Frequency Calculator
Every wave trades wavelength against frequency at a fixed speed: the faster the wave travels, the more cycles pass per second for a given length. Enter a wavelength and choose the wave’s medium, and this calculator returns its frequency in hertz through terahertz and its period too — for radio waves, microwaves, light, sound and anything else that oscillates, all from the single most useful division in wave physics.
The One Equation of Every Wave
A wave is a pattern repeating in space and marching in time, and its three measures are locked together by v = f x wavelength — speed equals frequency times wavelength. Fix the speed (the medium does that) and frequency and wavelength become a seesaw: halve one and the other doubles. This calculator runs the division f = v / wavelength and its companion T = 1 / f, the period — the seconds one cycle takes. The hertz, cycles per second, honours Heinrich Hertz, who first generated and detected the radio waves his name now measures. What changes across the entire electromagnetic spectrum — radio, microwave, infrared, light, X-rays — is only the wavelength; the speed in vacuum never changes, so every colour and every station is an address in this single equation, and this page is its universal translator between the length a wave occupies and the rate at which it repeats.
Worked Example: A 3-Metre Radio Wave
The defaults: a wavelength of 3 metres at light speed gives f = 299,792,458 / 3 = 99,930,819 Hz — 99.93 MHz, a period of 10.01 nanoseconds. That frequency is a place you have been: the middle of the FM radio band (87.5-108 MHz) is where 3-metre waves live, and the quarter-wave whip antenna on a car roof, about 75 cm long, is one quarter of this very wavelength — antenna engineering is wavelength arithmetic made of metal. Slide the inputs and the spectrum tours itself: at 700 nm (deep red light) the same division gives 4.28 x 10^14 Hz — 428 THz; at 12.24 cm it returns the microwave oven's 2.45 GHz; switch the medium to sound in air and a 0.78-metre wavelength returns 440 Hz, the A above middle C, the tuning note of orchestras. One formula, three kingdoms of physics, zero new mathematics.
Why the Medium Sets the Speed
Frequency is a property of the source — the oscillator, the string, the electron's jump — and it does not change when a wave crosses into a new medium; the wavelength does the adjusting, because the speed does. Light slows in glass (to about two-thirds of c in typical crown glass), so its wavelength shortens inside a lens while its frequency — and therefore its colour, which the eye reads by frequency-driven photon energy — stays fixed. Sound runs 4.3 times faster in water than in air and 17 times faster in steel, which is why a diver hears a boat's pitch oddly near yet its wavelength stretched. The calculator's medium list is short but the principle is complete: pick the speed honestly for the material at hand, and the division does the rest. (A custom speed can be explored by noting that frequency scales linearly — double the speed at fixed wavelength and you double the frequency.)
Frequency, Period and the Human Scales
The period column exists because some technologies think in time rather than rate: a 50 Hz mains supply (Europe) has a 20 ms period, a 60 Hz supply (North America) 16.67 ms — the numbers behind flicker, hum and the frame-timing of old televisions. Human hearing spans 20 Hz to 20 kHz, wavelengths in air from 17 metres down to 17 millimetres; human vision spans a mere octave, roughly 380-750 nm, frequencies of 400-790 THz, an astonishingly narrow window that this calculator's unit list (nanometres to kilometres) quietly frames. At the extremes the seesaw produces the famous numbers of the spectrum: the 21-centimetre hydrogen line at 1,420 MHz by which radio astronomers map the galaxy, and gamma rays whose periods under 10^-18 seconds belong to nuclear events. All of them are one division away from their wavelengths, which is the entire claim of this page.
Resonance: When Frequency Meets a Favourite
One extension of the division rules the built world: every structure, circuit and cavity has frequencies at which it responds greedily — its resonances — and the wavelength relation locates them. A room 3.43 metres wide holds a standing sound wave whose half-wavelength fits the width, at 50 Hz — the boomy bass note small studios fight. An LC circuit resonates where its components' reactances cancel, and the radio dial is a machine for sliding that resonance along this page's spectrum until it lands on a station's carrier. Bridges, wine glasses, microwave cavities (sized so the 12.24 cm wave forms its standing pattern, hot spots and all) — each is f = v/lambda with a boundary condition attached. The calculator gives the free-space numbers; resonance is what happens when the wave's length meets a length the world has chosen.
A Note on Units and Orders of Magnitude
Frequencies in the wild span more than twenty powers of ten, from the 50-60 Hz of mains power to the 10^20 Hz of gamma rays, and the prefixed units — kilo, mega, giga, tera, peta, exa — exist so that every worker quotes a number between 1 and 1,000 in their own band. The calculator chooses the fitting unit automatically and also prints the raw hertz, because spectrum allocations, datasheets and examination papers do not always agree on which convention they are using.
Related Tools
More from the Physics Calculators hub: the Wave Velocity Calculator — the third side of the v = f x wavelength triangle — the Energy to Wavelength Calculator, pricing photons by the same spectrum, and the Light Year Calculator for light's longer journeys.
Frequently Asked Questions
How do I convert wavelength to frequency?
Divide the wave's speed by the wavelength, in matching units: f (Hz) = v (m/s) / wavelength (m). For anything electromagnetic in vacuum or air the speed is 299,792,458 m/s; for sound use the medium's speed (343 m/s in air at 20 C). Work in metres throughout — the calculator's unit selector does that conversion for you — and read the answer in whichever of Hz, kHz, MHz, GHz or THz fits its size.
What is the frequency of visible light?
Roughly 400 to 790 terahertz: deep red at 700 nm is 428 THz, violet at 380 nm is 789 THz. The corresponding photon energies (E = h x f) run 1.65 to 3.26 electronvolts — the energy scale of chemistry, which is no coincidence: evolution built eyes for the band whose photons rearrange molecules gently enough to signal without destroying, the same band where the Sun's output peaks.
Why does frequency stay constant between media but wavelength change?
Cycles cannot pile up or vanish at a boundary: the rate at which wavefronts arrive at an interface must equal the rate at which they leave it, or the count of cycles would grow without bound on one side. So the frequency — set by the source — is continuous across the boundary, and since the speed changes inside the new medium, the wavelength (v / f) absorbs the whole adjustment. Refraction, lenses and the bending of sound around temperature layers all live inside this bookkeeping.
What is the difference between frequency and period?
Reciprocals: frequency counts cycles per second, period measures seconds per cycle, T = 1/f. Mains electricity at 60 Hz has a period of 16.67 ms; a pendulum swinging once per second has both frequency 1 Hz and period 1 s (their meeting point). Engineers quote frequency for signals and period for timing budgets; musicians call frequency pitch. The calculator prints both because each is the natural unit somewhere.
What frequency is 5G, and how long are its waves?
It depends on the band, which is the point of the calculator: low-band 5G near 600-900 MHz has wavelengths of 33-50 cm and travels far through walls; mid-band near 3.5 GHz sits at 8.6 cm; millimetre-wave 5G at 28 GHz is a 10.7 mm wave that rain and windows measurably block. Each generation of mobile technology climbs this page's spectrum trading range for capacity, and every trade is priced by f = c/lambda before a single tower is built.
How does frequency relate to photon energy?
By Planck's relation E = h x f, with h = 6.626 x 10^-34 joule-seconds: energy per photon is directly proportional to frequency. Your FM station's 100 MHz photons carry about 4 x 10^-7 electronvolts each (utterly harmless, and individually undetectable by chemistry), visible light's run 1.65-3.26 eV (the chemistry scale), and a gamma ray at 10^20 Hz carries 4 x 10^5 eV — enough to shatter molecules, which is the whole physical basis of radiation safety and of why the spectrum is policed by frequency bands, not wavelengths.
Can I use this for my Wi-Fi or radio station?
Yes — that is its home territory. Wi-Fi at 2.45 GHz has a wavelength of 12.2 cm (run it backwards: enter the wavelength to see the band, or trust the worked example), 5 GHz Wi-Fi sits at 6 cm, and an FM station at 101.1 MHz broadcasts a 2.97-metre wave. Antenna lengths, waveguide dimensions and interference spacings all follow from the wavelength the frequency implies, which is why this division is the first tool out of the box in radio work.