Wavelength Calculator

About the Wavelength Calculator

Every wave — light, radio, sound or a ripple on a pond — has a wavelength: the distance from one crest to the next. Wavelength decides a surprising amount. It sets the colour of light, the size of an aerial, how far a radio signal bends around hills, how deep a musical note sounds and how finely a microscope can see. It is linked to the wave's frequency and speed by one of the simplest equations in physics.

This wavelength calculator finds the wavelength of any wave from its frequency and speed — light and radio waves at the speed of light, sound in air, water or steel, or a speed you enter yourself. It can also find the wavelength of a photon from its energy in electronvolts. For electromagnetic waves it names the part of the spectrum, down to the colour of visible light, and gives the energy carried by each photon.

How to Use the Wavelength Calculator

Choose From frequency or From photon energy.

For frequency, enter the value, choose Hz, kHz, MHz, GHz or THz, and choose the type of wave, or enter a custom wave speed.

For photon energy, enter the energy in electronvolts.

The Formulas

  wavelength         λ = v ÷ f
  photon wavelength  λ = h × c ÷ E

  v = wave speed (m/s)          f = frequency (Hz)
  c = 299,792,458 m/s           h = 6.62607015 × 10⁻³⁴ J·s
  h × c ≈ 1,239.84 eV·nm

Step-by-Step Examples

An FM radio station at 100 MHz.

  λ = 299,792,458 ÷ 100,000,000 = 2.9979 m

Wi-Fi at 2.4 GHz: λ = 299,792,458 ÷ 2.4 × 10⁹ = 0.12491 m = 12.491 cm.

Concert A, 440 Hz, in air (343 m/s): λ = 343 ÷ 440 = 0.77955 m.

Green light at 540 THz: λ = 299,792,458 ÷ 5.4 × 10¹⁴ = 555.17 nm.

A 2 eV photon: λ = 1,239.84 ÷ 2 = 619.92 nm, orange-red light.

The Electromagnetic Spectrum

  Band           Wavelength             Example
  radio          1 m and longer         FM, TV, AM broadcasts
  microwaves     1 mm to 1 m            Wi-Fi, mobile phones, radar
  infrared       700 nm to 1 mm         heat radiation, remote controls
  visible        380 to 700 nm          violet, blue, green, yellow, red
  ultraviolet    10 to 380 nm           sunburn, black lights
  X-rays         0.01 to 10 nm          medical imaging
  gamma rays     below 0.01 nm          radioactive decay

Boundaries between bands are conventions, and sources draw them slightly differently.

Colours of Visible Light

Our eyes detect a narrow band of wavelengths, roughly 380 to 700 nanometres. The shortest look violet, then come blue (around 450 to 495 nm), green (495 to 570 nm), yellow (570 to 590 nm), orange (590 to 620 nm) and red (620 to 700 nm). Human vision is most sensitive in daylight to green-yellow light around 555 nm, which is why high-visibility clothing and emergency vehicles often use that colour. White light is a mixture of all these wavelengths, separated into a rainbow by a prism or raindrops.

Wavelength and Wave Speed

For a given wave speed, wavelength and frequency are inversely proportional: double the frequency and the wavelength halves. The speed depends on the medium. All electromagnetic waves travel through a vacuum at exactly 299,792,458 m/s, slightly slower in air and glass. Sound is far slower — about 343 m/s in air at 20 °C, around 1,480 m/s in water and about 5,960 m/s in steel — so sound waves of everyday frequencies have wavelengths from centimetres to many metres. When a wave passes from one medium into another, its frequency stays the same but its speed and wavelength change, which is what makes light bend as it enters water or a lens.

Photon Energy

Light behaves as a stream of particles, photons, as well as a wave. Each photon's energy is E = h f = h c ÷ λ, so shorter wavelengths carry more energy. Visible photons carry about 1.8 to 3.3 electronvolts. Ultraviolet photons carry more, enough to break chemical bonds in skin cells, and X-ray and gamma-ray photons carry thousands to millions of electronvolts. Radio photons, by contrast, carry a tiny fraction of an electronvolt, which is why radio waves are harmless at normal power levels.

Wavelength in Everyday Technology

Aerials are often designed as a quarter or half of the wavelength they receive, so FM car aerials are around 75 cm long, while phone antennas for gigahertz signals are just a few centimetres. Microwave ovens use 2.45 GHz radiation, about 12 cm long, which is why the metal mesh in the door, with holes only a few millimetres across, keeps the microwaves in while letting visible light through. Musical instruments work the same way: the longer the pipe or string, the longer the wavelength and the lower the note.

Wavelength and Diffraction

Waves bend around obstacles and spread out through gaps, an effect called diffraction, and it is strongest when the gap or obstacle is similar in size to the wavelength. Long-wave radio signals, hundreds of metres long, bend around hills and buildings, while short-wavelength light casts sharp shadows. Sound, with wavelengths of centimetres to metres, easily bends around doorways, which is why you can hear someone in the next room without seeing them.

Understanding Your Result

The headline is the wavelength, with a sensible prefix.

The in other units line gives it in metres, centimetres and millimetres, or nanometres.

The frequency and period line gives the frequency, wave speed and period.

The spectrum line names the part of the electromagnetic spectrum and the photon energy, or describes the sound wave.

When Should You Use This Calculator?

Use it for physics homework on waves and light.

Use it to design or check aerials and antennas.

Use it to find the colour of light of a given frequency.

Common Mistakes

Using the speed of light for sound. Choose the right type of wave.

Mixing MHz and GHz. Check the prefix of the frequency.

Forgetting that speed changes with the medium. Sound is faster in water and steel.

Confusing nanometres and micrometres. Visible light is hundreds of nanometres.