| European mains electricity | 5 × 1010 nHz | 50000 mHz |
| Concert pitch A above middle C | 4.4 × 1011 nHz | 440000 mHz |
| An FM radio station | 1 × 1017 nHz | 1 × 1011 mHz |
| A Wi-Fi band | 2.4 × 1018 nHz | 2.4 × 1012 mHz |
| A desktop processor clock | 3 × 1018 nHz | 3 × 1012 mHz |
The nanohertz is a unit of frequency equal to one billionth of a hertz. Its symbol is nHz. One nanohertz is one cycle per thousand million seconds, which is a little under thirty-two years, so a single oscillation at this frequency takes longer than most careers.
Almost nothing uses it, and then in 2023 it became one of the most discussed units in physics. Several pulsar timing array collaborations, working independently on four continents, reported evidence for a background of gravitational waves in the nanohertz band. The signal appears to come from pairs of supermassive black holes orbiting each other in the centres of merged galaxies across the whole history of the universe.
The measurement technique is remarkable. Millisecond pulsars are neutron stars that spin hundreds of times a second and emit a beam that sweeps past the Earth with extraordinary regularity, rivalling atomic clocks. A gravitational wave passing through the galaxy stretches and squeezes the space between the Earth and each pulsar, changing the arrival times of the pulses by a few hundred nanoseconds. By watching dozens of pulsars for two decades and looking for a specific pattern of correlation between them, astronomers detect waves whose wavelengths are measured in light years.
No instrument could work any other way at these frequencies. A detector must be comparable in size to the wavelength it seeks, and a nanohertz gravitational wave has a wavelength of tens of light years. The galaxy itself is the apparatus, and the pulsars are its markers.
The unit appears elsewhere only in the slowest of natural cycles. The precession of the Earth's axis takes about 26,000 years, roughly 1.2 nanohertz. Orbital variations in eccentricity, obliquity and precession that pace the ice ages, the Milankovitch cycles, run from about 0.5 nanohertz down to a tenth of that.
Below the nanohertz the concept of frequency becomes strained, because nothing has been observed long enough to see a full cycle, and the value is inferred from theory rather than counted.
One nanohertz equals 0.000000001 hertz, one cycle per thousand million seconds, or 0.001 microhertz.
The millihertz is a unit of frequency equal to one thousandth of a hertz. Its symbol is mHz. One millihertz is one cycle every thousand seconds, a little under seventeen minutes, so the unit describes things that repeat slowly enough to watch.
The lower-case m matters. A millihertz is a million times smaller than a megahertz, and the two are distinguished only by the case of the first letter. This is one of the few places in the SI where a typing error changes a quantity by six orders of magnitude, and it is a recurring source of confusion in documents that lose their capitalisation.
Seismology is the unit's natural home. A large earthquake sets the whole Earth ringing like a bell, and these free oscillations have periods of minutes to about an hour, placing them between roughly 0.3 and 5 millihertz. The gravest mode, in which the planet alternately expands and contracts as a sphere, has a period near twenty minutes. Measuring these frequencies is how the deep structure of the Earth was mapped before seismic tomography.
The Sun oscillates in the same range. Helioseismology studies pressure waves trapped inside the Sun, whose strongest signal is a five-minute oscillation at about 3.3 millihertz. Tracking millions of these modes reveals the Sun's internal rotation and the depth of its convection zone, information no telescope can obtain by looking at the surface.
Ocean tides sit far below even this. The principal lunar semidiurnal tide repeats every twelve hours and twenty-five minutes, which is about 0.022 millihertz, and the whole family of tidal constituents that tide tables are built from occupies the range below a tenth of a millihertz.
Engineering meets the unit in the sway of tall buildings and long bridges, whose fundamental modes fall between about 100 and 500 millihertz, and in the slow control loops of heating systems and chemical plant, where a process may take many minutes to respond to a change.
One millihertz equals 0.001 hertz, one cycle per 1000 seconds, or 1000 microhertz.