Quick answer: This wave frequency calculator uses f = v ÷ λ (wave speed divided by wavelength), or f = 1 ÷ T (one over the period). Enter any two of speed, wavelength or period and get the frequency in Hz, plus angular frequency.
Last reviewed: September 2026
Key facts
- f = v ÷ λ and f = 1 ÷ T — frequency is measured in hertz (Hz = cycles/second).
- Angular frequency ω = 2πf in radians per second — used in oscillation equations.
- Humans hear 20 Hz to 20 kHz; above that is ultrasound.
- For a fixed wave speed, higher frequency means shorter wavelength.
- Light's colour is its frequency: red ~4.3 × 1014 Hz, violet ~7.5 × 1014 Hz.
This free wave frequency calculator finds frequency from wave speed and wavelength, or from the period, and also gives angular frequency. Works for sound, light, radio and water waves with automatic unit conversions. Enter any two quantities and get all four results instantly.
Enter any two quantities and get all four: frequency, angular frequency, period and wavelength. Frequency, wavelength and period convert between common units automatically.
What is wave frequency?
Frequency counts how many complete wave cycles pass a point each second. One cycle per second is one hertz (Hz), named after Heinrich Hertz, who first generated and detected radio waves in the 1880s; the hertz became the SI unit of frequency in 1960. Two kinds of waves share the same mathematics: mechanical waves (sound, water, seismic waves) that need a medium, and electromagnetic waves (light, radio, X-rays) that travel through empty space at 299,792,458 m/s. In both cases the wave equation v = fλ ties frequency to wavelength through the wave speed — which is exactly what this wave frequency calculator solves.
Background: from vibrating strings to radio waves
The science of frequency began with music. In the 1630s, Marin Mersenne published the laws of vibrating strings in Harmonie universelle: a string's frequency rises with tension and falls with length and thickness — the physics behind every tuned instrument. In the 1860s, James Clerk Maxwell predicted that oscillating electric charges should radiate waves travelling at the speed of light; in 1887–1888 Heinrich Hertz proved it, producing and detecting radio waves in his laboratory. His work turned "frequency" from a property of strings and pendulums into the master dial of the electromagnetic spectrum, from power grids to gamma rays.
How to use this wave frequency calculator
- Pick a mode: speed + wavelength, period, or frequency + speed (to find wavelength).
- Enter the values and choose units (m/s, m/cm/mm/nm, s/ms/µs/ns, Hz/kHz/MHz).
- Read the frequency, angular frequency, period and wavelength.
- The tool flags when your frequency falls in the human hearing range.
Wave frequency formulas
f = 1 ÷ T
ω = 2πf
| Term | Meaning |
|---|---|
| f | Frequency in hertz (cycles per second). |
| v | Wave speed (e.g. 343 m/s for sound in air). |
| λ | Wavelength — distance between two consecutive crests. |
| T | Period — time for one complete oscillation. |
| ω | Angular frequency in radians per second. |
The physics behind the formulas
A wave moving at speed v covers one wavelength λ in one period T, so v = λ/T. Since frequency is cycles per second and period is seconds per cycle, f = 1/T — substituting gives the wave equation v = fλ, or f = v/λ.
Angular frequency ω = 2πf re-expresses the same oscillation in radians per second: one full cycle is 2π radians, so ω is the rate at which the wave's phase angle advances. Pendulums, springs and AC circuits are all described with ω because the mathematics of sines and cosines is simpler in radians than in whole cycles.
One subtlety: frequency is set by the source, while speed is set by the medium. When sound crosses from air into water, its speed jumps from 343 to ~1,480 m/s but its frequency stays fixed — the wavelength stretches instead (λ = v/f). That is why the "frequency + speed" mode exists: enter a frequency and a new medium's speed to get the new wavelength.
Worked examples
Sound wave: 343 m/s, wavelength 0.5 m
f = v ÷ λ = 343 ÷ 0.5 = 686 Hz. ω = 2π × 686 = 4,310 rad/s.
A tone between E5 (659 Hz) and F5 (698 Hz) on the piano — comfortably in the hearing range.
Oscillation with period 0.02 s
f = 1 ÷ T = 1 ÷ 0.02 = 50 Hz. ω = 2π × 50 = 314.16 rad/s.
The frequency of AC mains power in most of the world (60 Hz in the Americas).
FM radio at 100 MHz
λ = v ÷ f = 299,792,458 ÷ 100,000,000 = 3.00 m. T = 1 ÷ f = 10 ns.
FM broadcast antennas are sized around this wavelength — a half-wave dipole for 100 MHz is about 1.5 m long, which is why car antennas are roughly that length.
Common wave speeds
| Wave | Speed | Medium |
|---|---|---|
| Sound | 343 m/s | Air at 20°C |
| Sound | 1,480 m/s | Water |
| Light / radio | 299,792,458 m/s | Vacuum |
| Seismic P-waves | ~6,000 m/s | Earth's crust |
The electromagnetic spectrum: frequency and wavelength
All electromagnetic waves travel at c in a vacuum, so each frequency maps to exactly one wavelength (λ = c/f). The spectrum spans over 20 orders of magnitude:
| Band | Example frequency | Wavelength |
|---|---|---|
| Radio (AM) | 1 MHz | ~300 m |
| Radio (FM) | 100 MHz | ~3.00 m |
| Microwave (Wi-Fi) | 2.4 GHz | ~12.5 cm |
| Infrared | 3 × 1013 Hz | ~10 µm |
| Visible (green) | 5.45 × 1014 Hz | ~550 nm |
| Ultraviolet | 1 × 1015 Hz | ~300 nm |
| X-ray | 3 × 1018 Hz | ~0.1 nm |
| Gamma ray | 3 × 1020 Hz | ~1 pm |
Everyday frequencies worth knowing
| Source | Typical frequency |
|---|---|
| Earthquakes (seismic surface waves) | Below 20 Hz (infrasound) |
| Human speech | ~85–255 Hz |
| Piano tuning note A4 | 440 Hz |
| Dog whistle | ~23–54 kHz (ultrasound) |
| Medical ultrasound imaging | ~2–18 MHz |
Limitations
- Wave speed is assumed constant: sound's speed varies with temperature, humidity and altitude; light slows in glass and water (refraction). Enter the speed for your actual medium.
- Dispersion: in some media (deep water waves, optical fibres) different frequencies travel at different speeds; the calculator treats v as single-valued.
- Ideal sine waves: real signals contain harmonics and noise — the calculator reports the fundamental frequency only.
- Relativistic and quantum regimes: near light speed or at atomic scales, the classical wave equation needs relativistic or quantum corrections.
Frequently asked questions
What is the difference between frequency and period?
They are reciprocals: frequency counts cycles per second, period measures seconds per cycle (f = 1/T). A 50 Hz wave has a period of 0.02 s — 50 cycles fit into one second.
What is angular frequency used for?
Angular frequency ω = 2πf (rad/s) appears in equations for pendulums, springs and AC circuits, where mathematics is simpler with radians than with full cycles.
Can two waves have the same frequency but different speeds?
Yes — frequency is set by the source, while speed depends on the medium. The wavelength adjusts (λ = v/f), which is why sound bends when it moves between air and water.
Why is 50 Hz special?
It is the standard AC mains frequency in most of the world (60 Hz in the Americas). Mains hum picked up by audio equipment is almost always 50 or 60 Hz.
What is the highest frequency humans can hear?
About 20 kHz in young people, declining with age. Frequencies above that are ultrasound — used in medical imaging, dog whistles and sonar.
How do I convert wavelength to frequency?
Divide the wave speed by the wavelength: f = v ÷ λ, keeping units consistent (metres and metres per second give hertz). Select the "frequency + speed" mode in the wave frequency calculator above and it does the unit conversion for you.
Sources
- OpenStax College Physics — Wave properties, the wave equation and the electromagnetic spectrum
- HyperPhysics — Frequency, wavelength and wave-speed relations
- NIST — Speed of light in vacuum, 299,792,458 m/s exactly
- Britannica — Heinrich Hertz and the discovery of radio waves
Key takeaways
- f = v/λ; f = 1/T; ω = 2πf.
- Frequency in Hz, angular frequency in rad/s.
- Human hearing spans 20 Hz–20 kHz; ultrasound sits above it.
- Same frequency, different medium → different wavelength.
- Light's colour is its frequency — the whole EM spectrum obeys one equation.
- Enter the wave speed of your actual medium; it is not always 343 m/s.
Explore more tools
Related: Projectile Motion Calculator | Kinetic Energy Calculator
Comments
Leave a comment