Frequency
Frequency (f) is the number of cycles per second, measured in Hertz (Hz). Period T = 1/f. Angular frequency ω = 2πf. Wavelength λ = v/f. Fundamental to waves, oscillations, rotation, and signal processing.
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1 Hz = 1 cycle/s; 1 kHz = 1000 Hz; 1 MHz = 10⁶ Hz; 1 GHz = 10⁹ Hz. Human hearing: 20 Hz–20 kHz; visible light: ~400–790 THz. RPM to Hz: f = RPM/60; 3600 RPM = 60 Hz (AC power line). Angular frequency ω (rad/s) used in oscillations and AC circuits.
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Why: Frequency governs pitch (sound), color (light), radio channels, and rotation speed. Essential for acoustics, optics, RF, and mechanical vibration.
How: f = 1/T (cycles per second). ω = 2πf (radians per second). λ = v/f links wavelength to wave speed. RPM = 60f for rotation.
Run the calculator when you are ready.
🎵 Middle A (440 Hz)
Concert pitch A4 = 440 Hz
❤️ Human Heartbeat
Average resting: 72 BPM
⚡ AC Power (US)
60 Hz household electricity
📶 WiFi 5 GHz
5 GHz wireless signal
📻 FM Radio
100 MHz station
💻 CPU Clock
3.5 GHz processor
🚗 Car Engine
3000 RPM at highway speed
🔊 Sound Wave
1 kHz tone in air (343 m/s)
🕰️ Pendulum Clock
T = 2 seconds
🍽️ Microwave Oven
2.45 GHz cooking frequency
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For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
Human hearing range: 20 Hz (low rumble) to 20 kHz (high squeak); varies with age.
— Audiology research
Visible light: red ~400 THz, violet ~790 THz; frequency determines color.
— Optics textbooks
AM radio: 535–1705 kHz; FM: 88–108 MHz; WiFi 2.4 GHz and 5 GHz.
— FCC spectrum allocation
AC power: 60 Hz (Americas) or 50 Hz (Europe); period 16.7 ms or 20 ms.
— Electrical standards
What is Frequency?
Frequency (f) measures how often a periodic event occurs per unit time. It's the inverse of period (T). Measured in Hertz (Hz), where 1 Hz = 1 cycle per second. Frequency is fundamental to understanding waves, oscillations, rotation, and many natural and technological phenomena.
Basic Definition
Frequency is the number of complete cycles occurring per unit time. It quantifies repetition rate.
f = 1/T = N/t
Units of Frequency
Hz (Hertz) is the SI unit. Common multiples: kHz, MHz, GHz, THz.
1 kHz = 1,000 Hz
1 MHz = 1,000,000 Hz
1 GHz = 1,000,000,000 Hz
Wave Relationship
For waves, frequency relates to wavelength and wave speed through v = fλ.
λ = v/f = vT
How to Calculate Frequency
🧮 From Period
T = period (time for one complete cycle)
📊 From Wavelength
v = wave speed, λ = wavelength
Applications of Frequency
🎵 Audio & Music
Musical pitch (20 Hz - 20 kHz), instrument tuning, audio processing, speakers, and microphones.
📻 Radio & Communication
AM/FM radio, WiFi, cellular networks, Bluetooth, satellite communication, GPS signals.
💻 Electronics
CPU clock speeds, oscillators, timing circuits, signal processing, power supplies.
⚡ Power Systems
AC power frequency (50/60 Hz), grid synchronization, motor control, power quality.
🔬 Science
Spectroscopy, atomic clocks, MRI, oscillations, wave mechanics, optics.
🏥 Medicine
Ultrasound imaging, heart rate monitoring, EEG brain waves, therapy devices.
Complete Formula Reference
Frequency-Period
Wave Equation
Angular Frequency
RPM Conversion
Counting Method
Light Frequency
Electromagnetic Spectrum Reference
| Type | Frequency Range | Wavelength | Applications |
|---|---|---|---|
| Radio Waves | 3 kHz - 300 GHz | 1 mm - 100 km | Broadcasting, WiFi |
| Microwaves | 300 MHz - 300 GHz | 1 mm - 1 m | Radar, cooking, 5G |
| Infrared | 300 GHz - 430 THz | 700 nm - 1 mm | Heat sensing, remotes |
| Visible Light | 430 - 750 THz | 400 - 700 nm | Vision, displays |
| Ultraviolet | 750 THz - 30 PHz | 10 - 400 nm | Sterilization, tanning |
| X-rays | 30 PHz - 30 EHz | 0.01 - 10 nm | Medical imaging |
| Gamma Rays | >30 EHz | <0.01 nm | Cancer treatment |
Common Frequency Values
| Phenomenon | Frequency | Period |
|---|---|---|
| Human heartbeat | 1-2 Hz (60-120 BPM) | 0.5-1 s |
| Bass guitar (low E) | 41 Hz | 24 ms |
| Concert A (A4) | 440 Hz | 2.27 ms |
| AC Power (US) | 60 Hz | 16.7 ms |
| AC Power (EU) | 50 Hz | 20 ms |
| AM Radio | 530-1700 kHz | 0.6-1.9 μs |
| FM Radio | 88-108 MHz | 9-11 ns |
| WiFi 2.4 GHz | 2.4 GHz | 0.42 ns |
| Modern CPU | 3-5 GHz | 0.2-0.33 ns |
| Red Light | ~430 THz | ~2.3 fs |
Frequently Asked Questions
What's the difference between frequency and period?
They're reciprocals: f = 1/T. Frequency tells you how many cycles per second, while period tells you how long one cycle takes. High frequency means short period and vice versa.
Why is 440 Hz the standard for tuning?
A4 = 440 Hz was internationally standardized in 1955 as concert pitch. It's arbitrary but universally adopted. Historically, pitches varied from 400-480 Hz in different eras and locations.
Why are power grids 50 or 60 Hz?
These frequencies balance efficiency, transformer size, and motor performance. 60 Hz (Americas) and 50 Hz (most of world) became standards in early electrification and are now too entrenched to change.
What determines the frequency of light?
Light frequency is determined by the energy of the photon: E = hf (Planck's equation). Higher energy = higher frequency = shorter wavelength. This determines color in visible light.
Tips and Common Mistakes
✅ Best Practices
- • Use appropriate units (kHz for audio, GHz for RF)
- • Specify wave speed for wavelength calculations
- • Remember f and T are reciprocals
- • Check unit prefixes carefully (k, M, G, T)
❌ Common Mistakes
- • Confusing frequency (Hz) with angular frequency (rad/s)
- • Forgetting to convert unit prefixes
- • Using wrong wave speed for medium
- • Mixing up period and frequency
Practice Problems
Problem 1: Sound Wave
A sound wave in air (v = 343 m/s) has a wavelength of 0.5 m. What is its frequency and period?
f = v/λ = 343/0.5 = 686 Hz
T = 1/f = 1/686 = 1.46 ms
Problem 2: Radio Station
An FM radio station broadcasts at 101.5 MHz. What is the wavelength of the signal?
λ = c/f = (3×10⁸)/(101.5×10⁶) = 2.96 m
Problem 3: Engine RPM
A car engine runs at 4500 RPM. What is the frequency in Hz and the period of each revolution?
f = RPM/60 = 4500/60 = 75 Hz
T = 1/f = 1/75 = 13.3 ms per revolution
Wave Speeds in Different Media
| Medium | Speed (m/s) | Type |
|---|---|---|
| Vacuum (light) | 299,792,458 | EM waves |
| Air (20°C) | 343 | Sound |
| Water (25°C) | 1,497 | Sound |
| Seawater | 1,531 | Sound |
| Steel | 5,960 | Sound |
| Glass | 5,640 | Sound |
| Diamond | 12,000 | Sound |
| Helium (0°C) | 965 | Sound |
Musical Note Frequencies (Equal Temperament)
| Note | Octave 3 | Octave 4 | Octave 5 |
|---|---|---|---|
| C | 130.81 Hz | 261.63 Hz | 523.25 Hz |
| D | 146.83 Hz | 293.66 Hz | 587.33 Hz |
| E | 164.81 Hz | 329.63 Hz | 659.25 Hz |
| F | 174.61 Hz | 349.23 Hz | 698.46 Hz |
| G | 196.00 Hz | 392.00 Hz | 783.99 Hz |
| A | 220.00 Hz | 440.00 Hz | 880.00 Hz |
| B | 246.94 Hz | 493.88 Hz | 987.77 Hz |
Note: Each octave doubles the frequency. A4 = 440 Hz is the standard concert pitch.
Radio Frequency Bands
VLF (3-30 kHz)
Submarine communication, navigation
LF (30-300 kHz)
AM longwave radio, RFID
MF (300 kHz-3 MHz)
AM broadcast radio
HF (3-30 MHz)
Shortwave radio, amateur radio
VHF (30-300 MHz)
FM radio, TV, aircraft
UHF (300 MHz-3 GHz)
TV, WiFi, Bluetooth, cellular
SHF (3-30 GHz)
5G, radar, satellite
EHF (30-300 GHz)
Millimeter wave, 5G mmWave
Historical Development
🔬 Heinrich Hertz (1857-1894)
First to prove the existence of electromagnetic waves in 1887. The unit of frequency (Hz) is named in his honor.
📻 Guglielmo Marconi (1874-1937)
Pioneer of radio communication, sent first transatlantic radio signal in 1901 using frequencies around 820 kHz.
⚡ Nikola Tesla (1856-1943)
Developed AC power systems and demonstrated radio-controlled devices. Contributed to understanding of resonant frequencies.
🎵 Ancient Greeks
Pythagoras discovered mathematical relationships between string lengths and musical pitches around 500 BC—the first frequency relationships.
Unit Conversion Quick Reference
Frequency Prefixes
Period Prefixes
Key Relationships Summary
Double frequency
Half period
f ↔ 1/T
Double wavelength
Half frequency
v = fλ
One octave up
2× frequency
Musical intervals
60 RPM =
1 Hz
RPM = 60f
📚 Official Data Sources
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