Calculate frequency, period, angular frequency, and wavelength. Essential tool for electronics engineers, physicists, and audio professionals.
Frequency is the number of occurrences of a repeating event per unit of time. It is measured in hertz (Hz), which is one cycle per second. Period is the duration of time of one cycle in a repeating event, and it is the reciprocal of frequency.
Key Relationships:
| Frequency Range | Name | Typical Wavelength (in air) | Common Applications |
|---|---|---|---|
| 0.1 - 20 Hz | Sub-audio / Infrasound | > 17,000 m | Seismic waves, elephant communication |
| 20 - 20,000 Hz | Audio / Audible Sound | 17 m - 17 mm | Human hearing, music, speech |
| 20 kHz - 1 MHz | Ultrasonic | 17 mm - 0.34 mm | Medical imaging, cleaning, pest control |
| 3 kHz - 300 GHz | Radio Frequency (RF) | 100 km - 1 mm | Radio, TV, wireless communication |
| 300 MHz - 300 GHz | Microwave | 1 m - 1 mm | Radar, satellite communication, microwave ovens |
| 300 GHz - 430 THz | Infrared | 1 mm - 700 nm | Thermal imaging, remote controls, fiber optics |
| 430 - 750 THz | Visible Light | 700 - 400 nm | Human vision, photography, displays |
| 750 THz - 30 PHz | Ultraviolet | 400 - 10 nm | Black lights, sterilization, sun tanning |
These formulas are essential for converting between different frequency-related units:
Frequency to Period: T = 1 / f
Period to Frequency: f = 1 / T
Frequency to Angular Frequency: ω = 2πf
Angular Frequency to Frequency: f = ω / 2π
Frequency to Wavelength: λ = v / f
Wavelength to Frequency: f = v / λ
| Frequency | Period | Wavelength (in air) | Common Use |
|---|---|---|---|
| 0.1 Hz | 10 s | 3,000,000 km | Extremely low frequency (ELF) |
| 60 Hz | 16.67 ms | 5,000 km | AC power (North America) |
| 440 Hz | 2.27 ms | 78 cm | Musical note A4 (concert pitch) |
| 1 kHz | 1 ms | 300 m | Audio test tone |
| 100 kHz | 10 μs | 3 km | AM radio (low end) |
| 1 MHz | 1 μs | 300 m | AM radio, some microcontrollers |
| 100 MHz | 10 ns | 3 m | FM radio |
| 2.4 GHz | 417 ps | 12.5 cm | WiFi, Bluetooth, microwave ovens |
| 5 GHz | 200 ps | 6 cm | WiFi, radar |
| 500 THz | 2 fs | 600 nm | Green light |
In Western music, the standard tuning defines A4 (the A above middle C) as 440 Hz. Other notes are calculated using the equal temperament formula:
Formula: fn = fref × 2(n/12)
Where fref is the reference frequency (usually A4 = 440 Hz), n is the number of half steps from the reference note.
| Octave | C | D | E | F | G | A | B |
|---|---|---|---|---|---|---|---|
| 0 | 16.35 Hz | 18.35 Hz | 20.60 Hz | 21.83 Hz | 24.50 Hz | 27.50 Hz | 30.87 Hz |
| 1 | 32.70 Hz | 36.71 Hz | 41.20 Hz | 43.65 Hz | 49.00 Hz | 55.00 Hz | 61.74 Hz |
| 2 | 65.41 Hz | 73.42 Hz | 82.41 Hz | 87.31 Hz | 98.00 Hz | 110.00 Hz | 123.47 Hz |
| 3 | 130.81 Hz | 146.83 Hz | 164.81 Hz | 174.61 Hz | 196.00 Hz | 220.00 Hz | 246.94 Hz |
| 4 | 261.63 Hz | 293.66 Hz | 329.63 Hz | 349.23 Hz | 392.00 Hz | 440.00 Hz | 493.88 Hz |
| 5 | 523.25 Hz | 587.33 Hz | 659.25 Hz | 698.46 Hz | 783.99 Hz | 880.00 Hz | 987.77 Hz |
| 6 | 1046.50 Hz | 1174.66 Hz | 1318.51 Hz | 1396.91 Hz | 1567.98 Hz | 1760.00 Hz | 1975.53 Hz |
| 7 | 2093.00 Hz | 2349.32 Hz | 2637.02 Hz | 2793.83 Hz | 3135.96 Hz | 3520.00 Hz | 3951.07 Hz |
| 8 | 4186.01 Hz | 4698.63 Hz | 5274.04 Hz | 5587.65 Hz | 6271.93 Hz | 7040.00 Hz | 7902.13 Hz |
Technical Note: The speed of wave propagation (v) varies depending on the medium. For electromagnetic waves in vacuum, v = c = 299,792,458 m/s. For sound waves in air at 20°C, v ≈ 343 m/s. Always use the appropriate speed for accurate wavelength calculations.