science calculator

Frequency to Wavelength Converter

Convert electromagnetic frequency to wavelength in meters and nanometers using the speed of light.

Results

Wavelength (m)
0.00
Wavelength (nm)
599.58

How to use this calculator

  1. Decide what electromagnetic frequency you want to analyze (for example, a Wi‑Fi band, a radio channel, or an optical frequency in the visible/IR/UV range).
  2. Convert that frequency to hertz if it’s currently in MHz, GHz, or THz (for example, 2.4 GHz = 2.4 × 10⁹ Hz).
  3. Enter the frequency in Hz into the calculator.
  4. We divide the speed of light in vacuum by your frequency to compute wavelength in meters, then multiply by 10⁹ to show nanometers.
  5. Use the meter value for RF/antenna work and the nanometer value for optics and photonics context.

Inputs explained

Frequency (Hz)
The electromagnetic wave frequency in hertz. Use scientific notation for very large values (for example, 5e14 for 500 THz). If your frequency is in MHz, GHz, or THz, convert to Hz before entering.

How it works

For electromagnetic waves in vacuum, frequency f and wavelength λ are related by c = λ × f, where c is the speed of light in vacuum.

We use c = 299,792,458 meters per second by default. Rearranging gives wavelength λ = c ÷ f.

You enter frequency in hertz (cycles per second). Internally we compute λ in meters from this relationship.

To make results more useful for optics, we also convert meters to nanometers using 1 m = 10⁹ nm. This puts visible light (roughly 400–700 nm) and many laser lines into familiar units.

Because this is a simple analytic formula, the main requirement is that you enter frequency and interpret wavelength using consistent SI units.

Formula

λ = c / f, where c ≈ 2.99792458 × 10⁸ m/s in vacuum

When to use it

  • Choosing antenna lengths or feed‑line dimensions for RF projects by starting from frequency and getting quarter‑ or half‑wave dimensions.
  • Mapping optical frequencies or photon energies to wavelengths when selecting filters, lenses, or detectors in spectroscopy or imaging setups.
  • Relating different parts of the EM spectrum—radio, microwave, infrared, visible, ultraviolet, X‑ray—using wavelength instead of frequency for educational or lab work.
  • Cross‑checking textbook or datasheet values where some sources quote frequencies and others quote wavelengths, ensuring they are consistent.

Tips & cautions

  • Always convert your input frequency to hertz before entering it. For example, 100 MHz = 1e8 Hz, 2.4 GHz = 2.4e9 Hz, 560 THz ≈ 5.6e14 Hz.
  • Remember that wavelength shortens inside materials with refractive index n; the vacuum wavelength λ₀ relates to material wavelength by λ_material = λ₀ ÷ n.
  • For rough antenna design, a quarter‑wave dimension is λ ÷ 4 and a half‑wave is λ ÷ 2; use the meter output for those calculations.
  • Use scientific notation to avoid typing many zeros—this reduces input mistakes when working with very high‑frequency signals.
  • Assumes propagation in vacuum with speed c; it does not automatically adjust for refractive indices or waveguides where phase velocity differs from c.
  • Models a single frequency at a time; it does not address bandwidth, modulation sidebands, or spectral width.
  • Displays rounded values for readability; if you need very high precision for lab work, you may need to carry more significant figures manually.

Worked examples

Example 1: Green light at 560 THz

  • Convert 560 THz to Hz: 560 × 10¹² Hz = 5.6e14 Hz.
  • λ = c / f ≈ 2.9979e8 m/s ÷ 5.6e14 Hz ≈ 5.35e−7 m.
  • In nanometers: 5.35e−7 m × 10⁹ ≈ 535 nm, in the green portion of the visible spectrum.

Example 2: 2.4 GHz Wi‑Fi band

  • Frequency = 2.4 GHz = 2.4e9 Hz.
  • λ ≈ 2.9979e8 m/s ÷ 2.4e9 Hz ≈ 0.125 m (12.5 cm).
  • A quarter‑wave antenna would be roughly 0.125 ÷ 4 ≈ 3.1 cm long (in free space).

Example 3: 100 MHz FM radio

  • Frequency = 100 MHz = 1.0e8 Hz.
  • λ ≈ 2.9979e8 m/s ÷ 1.0e8 Hz ≈ 3.0 m.
  • This shows why FM broadcast antennas and wavelengths are on the order of meters.

Deep dive

Convert electromagnetic frequency to wavelength instantly using the speed of light in vacuum—ideal for RF design, antenna sizing, and optics homework.

Enter frequency in Hz (from kHz to THz) and see wavelength in meters and nanometers without manual unit conversions or mistakes.

Perfect for engineers, students, and hobbyists who need a fast λ = c / f conversion for everything from Wi‑Fi antennas to laser lines.

FAQs

Can I adjust for propagation in glass, water, or other media?
Yes, indirectly. Divide the speed of light c by the medium’s refractive index n to get an effective velocity (c_eff = c ÷ n), then use λ = c_eff ÷ f. This calculator uses vacuum c by default, so you would need to adjust f or c offline for precise in‑medium values.
What units should I use for frequency?
Enter frequency in hertz. If you have MHz, GHz, or THz, convert first (for example, 2.4 GHz = 2.4e9 Hz, 1 THz = 1e12 Hz). Using consistent SI units avoids scaling mistakes.
Does this work for all parts of the EM spectrum?
Yes, as long as you enter a frequency in hertz. The same λ = c / f relationship applies from radio waves through microwaves, infrared, visible light, ultraviolet, and X‑rays in vacuum.
Why doesn’t the calculator ask for medium or temperature?
To keep it simple, we assume vacuum speed of light. In many contexts, especially for quick design checks or homework problems, this is the assumption being used. For detailed modeling in specific media, you’d typically use more specialized tools.

Related calculators

This frequency-to-wavelength converter uses an ideal vacuum speed of light and is intended for educational and preliminary design purposes. It does not account for material properties, dispersion, or complex propagation effects. For high-precision engineering, safety-critical RF work, or scientific research, verify calculations with more detailed models and consult relevant standards or experts.