Wavelength and frequency calculator
Enter a wavelength or a frequency, get the other.
How do I convert wavelength to frequency?
Frequency = wave speed ÷ wavelength. For light, speed is exactly 299,792,458 m/s, so 500 nm green light has a frequency of 599.6 THz.
How do I find the wavelength of a radio station?
Wavelength = speed ÷ frequency: an FM station at 100 MHz has a wavelength of about 3.0 m; Wi-Fi at 2.4 GHz about 12.5 cm.
What is the energy of a photon?
E = h × f, with Planck's constant h = 6.62607015 × 10⁻³⁴ J·s. A 500 nm photon carries 3.97 × 10⁻¹⁹ J, or 2.48 electronvolts.
Can I use it for sound?
Yes — enter the speed of sound in the medium as the wave speed. Sound in air travels at roughly 343 m/s at room temperature, depending on temperature.
Why is the speed of light exact?
Since 1983 the meter has been defined from it, so c = 299,792,458 m/s by definition.
What wavelengths do visible light, FM radio and Wi-Fi have?
OpenStax University Physics, Volume 2, section 16.5, puts visible light between about 400 nm and 750 nm, which is roughly 400 to 750 THz. FM radio runs from 88 to 108 MHz, wavelengths of 2.78 to 3.41 m, and Wi-Fi uses microwaves from 2.4 to 5.0 GHz, 12.5 cm down to 6.0 cm.
How long are audible sound waves?
Humans hear roughly 20 Hz to 20 kHz. With the speed of sound at 343 m/s (20 °C) that is a wavelength of 17.2 m for the lowest tone and 1.7 cm for the highest (OpenStax University Physics, Volume 1, Example 17.1 gets 17 m and 1.7 cm at 30 °C). Enter 343 as the wave speed to reproduce it.
How do I convert a wavelength in nanometers to electronvolts?
Use E = hc ÷ λ, and hc = 1,239.84 eV·nm, so E in eV is 1,239.84 divided by the wavelength in nm. A 650 nm red laser photon has 1.907 eV, which is 3.056 × 10⁻¹⁹ J. Shorter wavelengths carry more energy per photon.
The formula and what it assumes
For any wave, the speed equals the wavelength times the frequency, v = λf (OpenStax University Physics, Volume 1, section 16.1, Eq. 16.1), and the period is T = 1 ÷ f. For light in vacuum v = c = 299,792,458 m/s exactly, and the photon energy is E = hf with h = 6.62607015 × 10⁻³⁴ J·s, also exact. The calculator uses c by default; for sound, water waves or light in a material, enter the wave speed in that medium. The frequency is set by the source, so for a given frequency a slower wave has a shorter wavelength.
Worked example: a 650 nm red laser
The wavelength is 650 × 10⁻⁹ m, so f = c ÷ λ = 299,792,458 ÷ 6.5 × 10⁻⁷ = 461.2 THz, and the period is 2.17 fs (10⁻¹⁵ s). The photon energy is E = hf = 1.907 eV. Going the other way, a station at 98.7 MHz has λ = c ÷ f = 3.04 m.
Common mistakes
Unit prefixes cause most errors: a wavelength in nm entered as µm is off by a factor of 1,000, and a frequency in MHz entered as GHz likewise. Another is using c for sound; sound travels at about 343 m/s in air, almost a million times slower. A third is confusing frequency f in hertz with angular frequency ω = 2πf in radians per second, which is a factor of 6.28. And the wavelength of light in glass or water is shorter than in vacuum for the same frequency, so use the speed in the medium, not c.
Sources: OpenStax University Physics, Volume 1, sections 16.1 (wave speed, Eq. 16.1) and 17.2 (Example 17.1); Volume 2, section 16.5 (the electromagnetic spectrum); the speed of light and the Planck constant are exact in the 2019 SI (NIST). Related: speed of sound calculator, photoelectric effect calculator, Doppler effect calculator and standing wave calculator.