ConverterHub

Wavelength from Frequency Calculator

Enter a frequency and unit to compute the electromagnetic wavelength.

Result

0.124914 m
12.4914 cm
1.2491e+8 nm

How it is calculated

The tool converts the frequency to hertz and divides the speed of light by it: λ = c / f with c = 299,792,458 m/s. The frequency is multiplied by 1 for Hz, 103 for kHz, 106 for MHz, 109 for GHz and 1012 for THz. The wavelength is then shown three ways: metres (six decimals), centimetres (four decimals) and nanometres in scientific notation. The frequency must be above zero. Unit names are case-sensitive; if the unit is missing or not exactly one of the five, MHz is used, so "ghz" in lowercase is treated as MHz. The speed of light is the vacuum value, so waves in cable, glass or other media travel more slowly and have a shorter wavelength.

Worked example

A Wi-Fi signal at 2.4 GHz. Frequency in hertz: 2.4 × 109 = 2,400,000,000 Hz. Wavelength: 299,792,458 / 2,400,000,000 = 0.124914 m. That is 12.4914 cm, which the tool also gives as 1.2491e+8 nm. A quarter-wave antenna for this signal would be about 3.1 cm long.

Try this example →

Common mistakes

  • Choosing the wrong unit. Typing 2.4 with MHz selected gives a wavelength 1000 times longer (about 125 m) than 2.4 GHz.
  • Using a unit with the wrong case such as ghz or mhz. The tool silently falls back to MHz.
  • Applying the result inside a coaxial cable or other medium. The vacuum value of c is used, so the wavelength in a cable is shorter by its velocity factor.
  • Reading the nanometre result as a plain number. It is in scientific notation, so 1.2491e+8 means 1.2491 × 108 nm.
  • Confusing period with wavelength. The period is 1/f in seconds; the wavelength is the distance covered in one period.

About this calculator

Every electromagnetic wave's wavelength and frequency are linked through the speed of light: λ = c / f, where c is the speed of light in a vacuum (299,792,458 m/s) and f is frequency in hertz. A higher frequency always means a shorter wavelength, and vice versa — a 100 MHz FM radio signal has a wavelength of about 3 meters, while visible light near 500 THz has a wavelength of roughly 600 nanometers.

RF and antenna engineers use this relationship to size antennas (often a fraction of a wavelength, like λ/4 or λ/2), physics students use it to move between the two most common ways of describing light or radio waves, and spectroscopists use it to convert between wavelength- and frequency-based measurements of light.

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