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Wavelength & Frequency Calculator

Convert wavelength to frequency and back.

Result

2.9979 m
1.0000 × 10⁸ Hz

How it is calculated

Light and radio waves obey c = f × λ with c = 299,792,458 m/s, the speed of light in a vacuum. The mode setting decides the direction. In frequency mode the value you enter is a frequency in hertz and the wavelength is λ = c / f in metres. In wavelength mode the value is a wavelength in metres and the frequency is f = c / λ in hertz. The value must be above zero. Both answers are shown in scientific notation with four decimals, for example 4.9965 × 10⁻⁷ m. When the power of ten would be 0, the number is shown alone, as 2.9979 m for 100 MHz. Waves in cables, glass or water travel slower than c, so their wavelength is shorter than this vacuum value.

Worked example

An FM radio station broadcasts at 100 MHz, which is 100,000,000 Hz, entered in frequency mode. Wavelength = 299,792,458 / 100,000,000 = 2.99792458 m, which the tool displays as 2.9979 m, about 3 metres. The frequency line repeats the input as 1.0000 × 10⁸ Hz.

Try this example →

Common mistakes

  • Typing 100 for 100 MHz; the tool needs hertz, so 100 MHz is 100000000.
  • Using wavelength mode while entering a frequency, or the other way round.
  • Entering a wavelength in nanometres or centimetres; the unit is metres, so 500 nm is 5e-7.
  • Misreading the scientific notation: × 10⁻⁷ means a very small number, and a result with no power of ten (such as 2.9979) is simply written out in full.
  • Applying the vacuum speed of light to a signal inside a cable or fibre, where waves are slower.

About this calculator

Every electromagnetic wave — radio, microwave, visible light, X-rays — obeys the fundamental relationship c = f · λ, where c is the speed of light in a vacuum (≈299,792,458 m/s), f is the wave's frequency, and λ is its wavelength. Because c is constant, frequency and wavelength are inversely proportional: doubling the frequency halves the wavelength, and vice versa. This calculator converts freely between the two, solving f = c/λ or λ = c/f.

Radio and RF engineers use this relationship to design antennas (whose optimal length is typically a fraction of the signal's wavelength), broadcast engineers use it to convert station frequencies to wavelengths, and physics and optics students use it to move between the frequency and wavelength descriptions of light, since spectroscopy, color science and quantum energy calculations (via E = hf) often require converting one to the other.

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Comments (1)

  • Editorial team

    The output is in scientific notation, so 2.4 GHz (enter 2400000000 Hz) shows 1.2491 × 10⁻¹ m, which is 12.49 cm. Radio designers use the wavelength to size antennas, often a fraction of it, but cables and real antennas run slower than the vacuum speed used here, so build dimensions are shorter. For quick practice, FM at 100 MHz gives close to 3 m. Which band or wave are you working with?

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