Frequency to Wavelength Converter
Common Conversions
| Hz | nm |
|---|---|
| 1000000000000 | 299800 |
| 5000000000000 | 59960 |
| 10000000000000 | 29980 |
| 50000000000000 | 5996 |
| 100000000000000 | 2998 |
| 300000000000000 | 999.3 |
| 428300000000000 | 700 |
| 500000000000000 | 599.6 |
| 600000000000000 | 499.7 |
| 700000000000000 | 428.3 |
| 1000000000000000 | 299.8 |
| 3000000000000000 | 99.93 |
Why this conversion matters in chemistry
Pump-probe spectroscopy crosses this conversion every time a tunable laser source needs to land on a UV-Vis absorption peak. A 500 THz laser line lands at 600 nm — the orange-red regime where many transition-metal chromophore d-d bands sit. The factor c = 299,792,458 m/s is exact by the SI definition of the meter, so λ in nm equals 2.998 × 10¹⁷ divided by frequency in Hz. The conversion is a unit step in any optical-spectroscopy workflow that crosses between source-side frequency specs and target-side wavelength data.
Formula
Where the factor comes from
This is the one pair on the length list where no prefix ladder is involved. Frequency and wavelength are different physical quantities joined by a wave speed through λ = c/ν, and the number doing the joining is the speed of light in vacuum: 299 792 458 m/s, fixed exactly since the meter was redefined in terms of it in 1983. Recast into the units this page wants, that is 2.997 924 58 × 10¹⁷ nm/s, and nanometers are that constant divided by hertz. The constant is exact by definition, but the relation is not universal. The c in it is the vacuum speed, and light crossing any real medium travels slower by the refractive index. Frequency is what survives an interface unchanged; wavelength is what compresses.
Precision and significant figures
The constant contributes nine exact figures, which is more than any spectrometer will ever need, so the arithmetic is never the limiting step. Two things upstream are. First the medium: air at ambient conditions has a refractive index near 1.00027, so a vacuum wavelength of 500 nm sits at about 499.86 nm when measured in air. That 0.14 nm shift is comparable to the wavelength accuracy of a routine benchtop instrument and larger than its reproducibility, so it is not safely ignored. Second, the frequency side is often known absurdly well — a stabilized source can carry ten figures or more. Report the wavelength to the digits your monochromator earns, not the digits the source offers.
Worked Examples
Green light — mid-visible, the calibration wavelength for many UV-Vis instruments.
Violet at the edge of visible — useful as the short-wavelength visible anchor.
Deep red at the long-wavelength visible edge.
Mid-UV — about the wavelength region for many photochemistry studies.
Common mistakes
Air wavelengths compared against vacuum values
A frequency converts to a vacuum wavelength unless you divide by the refractive index of whatever the light is actually crossing. Line lists assembled from older spectroscopy often quote air values above 200 nm and vacuum values below, switching partway down the table without much fanfare. Comparing a computed vacuum wavelength against an air-referenced line leaves you a few tenths of a nanometer out with nothing signalling it.
Interpolating a reciprocal relation linearly
Doubling the frequency halves the wavelength; it does not double it and it does not shift it by a fixed amount. Reading between two rows of a frequency-to-wavelength table by linear interpolation is wrong by an amount that grows with the gap between them. Convert each endpoint properly instead of averaging, particularly across the visible range, which spans a factor of two in both quantities.
THz entered where Hz was expected
Laser and microwave sources are specified in THz, GHz or MHz, and the constant here expects plain hertz. A 500 THz line is 5 × 10¹⁴ Hz and returns 599.6 nm; entering the bare 500 returns about 6 × 10¹⁴ nm, which is 600 kilometers. The failure is loud enough to catch, provided somebody looks at the magnitude before writing it down.