Frequency Calculatorf = 1 ÷ T · f = v ÷ λ
Frequency is the number of cycles per second, in hertz: f = 1 ÷ T, where T is the period. For a wave, f = v ÷ λ (wave speed over wavelength). Find the frequency from a period, from a wavelength and wave speed for sound, light or radio, or the period from a frequency. Audio results also show the nearest musical note and how far off-pitch it is.
Formula verified against OpenStax — University Physics, Volume 1 · NIST — SI Units
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Wave or signal
Sound in air ≈ 343 m/s · light in vacuum = 299,792,458 m/s.
Step-by-step working
What is frequency?
Frequency is how often a repeating event happens per second, measured in hertz (Hz). For waves it is the number of crests passing a point each second; for oscillations, the number of complete cycles per second.
Frequency sets the pitch of a sound, the colour of light, the station on a radio dial and the speed of a computer’s clock.
Quick answers
How do you calculate frequency from period?
Divide 1 by the period in seconds: f = 1 ÷ T. A 0.25 s period is 4 Hz; a 20 ms period is 50 Hz.
How do you find frequency from wavelength?
Divide the wave speed by the wavelength: f = v ÷ λ. A 1 m sound wave in air (343 m/s) is 343 Hz; a 1 m radio wave is 300 MHz.
What frequency is middle C?
Middle C (C4) is 261.63 Hz in standard tuning with A4 = 440 Hz. Each octave doubles the frequency.
What is the difference between frequency and period?
They are reciprocals: frequency counts cycles per second, period is seconds per cycle. For light, frequency also sets photon energy; see the photon energy calculator.
Frequency formulas
1 Hz = 1 cycle per second. Musical pitch: f = 440 × 2n/12 Hz for n semitones from A4.
| Symbol | Meaning | SI unit |
|---|---|---|
| f | Frequency | Hz |
| T | Period | s |
| v | Wave speed | m/s |
| λ | Wavelength | m |
| ω | Angular frequency | rad/s |
How to calculate frequency
- Measure the period: the time for one full cycle.
- Take the reciprocal: f = 1 ÷ T (in seconds).
- For a wave, divide its speed by its wavelength.
- Scale the units: 1 kHz = 10³ Hz, 1 MHz = 10⁶ Hz, 1 GHz = 10⁹ Hz.
Worked example: a 2 ms period
An oscilloscope shows a signal repeating every 2 ms. What is its frequency?
As sound in air it would have a wavelength of 343 ÷ 500 = 0.686 m and sound close to B4. Green laser light at 532 nm has f = c ÷ λ = 5.64 × 10¹⁴ Hz.
Frequencies across the spectrum
| Source | Frequency | Period |
|---|---|---|
| Human heartbeat (72 bpm) | 1.2 Hz | 0.83 s |
| Mains electricity | 50 / 60 Hz | 20 / 16.7 ms |
| Concert pitch A4 | 440 Hz | 2.27 ms |
| FM radio | 88–108 MHz | ≈ 10 ns |
| Wi-Fi | 2.4 / 5 / 6 GHz | 0.42 / 0.2 / 0.17 ns |
| Visible light | 400–790 THz | ≈ 2 fs |
Common mistakes to avoid
- Using a half-cycle as the period. T is peak to the next peak, not peak to trough.
- Mixing frequency and angular frequency. ω = 2πf, measured in rad/s, not Hz.
- Using the wrong wave speed. Sound in water is about 4.3× faster than in air.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Frequency Calculator: frequently asked questions
f = 1 ÷ T for a repeating signal, or f = v ÷ λ for a wave.
The hertz (Hz), one cycle per second.
About 20 Hz to 20 kHz for young adults. The upper limit falls with age.
Inversely: v = fλ. At a fixed wave speed, doubling the frequency halves the wavelength.
ω = 2πf, the rate of change of phase in radians per second.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 16.1–16.2, Traveling waves
- NIST — SI Units — the hertz
- Wikipedia — Piano key frequencies — equal-temperament note frequencies
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.