Wavelength Calculator

About Wavelength Calculator

The Wave Equation

Wavelength equals wave speed divided by frequency: lambda = v/f. For electromagnetic waves in vacuum, v = c = 299,792,458 m/s exactly (fixed by the 2019 SI redefinition, per NIST). For sound waves, v depends on the medium's density and elasticity.

Solve For	Formula	Example
Wavelength	lambda = v / f	343 m/s / 440 Hz = 0.780 m (concert A in air)
Frequency	f = v / lambda	3 x 10⁸ m/s / 550 nm = 5.45 x 10¹⁴ Hz (green light)
Wave speed	v = f x lambda	440 Hz x 0.780 m = 343 m/s (confirms speed of sound)

Worked example: FM radio station broadcasts at 101.5 MHz. Wavelength = 299,792,458 / 101,500,000 = 2.953 m. This is why FM antennas are about 75 cm long - one quarter of the wavelength.

Derived Wave Properties

The calculator also computes these related quantities from your input:

Property	Formula	Unit	What It Means
Period (T)	1 / f	seconds	Time for one complete wave cycle
Wave number (k)	2 pi / lambda	rad/m	Spatial frequency - cycles per metre (x 2 pi)
Angular frequency (omega)	2 pi x f	rad/s	How fast the wave oscillates in radians per second
Photon energy (EM only)	E = hf	eV or J	Energy of one photon at this frequency

The Electromagnetic Spectrum

Region	Wavelength Range	Frequency Range	Photon Energy	Common Uses
Radio (AM)	100 m - 10 km	30 kHz - 3 MHz	0.12 - 12 neV	AM radio, navigation
Radio (FM)	1 - 10 m	30 - 300 MHz	0.12 - 1.24 ueV	FM radio, TV broadcast
Microwave	1 mm - 1 m	300 MHz - 300 GHz	1.24 ueV - 1.24 meV	WiFi, radar, cooking
Infrared	700 nm - 1 mm	300 GHz - 430 THz	1.24 meV - 1.77 eV	Remote controls, thermal imaging
Visible (red)	620 - 700 nm	430 - 484 THz	1.77 - 2.00 eV	Human vision
Visible (green)	495 - 570 nm	526 - 606 THz	2.18 - 2.50 eV	Human vision (peak sensitivity)
Visible (blue/violet)	380 - 495 nm	606 - 789 THz	2.50 - 3.26 eV	Human vision
Ultraviolet	10 - 380 nm	789 THz - 30 PHz	3.26 - 124 eV	Sterilisation, sunburn
X-ray	0.01 - 10 nm	30 PHz - 30 EHz	124 eV - 124 keV	Medical imaging, security
Gamma ray	Below 0.01 nm	Above 30 EHz	Above 124 keV	Cancer treatment, nuclear physics

Higher frequency means shorter wavelength and more energy per photon. This is why gamma rays can penetrate materials and damage DNA, while radio waves pass through your body harmlessly.

Speed of Sound in Different Media

Sound waves are mechanical - they need a medium to travel through. The speed depends on the material's density and elasticity.

Medium	Speed (m/s)	Wavelength of 440 Hz	Notes
Air (20 °C)	343	0.780 m	Increases ~0.6 m/s per °C
Air (0 °C)	331	0.752 m	Used in older reference tables
Helium	1,007	2.289 m	Why voices sound high in helium
Water (20 °C)	1,482	3.368 m	Sonar, underwater acoustics
Seawater	1,531	3.480 m	Varies with salinity and depth
Steel	5,960	13.545 m	Ultrasonic testing, rail inspection
Diamond	12,000	27.273 m	Fastest common solid

Sound travels about 4.4 times faster in water than in air, and about 17 times faster in steel. This is why you can hear a distant train by putting your ear to the track long before you hear it through the air.

Photon Energy and Planck's Equation

For electromagnetic waves, each photon carries energy E = hf, where h is Planck's constant (6.626 x 10⁻³⁴ J s). Since f = c/lambda, this can also be written E = hc/lambda. Shorter wavelength means higher photon energy. A single photon of violet light (400 nm) carries about 3.1 eV of energy, while a radio photon at 100 MHz carries only 0.41 micro-eV - a factor of about 7.5 million less.

For energy-mass relationships at extreme energies, the E = mc² calculator converts between mass and energy. For sound-related speed calculations, the velocity calculator solves v = d/t problems. All calculations run in your browser with no data sent to any server.

Why Sound Speed Varies With the Medium

Sound speed follows v = sqrt(K / rho), where K is the bulk modulus (stiffness) and rho is the density of the medium. Stiffer materials carry sound faster; denser ones slow it down. That explains why steel (very stiff) beats water, which beats air, despite air being the least dense. Temperature matters for gases: the speed of sound in dry air rises by about 0.6 m/s for every 1 °C, which is why an outdoor concert in summer sounds slightly different to one in winter for a listener far from the stage.

Humidity and altitude also shift the figure. The Engineering ToolBox lists dry air at sea level at 343 m/s at 20 °C, rising to around 349 m/s at 30 °C. At 10 km altitude where commercial jets cruise, air is cold enough that sound drops to roughly 295 m/s, which is why the threshold Mach 1 for a passenger airliner is a smaller true airspeed at altitude than at ground level.

Worked example: a submarine sonar emits a 25 kHz pulse in seawater at 1,531 m/s. Wavelength = 1,531 / 25,000 = 0.0612 m (6.12 cm). This short wavelength is what gives sonar good angular resolution for detecting objects.

What Is a Good Reference for Visible Light Wavelengths?

The human eye sees wavelengths from about 380 nm (violet) to 700 nm (red), per the International Commission on Illumination (CIE). Peak photopic sensitivity is near 555 nm (yellow-green) in daylight, shifting to 507 nm (green-blue) in low light (the Purkinje shift). This is why emergency exit signs and high-visibility workwear use yellow-green colours.

Colour	Wavelength (nm)	Frequency (THz)	Typical Source
Deep red	700	428	Diode laser, sunset
Orange	610	492	Sodium streetlights (589 nm)
Yellow	580	517	Sun peak emission
Green	530	566	Plant reflection, LEDs
Cyan	490	612	Tropical ocean water
Blue	470	638	Clear sky (Rayleigh scatter)
Violet	400	750	Blacklight edge, some LEDs

Lasers are defined by a single dominant wavelength: a 532 nm green laser pointer is a frequency-doubled Nd:YAG (originally 1064 nm infrared), while a 650 nm red laser pointer uses a gallium-indium-phosphide diode. The BIPM maintains the official colour-matching functions that underpin all industrial colour standards.

How Wavelength Sets the Size of Antennas

A quarter-wave antenna has physical length of lambda/4, because that geometry maximises radiation efficiency for a given frequency. This is why antenna size scales inversely with frequency.

Service	Frequency	Wavelength	Typical Antenna Length (lambda/4)
LW radio	198 kHz (BBC R4)	1,514 m	Not practical - uses a loaded loop
AM MW	1 MHz	300 m	75 m tower (or loaded short whip)
FM radio	100 MHz	3 m	75 cm car aerial
DAB / TV	200-800 MHz	37-150 cm	9-38 cm
4G mobile	2.1 GHz	14.3 cm	3.6 cm (hidden inside phone)
Wi-Fi	2.4 GHz	12.5 cm	3.1 cm
5G mmWave	28 GHz	10.7 mm	2.7 mm (array of hundreds)
Starlink uplink	14 GHz (Ku-band)	21.4 mm	Phased-array dish

5G mmWave is why recent mobile phones carry dozens of tiny antennas in an array: each element is only a few millimetres long, but the array shapes a beam that compensates for the short wavelength's poor building penetration. For the energy carried by these photons, the kinetic energy calculator handles KE = 1/2 m v^2 for mechanical waves and particles.

Common Mistakes When Using the Wave Equation

Mixing units is the top mistake. If frequency is in MHz and speed in m/s, a direct division gives wavelength in units of (m/s)/(1/s) = m only after the MHz is converted back to Hz (x 10^6). The calculator handles this automatically when you pick a unit from the dropdown, but hand-calculations routinely trip on prefixes. A 2.4 GHz signal is 0.125 m (12.5 cm), not 1.25 x 10^8 m.

A second pitfall: assuming light travels at c in materials. Light slows in glass to about 2.0 x 10^8 m/s (refractive index n = 1.5), and in water to about 2.25 x 10^8 m/s (n = 1.33). The frequency stays constant as light enters a new medium, but wavelength shortens by 1/n. This is why a straw in a glass of water looks bent - it is refraction, not a wavelength calculator bug.

A third pitfall: confusing group velocity with phase velocity in dispersive media. The wave equation lambda = v/f uses phase velocity, which is what matters for resonance, antenna length, and cavity dimensions. Group velocity governs how a pulse envelope travels and matters for fibre-optic timing and pulse dispersion in GPS signals. For most everyday calculations the two match closely, but ignoring the distinction can cause errors above 1% in optics and acoustics textbook problems.

Sources

• NIST - Speed of Light in Vacuum
• NIST - SI Units and Fundamental Constants (Planck's constant, h)
• NASA Goddard - The Electromagnetic Spectrum
• CIE - International Commission on Illumination (photopic luminosity function)
• Engineering ToolBox - Speed of Sound in Solids, Liquids, and Gases
• BIPM - SI Brochure (9th edition, 2019 redefinition)
• ARRL - Antenna Basics (quarter-wave radiator theory)