Wavelength Calculator

A wavelength calculator converts a frequency into the physical length of one wave cycle using λ = v ÷ f. An FM station at 101.1 MHz has a wavelength of 299,792,458 ÷ 101,100,000 = 2.9653 meters, which is 9.73 feet. Enter a frequency, pick light or sound, and read the answer in meters, inches and feet at once.

The same tool runs in reverse. Give it a wavelength and it returns the frequency, and give it both and it returns the wave speed. Every mode uses one exact relation, so there is no estimate, no rounding fudge and no table lookup involved: the answer is as precise as the number you type in.

How the wavelength formula works

A wave carries a repeating pattern through space. Frequency counts how many complete cycles pass a fixed point every second, measured in hertz. Wavelength measures the distance between two matching points on the pattern, crest to crest or trough to trough, in meters. Multiply them and you get how far the pattern travels per second, which is the wave speed:

Here λ (lambda) is the wavelength in meters, f is the frequency in hertz, and v is the speed of the wave in meters per second. The three forms are the same equation rearranged, so any two known values give you the third. For electromagnetic waves traveling through vacuum, v is the speed of light c, which the International System of Units fixes at exactly 299,792,458 meters per second. For sound in dry air at 20 °C, v is about 343 meters per second, a figure that shifts with temperature.

Worked example: an FM broadcast at 101.1 MHz

Suppose you want the wavelength of an FM signal at 101.1 megahertz, and the quarter-wave element length for an antenna at that frequency.

• Step 1 - convert the frequency to hertz. 101.1 MHz × 1,000,000 = 101,100,000 Hz.
• Step 2 - pick the wave speed. A radio wave in air travels at essentially the vacuum speed of light, so v = 299,792,458 m/s.
• Step 3 - divide. λ = 299,792,458 ÷ 101,100,000 = 2.9653 meters.
• Step 4 - convert to US units. 2.9653 ÷ 0.3048 = 9.73 feet, or 116.74 inches.
• Step 5 - take a quarter. 2.9653 ÷ 4 = 0.7413 meters = 29.19 inches, the theoretical quarter-wave element.
• Step 6 - the period. One cycle lasts 1 ÷ 101,100,000 = 9.8912 × 10⁻⁹ seconds, about 9.89 nanoseconds.

A half-wave dipole for that station would be 1.483 meters (4.86 feet) tip to tip before trimming. If you cut a quarter-wave matching stub from coaxial cable with a velocity factor of 0.66, the physical length shrinks to 0.489 meters, about 19.26 inches, because the wave travels slower inside the cable than it does in free space.

Second worked example: green light at 550 nm

Now run the calculation the other way. Green light in the middle of the visible band has a wavelength of 550 nanometers, which is 5.5 × 10⁻⁷ meters. The frequency is f = 299,792,458 ÷ 5.5 × 10⁻⁷ = 5.4508 × 10¹⁴ Hz, usually written as 545.08 THz. The photon energy follows from E = hc ÷ λ: (6.62607015 × 10⁻³⁴ × 299,792,458) ÷ 5.5 × 10⁻⁷ = 3.6117 × 10⁻¹⁹ joules. Dividing by the elementary charge gives 2.2543 electronvolts, the number a physicist or a solar-cell engineer would quote. Drop that same beam into water, where the refractive index is about 1.333, and the wavelength shortens to roughly 412.60 nm while the frequency stays at 545.08 THz. Frequency is set by the source; wavelength depends on the medium.

How to use this calculator

Start by choosing what you are solving for. Wavelength mode wants a frequency, Frequency mode wants a wavelength, and Wave speed mode wants both and multiplies them. Next choose the wave type. Light / radio loads the exact speed of light and unlocks the photon-energy read-out. Sound in air loads 343 m/s. Custom speed lets you type any speed in meters per second, with one-tap buttons for fresh water at 1,481 m/s, air at 0 °C at 331.3 m/s, and steel at 5,120 m/s.

Then type the value and choose its unit. Frequencies accept Hz, kHz, MHz, GHz and THz; wavelengths accept nanometers, micrometers, millimeters, centimeters, meters, kilometers, inches and feet. The result card shows the headline number in the most readable unit, then repeats it in meters, inches and feet, plus the wave period. Below that a summary table lists frequency, wavelength, wave speed, half wavelength, quarter wavelength and, for light, the photon energy in electronvolts and joules. The quick-example buttons load common cases such as FM radio, Wi-Fi and concert A so you can see the tool working before entering your own numbers.

Who this calculator is for

Physics and chemistry students use it for homework on the wave equation, the electromagnetic spectrum and photon energy. Ham radio operators, CB users and antenna builders use it to size quarter-wave and half-wave elements. Audio engineers and studio owners use the sound mode to work out room modes and how much space a bass wave actually needs. Wi-Fi installers use it to understand why 2.4 GHz bends around a wall better than 6 GHz. Photographers, aquarium keepers, gardeners running grow lights and anyone reading an LED spectrum chart use the nanometer side to translate a wavelength into a color and an energy.

Key terms in one place

• Wavelength (λ) - the distance between two matching points on consecutive cycles, in meters.
• Frequency (f) - cycles per second, in hertz. One kilohertz is 1,000 Hz, one megahertz is 1,000,000 Hz.
• Period (T) - the time for one cycle, T = 1 ÷ f. A 440 Hz tone has a period of 0.00227 seconds.
• Wave speed (v) - how fast the pattern travels, set by the medium, not by the source.
• Amplitude - the height of the wave. It sets loudness or brightness and does not affect the wavelength at all.
• Wavenumber - cycles per unit length, the reciprocal of wavelength, common in spectroscopy as cm⁻¹.
• Refractive index (n) - how much a medium slows light. The wavelength inside the medium is the vacuum wavelength divided by n.
• Velocity factor - the fraction of the speed of light at which a signal travels inside a cable, typically 0.66 to 0.85 for coax.

Radio bands and their wavelengths

Radio spectrum is divided into decade bands, each one covering a factor of ten in frequency and therefore a factor of ten in wavelength. The wavelengths below were computed with λ = c ÷ f at the two edges of each band, which is where band nicknames such as "shortwave" and "the 10-meter band" come from.

Notice the pattern: every tenfold rise in frequency shrinks the wavelength by a factor of ten, so a wave that spans a city block at HF fits in your palm at UHF.

Wavelength of common US frequencies

These are free-space wavelengths computed with λ = c ÷ f, plus the quarter-wave length that antenna builders reach for first. Real elements come out a few percent shorter once end effects and conductor thickness are taken into account.

Visible spectrum: wavelength, frequency and photon energy

The frequencies and energies below were computed from each wavelength with f = c ÷ λ and E = hc ÷ λ. Color boundaries are approximate because human color perception blends smoothly, but the physics numbers are exact for the wavelength shown.

Sound wavelengths in air at 20 °C

Sound travels roughly a million times slower than light, so audible wavelengths are measured in feet rather than nanometers. Every figure below uses v = 343 m/s.

This table explains a lot of practical audio. A 100 Hz wave is 11.25 feet long, longer than most ceilings are high, so bass energy piles up into room modes that no amount of foam on the wall will absorb. Meanwhile a 10 kHz wave is only 1.35 inches long, short enough that turning your head changes what you hear.

What changes the answer

• The medium. Wave speed belongs to the medium. Sound moves at about 343 m/s in air, 1,481 m/s in fresh water and roughly 5,120 m/s in steel, so the same 1,000 Hz tone measures 0.343 m, 1.481 m and 5.12 m respectively.
• Temperature, for sound. The approximation v = 331.3 + 0.606 × T (T in °C) puts air at 331.3 m/s at freezing and 343.4 m/s at 20 °C. That is a 3.5 percent swing in every sound wavelength between a cold morning and a warm room.
• Refractive index, for light. Light slows by the factor n inside a material, so the wavelength shortens by the same factor while the frequency stays fixed. Water at n = 1.333 turns 550 nm into 412.60 nm.
• Cable velocity factor. Inside coax a signal travels at 0.66 to 0.85 of the free-space speed, so a quarter-wave stub is physically shorter than the free-space quarter wave by that same factor.
• Unit prefixes. Most wrong answers come from a factor of 1,000 in the prefix, not from the formula. Confirm whether you meant kHz or MHz before trusting the number.

Practical tips

• For a fast mental estimate of radio wavelength in meters, divide 300 by the frequency in MHz. At 101.1 MHz that gives 2.97 m against the exact 2.9653 m, close enough for a first cut.
• For sound in a warm room, divide 1,125 by the frequency in hertz to get feet, since 343 m/s is about 1,125 feet per second. A 100 Hz note lands at 11.25 feet.
• Light covers about one foot per nanosecond in vacuum (1.0167 ns per foot to be exact), a handy check when you are reasoning about cable delay or radar range.
• When sizing an antenna, cut long and trim. Calculated quarter waves are theoretical maxima and real elements always end up a little shorter.
• Keep everything in SI units while you calculate, then convert once at the end. Mixing inches into a formula that expects meters is the fastest way to a wrong answer.

Limitations of this calculator

The wave relation itself is exact, but the inputs carry the assumptions. The light mode uses the vacuum speed, which is fine for radio in air and for light in air to about four decimal places, but not for light in glass, water or optical fiber unless you switch to the custom mode and divide the speed by the refractive index. The sound preset is dry air at 20 °C; humidity, altitude and temperature all move that number. Antenna results are free-space figures and ignore end effects, ground planes, nearby metal and cable velocity factor. The photon energy read-out assumes a photon traveling in vacuum. Nothing here models Doppler shift, dispersion, standing waves, interference or relativistic corrections, and the tool is intended for learning, planning and estimation rather than for certification or safety work.

Related tools on this site

Waves are one kind of rate, and our other math tools handle the neighboring questions. The Velocity Calculator finds how fast an object moves with v = d ÷ t rather than how fast a pattern propagates, which is what you want when the thing traveling is a car and not a wave. The Density Calculator solves the same three-variable shape for mass, volume and density, so use it when the ratio you need is kilograms per cubic meter instead of meters per cycle. The Unit Converter is the right stop when you only need to move a length between meters, feet and inches with no physics attached. And the Scientific Notation Calculator helps when the exponents in a wavelength problem get unwieldy and you want to check a power of ten by hand.

Sources

The wave relation λ = v ÷ f and the photon-energy relation E = hc ÷ λ are exact definitions of physics and need no external source; every table on this page was computed from them. The constants and unit definitions used come from the following standards bodies:

• National Institute of Standards and Technology (NIST) - SI units and the defining constants, including the speed of light in vacuum (299,792,458 m/s), the Planck constant (6.62607015 × 10⁻³⁴ J·s) and the elementary charge (1.602176634 × 10⁻¹⁹ C), all exact by definition.
• National Institute of Standards and Technology (NIST) - Special Publication 811, Guide for the Use of the International System of Units, source of the exact conversions 1 inch = 0.0254 m and 1 foot = 0.3048 m.
• National Institute of Standards and Technology (NIST) - CODATA fundamental physical constants.