Compute frequency, wavelength, period and wave velocity from the universal wave equation v = λ × f = λ / T. Pick one of 20 medium presets, enter any one wave property, and the rest update live.
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Frequency is the number of complete wave cycles that pass a fixed point each second. The SI unit is the hertz, defined by the National Institute of Standards and Technology as one cycle per second, or s⁻¹. A 60 Hz electrical signal completes sixty cycles every second. A 20 kHz audio tone completes twenty thousand.
The quantity shows up wherever something repeats: alternating current, sound pressure, radio carriers, ocean swells, seismic vibrations, even the color of light. What changes between those domains is the wave velocity, not the definition of frequency itself. A 440 Hz tone has the same frequency in air and in water. Its wavelength does not. That distinction matters because most real-world decisions transducer sizing, antenna length, acoustic treatment thickness depend on wavelength, not frequency alone. The calculator keeps the two linked through the wave velocity you select.
Divide the wave velocity by the wavelength. If a 1,480 m/s sound wave in freshwater has a wavelength of 0.25 m, the frequency is 5,920 Hz. The calculator does that division automatically once you enter the wavelength.
Pick a medium preset, or leave it on custom and type your own wave velocity in m/s.
Enter a wavelength and choose its unit from the dropdown.
The frequency field fills in with the result in your selected frequency unit.
The period field fills in as the reciprocal of frequency.
Switch any unit dropdown to convert the visible number without recalculating from scratch.
Read the verdict banner for a plain-language description of where the frequency sits in the acoustic or electromagnetic spectrum.
Frequency equals wave velocity divided by wavelength. Period equals one divided by frequency. Those two relationships are the entire calculator.
Formula: f = v ÷ λ and T = 1 ÷ f
The wave velocity v is the speed at which the disturbance travels through the medium, in meters per second. Wavelength λ is the physical distance between consecutive crests, in meters. Frequency f is cycles per second, in hertz. Period T is seconds per cycle. Multiply frequency by wavelength and you recover velocity. Divide velocity by wavelength and you recover frequency.
A hydroacoustics technician is modeling a sonar pulse in freshwater at 1,480 m/s. The measured wavelength is 2.5 m. What frequency and period does that correspond to?
Step one: divide velocity by wavelength. 1,480 ÷ 2.5 = 592 Hz. Step two: invert the frequency. 1 ÷ 592 = 0.001689 s, or 1.689 ms. The period is about 1.69 milliseconds. A 592 Hz tone sits within the audible range, though underwater it would be perceived differently than in air. The wavelength of 2.5 m is also physically meaningful: a sonar array designed for this frequency needs element spacing well below 2.5 m to steer the beam without grating lobes.
These longitudinal wave velocities come from material property tables compiled in Adiabatic Compressibility on ScienceDirect. They represent typical values at room temperature and pressure. Actual sound speed varies with temperature, salinity, and material grade.
| Medium | Longitudinal sound speed |
|---|---|
| Air (20 °C) | 343 m/s |
| Freshwater | about 1,500 m/s |
| Seawater | about 1,520 m/s |
| Human tissue | about 1,540 m/s |
| Aluminum | 6,400 m/s |
| Mild steel | 6,000 m/s |
| Concrete | 2,500–5,000 m/s |
| Wood | about 3,500 m/s |
| Diamond | 18,600 m/s |
These bands describe where a calculated frequency sits. The acoustic divisions follow the conventional 20 Hz and 20 kHz limits for human hearing, documented by the EPFL GraphSearch audio frequency reference. The radio bands follow the ITU Radio Regulations band numbering.
| Band or threshold | Typical frequency range |
|---|---|
| Infrasound | below 20 Hz |
| Audible sound | 20 Hz to 20 kHz |
| Ultrasound | above 20 kHz |
| Diagnostic medical ultrasound | 2–12 MHz |
| ELF radio (ITU band 1–3) | 3–3,000 Hz |
| VLF (ITU band 4) | 3–30 kHz |
| LF (ITU band 5) | 30–300 kHz |
| MF (ITU band 6) | 300–3,000 kHz |
| HF (ITU band 7) | 3–30 MHz |
| VHF (ITU band 8) | 30–300 MHz |
| UHF (ITU band 9) | 300–3,000 MHz |
| SHF (ITU band 10) | 3–30 GHz |
| EHF (ITU band 11) | 30–300 GHz |
Visible light occupies roughly 400–750 THz, which is far above the radio bands in this table. The tool’s verdict banner switches between acoustic and electromagnetic descriptions based on whether the entered velocity is within 0.1% of the speed of light.
The frequency a wave carries is set by its source, not by the medium it travels through. But the number the calculator returns depends on what you enter and which assumptions the tool makes.
Wave velocity input. Frequency scales linearly with velocity for a fixed wavelength. Doubling the velocity doubles the frequency.
Wavelength measurement. A 10% error in wavelength produces a 10% error in frequency. Small wavelength inputs amplify unit-conversion mistakes.
Medium temperature. Sound speed in air rises about 0.6 m/s per °C, so a 343 m/s preset at 20 °C understates frequency slightly on a hot day.
Pressure and salinity. Seawater sound speed shifts with depth and salinity; the 1,520 m/s preset is a surface approximation.
Material anisotropy. Wood and rolled metal have direction-dependent sound speeds. A single velocity presumes isotropic behavior.
Dispersion. In waveguides and near resonance, velocity varies with frequency, so a single-velocity equation becomes an approximation.
Period is the reciprocal of frequency. A 250 Hz wave has a period of 0.004 seconds, or 4 milliseconds. The calculator updates both fields together so you don’t have to invert manually.
Divide the wave velocity by the wavelength. If the wave travels at 343 m/s and the wavelength is 0.5 m, the frequency is 686 Hz. The unit dropdowns handle centimeters, millimeters, nanometers, and other wavelength units.
One hertz is one complete cycle per second. The National Institute of Standards and Technology defines the hertz as the SI derived unit for frequency, equivalent to s⁻¹. It applies to any periodic phenomenon, from sound to radio to seismic waves.
Ultrasound starts above the upper limit of human hearing, conventionally 20 kHz. Diagnostic medical ultrasound typically uses 2–12 MHz, as described in the ScienceDirect ultrasound energy reference. Higher frequencies give better resolution but penetrate less tissue.
About 1,500 m/s in freshwater and 1,520 m/s in seawater at typical surface conditions. The calculator’s presets use 1,480 m/s and 1,520 m/s respectively. Temperature and salinity shift these values by a few percent.
The source determines how many cycles are generated per second. The medium determines how fast those cycles travel and therefore how far apart they are. Frequency is conserved across a boundary; wavelength and velocity change together.
Visible light spans roughly 400–750 THz, corresponding to wavelengths around 400–750 nm. The SPIE electromagnetic spectrum reference places the visible band in that range. The calculator’s light-in-vacuum preset lets you compute exact wavelengths for any visible frequency.
Yes. Enter the speed of light as the wave velocity, then type a frequency in MHz or GHz. The wavelength field will return the free-space wavelength. The tool does not account for dielectric loading, velocity factor in coax, or waveguide cutoff.
The calculator treats non-positive inputs as invalid and clears the computed fields. Frequency, wavelength, period, and velocity must all be greater than zero for a physical wave.
They are engineering approximations, not calibration standards. Light in vacuum is exact. Sound in air at 20 °C uses 343 m/s, a standard textbook value that matches the University of Michigan acoustics reference. Solid and liquid values are rounded from published tables.
Angular frequency, denoted ω, equals 2π times the ordinary frequency. It is measured in radians per second. The calculator’s related-quantities table reports angular frequency alongside the hertz value.
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