Frequency to Wavelength Calculator

Frequency to Wavelength Calculator

Use this frequency to wavelength calculator to convert frequency (f) into wavelength (λ) in your chosen medium. Supports vacuum/air and common materials via refractive index or custom wave speed.

Frequency to Wavelength Calculator – Convert f to λ Instantly

This frequency to wavelength calculator converts a signal’s frequency f into its wavelength λ for a chosen medium. You can select vacuum (speed of light), air, water, glass, optical fiber, or enter a custom refractive index or wave speed. The tool also returns the wave’s period, wavenumber, and spatial frequency, plus unit conversions to meters, centimeters, millimeters, micrometers, nanometers, feet, and inches.

Wavelength Basics

Wavelength is the spatial period of a wave — the distance over which the wave’s shape repeats. For electromagnetic waves, wavelength depends on the wave’s frequency and the speed of propagation in the medium. In simple form: λ = v / f. In vacuum, the speed of light c is a defined constant (299 792 458 m/s). (NIST CODATA – Speed of light) For a medium with refractive index n, light slows to v = c/n, so wavelength shortens by the same factor.

Formula Used by the Frequency Wavelength Converter

λ = v / f,   where v = c / n   (electromagnetic waves)
T = 1 / f   (period)
k = 2π / λ  (wavenumber, rad/m)
σ = 1 / λ   (spatial frequency, cycles/m)

The wavelength from frequency calculator follows these relationships directly and presents coherent results across unit systems.

Mediums and Refractive Index

Electromagnetic waves in media travel slower than in vacuum. Typical refractive indices at visible wavelengths are approximately: air ≈ 1.00027, water ≈ 1.333, common glass ≈ 1.50, optical fiber ≈ 1.468. A higher n means shorter λ for the same f. Note that real materials are dispersive: n varies with wavelength. For precise optical work, use a wavelength-specific index from the datasheet. (Britannica – Wavelength, HyperPhysics – Wavelength)

Units You Can Work With

  • Frequency: Hz, kHz, MHz, GHz, THz
  • Wavelength: m, cm, mm, µm, nm, ft, in
  • Derived: Period (s), Wavenumber (rad/m), Spatial frequency (cycles/m)

This makes the frequency to wavelength calculator equally useful for RF (meters, centimeters), microwaves (centimeters, millimeters), and optics (µm, nm).

How to Use the Calculator (Step by Step)

  1. Enter the frequency value and select the unit (Hz through THz).
  2. Choose a medium: vacuum, air, water, glass, optical fiber, or set a custom n or custom speed v.
  3. Click Calculate. The tool outputs wavelength and handy conversions, plus the period, wavenumber, and spatial frequency.
  4. Use the Custom v option for non-EM waves (e.g., surface waves, coax cables with specific velocity factor).

Worked Examples

1) 100 MHz (FM radio) in Air

f = 100 MHz, air n ≈ 1.00027 → v ≈ c/1.00027 ≈ 299 711 000 m/s. λ = v/f ≈ 2.99711 m. Period T ≈ 10 ns. k ≈ 2.095 rad/m; spatial frequency ≈ 0.334 cycles/m.

2) 2.4 GHz (Wi-Fi) in Free Space

f = 2.4 GHz, vacuum → λ = c/f ≈ 0.1249 m = 12.49 cm. Often antennas use λ/2 or λ/4 dimensions.

3) 193.5 THz (Telecom C-Band) in Fiber

Assume n ≈ 1.468 → v ≈ 204 190 000 m/s; λ = v/f ≈ 1.055 µm (≈ 1055 nm). Dispersion makes exact n wavelength-dependent, so consult your fiber datasheet.

Common Use Cases

  • RF & Antennas: antenna element length vs. operating frequency; choosing λ/2 dipoles, λ/4 monopoles.
  • Microwave engineering: waveguide dimensions scale with wavelength; cutoff depends on λ.
  • Optics & Photonics: converting THz or wavenumbers to wavelength in nm/µm; refractive index effects.
  • Cable propagation: velocity factor in coax reduces effective wave speed (use custom v).

Period, Wavenumber and Spatial Frequency

Frequency specifies how fast a wave oscillates in time; period is its inverse (seconds per cycle). Wavenumber is spatial angular frequency (radians per meter), and spatial frequency is cycles per meter. The frequency wavelength converter bundles all four so you can switch between timing and geometry comfortably.

Accuracy Notes

  • Vacuum speed of light is exact by definition (299 792 458 m/s).
  • Air index depends slightly on temperature, pressure, humidity, and wavelength; n ≈ 1.00027 is a typical reference.
  • Dispersion: many materials have n(λ). For tight tolerances, use wavelength-specific n, not a single constant.
  • Non-EM waves: if you enter a custom speed for acoustic or mechanical waves, ensure the speed corresponds to your medium and frequency band.

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Further Reading

Disclaimer: This frequency to wavelength calculator is for educational purposes. Results assume linear, non-dispersive media unless you provide a custom speed or index. For precision optics or RF compliance, consult standards and material datasheets.