Frequency Counter Calculator

Calculate frequency, period, angular frequency, and wavelength. Essential tool for electronics engineers, physicists, and audio professionals.

Frequency ↔ Period
Frequency ↔ Wavelength
Angular Frequency
Musical Notes

Frequency to Period Formula: T = 1 / f

Period to Frequency Formula: f = 1 / T

Angular Frequency Formula: ω = 2πf = 2π / T

Where: f = frequency (Hz), T = period (s), ω = angular frequency (rad/s)

Enter frequency value (e.g., 440 Hz = musical note A4)
Enter period value (e.g., 2.2727 ms ≈ period of 440 Hz)
rad/s
Angular frequency in radians per second
Enter frequency value
Enter wavelength value
Vacuum (c = 299,792,458 m/s)
Air (Sound, 343 m/s at 20°C)
Water (Sound, 1,480 m/s)
Steel (Sound, 5,000 m/s)
Custom
Speed of wave propagation in the medium
rad/s
Enter angular frequency in radians per second
Hz
Frequency in hertz (Hz)
s
Period in seconds
Select a musical note or enter custom frequency
Hz
Or enter custom frequency to find nearest note
A4 = 440 Hz (Modern Standard)
A4 = 432 Hz (Verdi Tuning)
A4 = 415 Hz (Baroque)
Custom
C4
C#4
D4
D#4
E4
F4
F#4
G4
G#4
A4
A#4
B4
C5
Calculating...

Understanding Frequency and Period

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 (f): Number of cycles per second (Hz)
  • Period (T): Time for one complete cycle (seconds)
  • Angular Frequency (ω): Frequency expressed in radians per second (rad/s)
  • Wavelength (λ): Spatial period of a wave - distance over which the wave's shape repeats

Frequency Range Classification

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

Conversion Formulas

These formulas are essential for converting between different frequency-related units:

1

Frequency to Period: T = 1 / f

2

Period to Frequency: f = 1 / T

3

Frequency to Angular Frequency: ω = 2πf

4

Angular Frequency to Frequency: f = ω / 2π

5

Frequency to Wavelength: λ = v / f

6

Wavelength to Frequency: f = v / λ

Common Frequency Reference Values

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

Musical Note Frequencies

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.

Frequently Asked Questions

Frequency (f) is the number of cycles per unit time, measured in hertz (Hz). Period (T) is the time duration of one complete cycle, measured in seconds. They are inversely related: f = 1/T and T = 1/f. For example, a frequency of 100 Hz corresponds to a period of 0.01 seconds (10 ms).

Angular frequency (ω) is the frequency expressed in radians per second rather than cycles per second. While regular frequency (f) tells you how many complete cycles occur in one second, angular frequency tells you how many radians of phase are covered in one second. The relationship is ω = 2πf. Angular frequency is particularly useful in physics and engineering when dealing with rotational motion or oscillatory systems described by sine and cosine functions.

To calculate wavelength (λ) from frequency (f), you need to know the speed of wave propagation (v) in the medium. The formula is λ = v / f. For electromagnetic waves in vacuum, v = c = 299,792,458 m/s. For sound waves in air at 20°C, v ≈ 343 m/s. For example, a 100 MHz radio wave in vacuum has a wavelength of approximately 3 meters (299,792,458 / 100,000,000 = 2.9979 m).

A4 = 440 Hz became the international standard in 1939 when it was adopted by an international conference in London. This standardization allows musicians from different countries to play together in tune. Before standardization, tuning varied widely: Baroque music was often tuned to A4 = 415 Hz, while some orchestras in the 19th century used A4 = 435 Hz. The 440 Hz standard provides a practical compromise that works well for most instruments and vocal ranges.

The typical human hearing range is from 20 Hz to 20,000 Hz (20 kHz), although this range decreases with age and exposure to loud noises. Children can often hear frequencies up to 20 kHz, while most adults over 30 cannot hear above 15-16 kHz. The most sensitive range for human hearing is between 2,000 and 5,000 Hz, which corresponds to the frequencies most important for understanding speech.