How this calculator works
Spectroscopic wavenumber counts complete cycles in a unit distance. Angular wavenumber measures phase change in radians over that distance. Both have inverse-length dimensions, but their numerical values differ by 2 pi. Choose the matching input mode before entering a number. The reference table converts reciprocal centimetres to micrometres without needing a wave speed. Frequency conversion uses the selected phase speed. Vacuum light uses the exact SI speed; sound presets are rounded room-temperature references. For dispersive media, use phase speed at the frequency in question.
Formula
Spectroscopic wavenumber sigma = 1/lambda; angular wavenumber k = 2 pi sigma; f = v sigma; lambda = v/f. In spectroscopy units, lambda in micrometres = 10000 / sigma in 1/cm. One inverse centimetre equals 100 inverse metres.
Worked example
A wavelength of 0.01 mm, or 10 micrometres, gives a spectroscopic wavenumber of 1000 cm^-1 and an angular wavenumber of 628318.5307 rad/m. In vacuum its frequency is 29.9792458 THz. For a different example, a 3 Hz wave travelling at 12 m/s has wavelength 4 m, spatial wavenumber 0.25 m^-1 and angular wavenumber 1.570796327 rad/m.
Advertisement
Frequently asked questions
Does 1000 cm^-1 mean a wavelength of 1000 cm?
No. The minus-one exponent means reciprocal centimetres. Invert the value with consistent units: 1000 cm^-1 corresponds to 0.001 cm, or 10 micrometres.
Which convention does an infrared spectrum normally use?
Spectroscopic wavenumber is the reciprocal of vacuum wavelength. Use the cycles-per-length input and the vacuum light reference when converting that coordinate to frequency.
Why does the angular unit selector also say 1/m?
Radian is dimensionless in SI. On the angular field, 1/m therefore represents radians per metre; on the spectroscopic field it represents cycles per metre. The field label identifies the convention.
Can I enter a Raman shift?
This tool treats the input as an absolute wavenumber. A Raman shift is a difference between incident and scattered spectroscopic wavenumbers; it needs the incident laser coordinate to recover the scattered wavelength.
Where are the glass or metal presets?
Use custom phase speed for a particular material and condition. Optical speed depends on refractive index and wavelength; solid sound speeds also depend on composition and the wave type.