Wavelength Calculator

How to use this calculator

Select what you want to find: wavelength (λ), frequency (f), or wave speed (v). Enter the two known values. Use the wave speed presets to select from common media: sound in air (343 m/s), sound in water (1480 m/s), sound in steel (5120 m/s), or the speed of light in vacuum (299,792,458 m/s).

The calculator shows the result in metres along with a convenient unit (nanometres for visible light, centimetres for radio waves). An electromagnetic spectrum classification card shows where the frequency falls.

The wave equation

All periodic waves, from sound to light to water ripples, obey the same fundamental relationship between wavelength, frequency, and wave speed:

Where v is the wave speed in metres per second, f is the frequency in hertz, and λ (lambda) is the wavelength in metres. Rearranging:

Wavelength and frequency are inversely proportional at constant wave speed. Double the frequency and the wavelength halves. This is why high-pitched sounds (high frequency) have shorter wavelengths than low-pitched sounds (low frequency), and why X-rays (very high frequency) have far shorter wavelengths than radio waves (low frequency).

Period T is the reciprocal of frequency: T = 1/f. The wave equation can also be written v = λ/T.

The electromagnetic spectrum

Electromagnetic waves travel at the speed of light in vacuum: c = 299,792,458 m/s. The full spectrum spans an enormous range of frequencies and wavelengths.

Type	Wavelength range	Frequency range
Radio waves	> 1 mm	< 300 GHz
Microwaves	1 mm – 1 m	300 MHz – 300 GHz
Infrared	700 nm – 1 mm	300 GHz – 430 THz
Visible light	380 nm – 700 nm	430 THz – 790 THz
Ultraviolet	10 nm – 380 nm	790 THz – 30 PHz
X-rays	0.01 nm – 10 nm	30 PHz – 30 EHz
Gamma rays	< 0.01 nm	> 30 EHz

The boundaries between regions are not sharp: they are conventional, and some sources define them slightly differently. The physics is continuous: a 350 nm photon is ultraviolet while a 400 nm photon is violet light, yet they behave similarly.

Visible light wavelengths and colour

The human eye detects electromagnetic radiation in a narrow band from about 380 nm (violet) to 700 nm (red). Different wavelengths within this range are perceived as different colours.

Colour	Wavelength range
Violet	380 – 450 nm
Blue	450 – 495 nm
Green	495 – 570 nm
Yellow	570 – 590 nm
Orange	590 – 620 nm
Red	620 – 700 nm

White light is a mixture of all these wavelengths. A glass prism separates white light into its constituent colours because different wavelengths travel at slightly different speeds in glass (dispersion): violet bends more than red. This is also why raindrops produce rainbows.

Lasers emit a single wavelength (monochromatic light). A red laser pointer typically emits at 635-680 nm, a green pointer at 520-532 nm, and a violet pointer at 405 nm.

Sound wavelengths

Sound is a mechanical wave: pressure oscillations propagating through a medium. Its speed depends on the medium’s elasticity and density, not on frequency. In air at 20°C, sound travels at 343 m/s.

The long wavelengths of low-frequency sound let it diffract easily around obstacles, which is why bass sounds carry through walls better than treble. High-frequency sound (short wavelength) travels more directionally and is absorbed more readily by soft materials.

Wave speed in different media

The speed of sound varies substantially between materials:

Medium	Speed of sound
Air (0°C)	331 m/s
Air (20°C)	343 m/s
Water (20°C)	1,481 m/s
Seawater	~1,525 m/s
Wood (along grain)	~3,000 – 5,000 m/s
Concrete	~3,000 m/s
Steel	~5,120 m/s
Diamond	~12,000 m/s

Sound speed in gases increases with temperature: v ∝ √T (kelvin). At 0°C (273 K), v = 331 m/s; at 20°C (293 K), v = 331 × √(293/273) = 343 m/s. This is why musicians tune instruments after warming up: a cooler instrument (and cooler air column inside wind instruments) produces slightly lower pitches.

For electromagnetic waves, speed depends on the medium’s refractive index n: v = c/n. Glass has n ≈ 1.5, so light travels at about c/1.5 = 200,000 km/s in glass. Water has n ≈ 1.33. Diamonds have n ≈ 2.42, which makes light slow significantly and contributes to their brilliance.

De Broglie wavelength

In quantum mechanics, particles have wave properties as well as particle properties. Louis de Broglie proposed in 1924 that all matter has an associated wavelength:

Where h is Planck’s constant (6.626 × 10⁻³⁴ J·s), m is mass, and v is velocity.

For everyday objects, this wavelength is vanishingly small. A 1 kg ball moving at 1 m/s has λ = 6.626 × 10⁻³⁴ m, far smaller than any atomic nucleus. Wave behaviour is completely undetectable.

For electrons, the de Broglie wavelength is significant. An electron accelerated through 100 V has a wavelength of about 0.12 nm, comparable to atomic spacings. This is why electron microscopes can image individual atoms: the wavelength is short enough. Light microscopes using visible light (400-700 nm wavelength) cannot resolve features smaller than about 200 nm because of diffraction limits.

Wavelength in fiber optics

Fiber optic communications transmit data as pulses of light through glass fibers. The choice of wavelength is critically important.

Wavelength windows: Silica glass is most transparent in three windows: 850 nm, 1310 nm, and 1550 nm. The 1550 nm window has the lowest attenuation (loss per km) and is used for long-haul communications.

Wavelength division multiplexing (WDM): Multiple wavelengths of light (different colours) are sent through a single fiber simultaneously, each carrying an independent data stream. Dense WDM (DWDM) can multiplex 80 or more channels spaced 0.8 nm apart, dramatically increasing fiber capacity.

Dispersion: Different wavelengths travel at slightly different speeds in glass (chromatic dispersion). Over long distances, a short pulse spreads out because its components arrive at different times. Dispersion-shifted fiber and dispersion compensation modules manage this to enable high-speed transmission over thousands of kilometres.

Radar and antenna wavelength

Radio and radar systems design antennas sized to match the wavelength of the transmitted signal. Efficient antenna operation requires the antenna to be a specific fraction of the wavelength, typically half or quarter wavelength.

Radar systems use microwave wavelengths. Weather radar typically operates at 10 cm (3 GHz, S-band) or 5 cm (5.5 GHz, C-band). Aircraft surveillance radar uses 23 cm (L-band). The choice involves trade-offs: shorter wavelengths can detect smaller targets and give better resolution, but are more attenuated by rain.

Wavelength and diffraction

Diffraction is the bending of waves around obstacles and through openings. The degree of diffraction depends on the ratio of wavelength to obstacle size:

Where d is the obstacle or opening size. When λ >> d, diffraction is strong: waves spread widely after passing through the gap. When λ << d, diffraction is negligible and waves travel in nearly straight lines.

This is why:

• Sound (long wavelengths, 17 mm to 17 m) diffracts around buildings and through doorways easily
• AM radio (wavelengths of 180 m to 560 m) diffracts over hills and around the curvature of the Earth
• FM radio (wavelengths of 3 m) diffracts less, giving line-of-sight coverage
• Light (wavelengths of 400-700 nm) appears to travel in straight lines at human scales, but diffracts visibly through very narrow slits (diffraction gratings, CD surfaces, thin slits)
• X-rays (wavelengths of 0.01-10 nm) diffract from atomic crystal lattices, which is the basis of X-ray crystallography used to determine protein structures