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Wavenumber from Wavelength — result sheet
Calculate spatial wavenumber, cycles per metre, and frequency from wavelength and propagation speed.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: k = 2π/λ; spatial frequency = 1/λ; f = v/λ, with wavelength converted to metres.
Wavenumber is the angular phase change per metre, so it is 2π divided by wavelength. The related spatial frequency is cycles per metre, while dividing propagation speed by wavelength gives ordinary frequency. Keeping both reciprocal conventions visible prevents confusing k with 1/λ.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Wavelength — nm; minimum 1.0E-6; maximum 1000000000
- Wave speed — m/s; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Wavelength | 500 |
| Wave speed | 299792458 |
A 500 nm wave has k ≈ 12,566,370.61 rad/m, 2,000,000 cycles/m, and frequency ≈ 599.585 THz.
Assumptions and limits
- The wavelength and propagation speed describe the same steady wave and the entered wavelength is positive.
- The angular wavenumber is returned in radians per metre, while cycles per metre is the ordinary spatial frequency.
- Dispersion, medium changes, refraction, and wave-packet bandwidth are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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