About the Wavelength and Frequency Calculator
This wavelength and frequency calculator converts between the two using the wave equation v = f × λ. Choose whether you know the frequency or the wavelength, pick the medium — light or radio in a vacuum, sound in air, sound in water, or a custom wave speed — and it returns the other quantity along with the period and, for electromagnetic waves, the photon energy.
It covers everyday questions such as the wavelength of a 2.4 GHz Wi-Fi signal or an FM radio station, what colour a 500 nm laser is, how long a 440 Hz sound wave is, and how many electronvolts a photon carries. Students can use it to check spectroscopy and wave homework.
The speed of light is the exact SI value 299,792,458 m/s. Sound speeds use 343 m/s for dry air at 20 °C and 1,482 m/s for pure water at 20 °C (NPL, Bilaniuk and Wong equation); both change with temperature, so enter a custom speed for other media or conditions. The numeric wavelength field switches between meters and nanometers depending on size, and photon energy is shown only for electromagnetic waves where it is large enough to display — the table lists every value in scientific notation.
How to use the wavelength and frequency calculator
- 1Choose whether you know the wavelength or the frequency.
- 2Enter the value and select its unit.
- 3Pick the medium: light/radio, sound in air, sound in water or a custom speed.
- 4Read the converted value, period and (for light) photon energy.
- 5Check the table for wavenumber, angular frequency and spectrum band.
Formula and method
Every wave obeys v = f × λ: the speed equals the number of cycles per second times the length of each cycle. So if you know the speed of the wave in its medium, wavelength and frequency are simply inversely proportional — doubling the frequency halves the wavelength. The period is the time for one cycle, the reciprocal of frequency.
For light and other electromagnetic radiation, each photon carries energy E = h × f, where h is Planck’s constant (6.62607015 × 10⁻³⁴ J·s, exact). Dividing by the elementary charge converts joules to electronvolts. Sound waves are mechanical, so photon energy does not apply to them.
- λ
- Wavelength (m)
- f
- Frequency (Hz)
- v
- Wave speed in the medium (c = 299,792,458 m/s for light in vacuum)
- T
- Period (s)
- E
- Photon energy (J or eV)
- h
- Planck constant, 6.62607015 × 10⁻³⁴ J·s
Worked examples
Frequency of 500 nm green light
f = 299,792,458 ÷ 500 × 10⁻⁹ = 5.996 × 10¹⁴ Hz (about 600 THz). Each photon carries h × f ≈ 3.97 × 10⁻¹⁹ J, or 2.48 eV.
Wavelength of a 100 MHz FM radio station
λ = 299,792,458 ÷ 100,000,000 ≈ 3.00 m. That is why a quarter-wave FM antenna is about 75 cm long.
Length of a 440 Hz sound wave in air
Concert A at 440 Hz in air (343 m/s) has λ = 343 ÷ 440 ≈ 0.78 m — each pressure wave is about 78 cm long.
Wavelength of 2.4 GHz Wi-Fi
λ = 299,792,458 ÷ 2.4 × 10⁹ ≈ 0.125 m, or 12.5 cm — the same band microwave ovens use.
Frequently asked questions
How do you convert frequency to wavelength?+
Divide the wave speed by the frequency: λ = v/f. For light and radio in a vacuum use c = 299,792,458 m/s; for sound in air use about 343 m/s at 20 °C.
What is the relationship between wavelength and frequency?+
They are inversely proportional for a given wave speed. A higher frequency means a shorter wavelength, and their product always equals the wave speed in that medium.
How do I calculate the energy of a photon?+
Use E = hf, or E = hc/λ, where h = 6.626 × 10⁻³⁴ J·s. For wavelengths in nanometers a handy shortcut is E (eV) ≈ 1239.84 ÷ λ (nm).
What wavelength range is visible light?+
Human eyes see roughly 380 nm (violet) to 700 nm (red). Shorter wavelengths are ultraviolet and longer ones are infrared, both invisible to us.
Why does the medium matter?+
Frequency is set by the source, but speed depends on the medium. Sound travels about 4.3 times faster in water than in air, so the same note has a wavelength about 4.3 times longer underwater.