Hertz to Terahertz Converter
Common Conversions
| Hz | THz |
|---|---|
| 100000000000 | 0.1 |
| 500000000000 | 0.5 |
| 1000000000000 | 1 |
| 2000000000000 | 2 |
| 5000000000000 | 5 |
| 10000000000000 | 10 |
| 25000000000000 | 25 |
| 50000000000000 | 50 |
| 100000000000000 | 100 |
| 1000000000000000 | 1000 |
Why this conversion matters in chemistry
Terahertz time-domain spectroscopy probes molecular-scale vibrations from 0.1 to 10 THz — the regime where intermolecular hydrogen-bonding networks and skeletal phonon modes show up. The technique discriminates pharmaceutical polymorphs by their distinct lattice-mode fingerprints. A 1 THz resonance is 1 × 10¹² Hz, equivalently 33.4 cm⁻¹ in FTIR wavenumbers and 4.14 meV in photon energy. The ratio of 10⁻¹² THz per Hz is just the tera prefix. The conversion is mostly bookkeeping that takes a raw frequency-counter reading into the THz form a far-infrared spectrum is plotted in.
Formula
Where the factor comes from
The factor itself is beyond argument — tera is 10¹² by definition, so THz = Hz ÷ 10¹². What deserves attention is that terahertz values almost never arrive from counting cycles — nothing counts 10¹² events per second directly. A time-domain instrument samples an electric-field waveform against a mechanical delay line and Fourier transforms it, which means the frequency axis is built out of a length measurement, and length rests on the defined speed of light, 299792458 m/s. That same fixed c makes the far-infrared bridge exact as well: one wavenumber equals 2.99792458 × 10¹⁰ Hz, so 1 THz is 33.3564095 cm⁻¹ with no measurement uncertainty anywhere in the chain. Only the sampled waveform underneath carries error.
Precision and significant figures
Terahertz peaks are usually quoted to two or three significant figures, and the reason is not the conversion — it is spectral resolution. In a time-domain measurement the frequency resolution is the reciprocal of the scan length, so a 50 picosecond delay window gives about 20 GHz, or 0.02 THz. A feature reported as 1.234 THz from a scan that short claims a digit the data cannot support; 1.23 THz is what was measured. Because the 10¹² factor is exact, convert the raw hertz value at full precision and round once, at the end, to whatever the scan length justifies. Rounding before converting throws digits away for nothing.
Worked Examples
The conversion anchor — the lower edge of the far-IR region.
10 THz — the upper end of the THz window, transitioning into mid-IR.
The microwave-THz boundary, where rotational spectroscopy starts to overlap with vibrational modes.
Common mistakes
GHz and THz slipping by a thousand
Below about 1 THz most hardware and most literature switch to gigahertz, so the same resonance appears as 300 GHz in one source and 0.3 THz in another. Pulling numbers from both without checking the axis label produces a thousand-fold error that still looks like a physically sensible frequency. Read the unit before you read the value.
Treating wavenumbers as terahertz directly
Far-infrared work moves constantly between cm⁻¹ and THz, and the two are not interchangeable: one terahertz is 33.356 cm⁻¹, not one and not thirty. A lattice mode at 100 cm⁻¹ sits at 3.00 THz. Substituting the numbers without that factor misplaces the feature by more than the width of the entire measurement window.
Ignoring refractive index inside the sample
Converting terahertz frequency to wavelength with c alone gives the vacuum wavelength — about 300 micrometers at 1 THz. Inside a pressed pellet or a polymer window the phase velocity is lower, so the wavelength there is shorter by the refractive index. Path-length and etalon-spacing arguments built on the vacuum figure will come out wrong.