Calculate frequency, wavelength, and period. Convert between Hz, kHz, MHz, and GHz.
Last reviewed: May 2026
Frequency quantifies how often a periodic event repeats per unit of time. It is one of the most fundamental concepts in physics, engineering, music, and telecommunications. Whether describing the vibration of a guitar string, the oscillation of an alternating current, or the electromagnetic waves carrying your phone call, frequency tells you how many complete cycles occur each second.1
The standard unit of frequency is the hertz (Hz), named after German physicist Heinrich Hertz who first proved the existence of electromagnetic waves in 1887. One hertz equals one cycle per second. In practice, most applications deal with much higher frequencies — audio signals range from 20 Hz to 20 kHz, radio waves span kHz to GHz, and visible light oscillates at hundreds of terahertz.
Frequency is intrinsically linked to three other quantities: period (T = 1/f), wavelength (λ = v/f), and energy (E = hf, where h is Planck's constant). These relationships connect frequency to virtually every branch of physics — from classical mechanics and acoustics to quantum mechanics and relativity.2
The three core equations connecting frequency to other wave properties are essential for any calculation involving waves or oscillations:
Frequency and period: f = 1/T and T = 1/f. A signal cycling 60 times per second has a frequency of 60 Hz and a period of 16.67 milliseconds. These are exact reciprocals — knowing one immediately gives you the other.
Frequency and wavelength: λ = v/f and f = v/λ, where v is the wave's propagation speed. For electromagnetic waves in vacuum, v = c ≈ 3 × 10⁸ m/s. For sound in air at 20°C, v ≈ 343 m/s. The inverse relationship means doubling the frequency halves the wavelength.
Angular frequency: ω = 2πf (in radians per second). Angular frequency appears throughout physics and engineering in equations describing circular motion, resonance, and AC circuits. Converting between ω and f is simply dividing or multiplying by 2π.3
| Frequency Range | Name | Common Applications |
|---|---|---|
| 0–20 Hz | Infrasound | Earthquake detection, animal communication, structural monitoring |
| 20 Hz – 20 kHz | Audible sound | Music, speech, hearing tests, audio engineering |
| 20 kHz – 1 GHz | Ultrasound / Radio | Medical imaging, AM/FM radio, television, radar |
| 1 GHz – 300 GHz | Microwave | WiFi, cell phones, satellite communication, microwave ovens |
| 300 GHz – 430 THz | Infrared | Thermal imaging, remote controls, fiber optics |
| 430 THz – 770 THz | Visible light | Vision, photography, displays, solar energy |
| 770 THz – 30 PHz | Ultraviolet / X-ray | Sterilization, medical imaging, material analysis |
Sound frequency determines pitch — higher frequencies produce higher-pitched sounds. The standard tuning reference is A4 = 440 Hz (the A above middle C on a piano). Each octave doubles the frequency: A3 = 220 Hz, A5 = 880 Hz. The entire range of a standard 88-key piano spans from 27.5 Hz (A0) to 4,186 Hz (C8).4
Human perception of pitch is logarithmic, not linear — we perceive equal ratios as equal intervals. The interval from 100 Hz to 200 Hz (a ratio of 2:1, or one octave) sounds the same as the interval from 1,000 Hz to 2,000 Hz (also 2:1). This is why the musical scale uses multiplicative ratios rather than additive steps. In equal temperament tuning, each semitone multiplies the frequency by the twelfth root of 2 (approximately 1.0595).
| Note | Frequency (Hz) | Note | Frequency (Hz) |
|---|---|---|---|
| C4 (Middle C) | 261.63 | G4 | 392.00 |
| D4 | 293.66 | A4 | 440.00 |
| E4 | 329.63 | B4 | 493.88 |
| F4 | 349.23 | C5 | 523.25 |
In electronics, frequency defines the behavior of alternating current (AC) circuits, signal processing systems, and communication channels. The US electrical grid operates at 60 Hz, while most of the world uses 50 Hz. This frequency determines transformer design, motor speed, and the characteristic hum of electrical equipment.
Telecommunications rely on precisely controlled frequencies. WiFi operates at 2.4 GHz and 5 GHz bands. 5G cellular networks use frequencies from 600 MHz to 39 GHz, with millimeter wave bands above 24 GHz offering extremely high bandwidth but limited range. Radio stations are assigned specific frequencies to prevent interference — FM radio spans 88–108 MHz, while AM radio covers 530–1,700 kHz.5
Every physical object has natural frequencies at which it vibrates most readily — called resonant frequencies. When an external force matches an object's natural frequency, the amplitude of vibration increases dramatically (resonance). This phenomenon explains why singers can shatter wine glasses, why bridges can oscillate dangerously in wind, and why buildings must be designed to avoid resonance with seismic frequencies.
In engineering, resonance is both a tool and a hazard. Musical instruments are designed to resonate at specific frequencies for rich sound production. Conversely, mechanical engineers must ensure that rotating machinery, vehicle suspensions, and structural elements do not operate near their resonant frequencies, which could cause catastrophic failure. The famous 1940 collapse of the Tacoma Narrows Bridge is a classic example of destructive resonance.1
Frequency affects daily life in countless ways beyond the obvious applications in music and telecommunications. Your household electricity alternates at 60 Hz in the Americas and 50 Hz in most of the rest of the world — this is why some devices designed for one region may hum or malfunction in the other. Fluorescent lights flicker at twice the power line frequency (120 Hz in the US), which is fast enough that most people do not perceive it, although it can cause headaches and eyestrain in sensitive individuals. LED lights driven by cheap electronic drivers may flicker at lower frequencies that are noticeable on camera.
Your microwave oven operates at 2.45 GHz — chosen because this frequency is efficiently absorbed by water molecules, which vibrate and generate heat. WiFi also uses the 2.4 GHz band (and the 5 GHz band), which is why microwave ovens can sometimes interfere with wireless connections. The 2.4 GHz band is technically an ISM (Industrial, Scientific, and Medical) band, originally reserved for equipment that generates electromagnetic energy for non-communication purposes.
Medical ultrasound typically uses frequencies between 1 and 20 MHz — high enough to produce detailed images of internal body structures but low enough to penetrate tissue adequately. Higher frequencies provide better image resolution but less penetration depth, which is why different transducer frequencies are used for different types of examinations. Fetal imaging commonly uses 3.5–5 MHz, while musculoskeletal imaging may use 7–15 MHz for shallow structures.5
The Doppler effect describes how the observed frequency of a wave changes when the source and observer are moving relative to each other. An ambulance siren sounds higher pitched as it approaches (frequency compressed) and lower pitched as it moves away (frequency stretched). The magnitude of the frequency shift depends on the relative velocity compared to the wave speed.
For sound waves, the observed frequency f_obs = f_source × (v + v_observer) / (v + v_source), where v is the speed of sound, v_observer is the observer's velocity toward the source (positive approaching), and v_source is the source's velocity away from the observer (positive receding). For electromagnetic waves (light, radar), the relativistic Doppler formula applies, and the shift is used in radar speed guns, astronomical redshift measurements, and medical Doppler ultrasound to measure blood flow velocity. Police radar guns emit microwave signals at a known frequency and measure the shifted frequency of the reflected wave to calculate vehicle speed with high precision.1
Converting between frequency units involves multiplying or dividing by powers of 1,000. From hertz: 1 kHz = 10³ Hz, 1 MHz = 10⁶ Hz, 1 GHz = 10⁹ Hz, 1 THz = 10¹² Hz. From period to frequency, take the reciprocal: a period of 5 milliseconds equals 1/0.005 = 200 Hz. From angular frequency (ω in rad/s) to linear frequency: f = ω / (2π). From RPM to Hz: f = RPM / 60. These conversions are essential when working across different engineering disciplines that use different unit conventions.3
→ Remember f and T are reciprocals. If you know the period, frequency = 1/period. If you know the frequency, period = 1/frequency. This is the most fundamental relationship in wave physics.
→ Use the correct wave speed. Light travels at 3 × 10⁸ m/s in vacuum. Sound travels at ~343 m/s in air (varies with temperature). Using the wrong speed produces wavelength errors of six orders of magnitude.
→ Watch your units. Mixing Hz with kHz, or seconds with milliseconds, is the most common source of calculation errors. Convert everything to base units (Hz and seconds) before computing, then convert results to convenient units.
→ Angular vs. linear frequency matters in formulas. Physics textbooks often use ω (angular frequency, rad/s) in equations like ω = 2πf. Always check whether a formula calls for f (in Hz) or ω (in rad/s) before substituting.
See also: Wavelength · Decibel · Speed of Sound · Energy Converter · Unit Converter