# What is the frequency?

Finds a frequency in hertz from the period (f = 1/T), from a wave’s speed and wavelength (f = v/λ), or from the angular frequency (f = ω/2π), with the period, angular frequency and cycles per minute.

- Page: https://www.acalculator.org/physics/frequency-calculator
- JSON spec: https://www.acalculator.org/physics/frequency-calculator.json
- Version: 4e5c0d39b0f3

## Default answer

Example with the default inputs (Find the frequency from Period, Period 20 ms): The frequency is 50 Hz, one cycle every 0.02 s.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | Find the frequency from | Work out the frequency from the period, from a wave’s speed and wavelength, or from the angular frequency. |
| T | Period | The time for one full cycle. |
| v | Wave speed | How fast the wave travels: about 343 m/s for sound in air at 20 °C. |
| l | Wavelength | The distance between two crests of the wave. |
| w | Angular frequency (rad/s) | The angular frequency ω in radians per second. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| hz | Frequency (Hz) | The frequency in hertz: cycles per second. |
| khz | Frequency (kHz) | The same frequency in kilohertz. |
| period | Period (s) | The time for one cycle, T = 1 ÷ f, in seconds. |
| omega | Angular frequency (rad/s) | ω = 2π f, in radians per second. |
| perMinute | Cycles per minute | f × 60, the same as rpm for something that turns. |

## Method

f = 1 ÷ T; f = v ÷ λ; f = ω ÷ 2π.

## Assumptions

- The motion repeats at a steady rate (periodic motion), and the wave speed is the speed in the medium the wave travels through.
- Exact unit sizes: 1 ms = 0.001 s; 1 mph = 0.44704 m/s; 1 km/h = 1/3.6 m/s; 1 ft = 0.3048 m; 1 in = 0.0254 m.

## Worked examples

1. from = period, T = 0.02 gives hz = 50, perMinute = 3,000, omega = 314.159265. Source: OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (f = 1 ÷ T; ω = 2πf), https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion.
2. from = wave, v = 343, l = 0.78 gives hz = 439.74359. Source: OpenStax, University Physics Volume 1, §16.1 Traveling Waves (v = λ ÷ T = λ f), https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves.
3. from = period, T = 2 gives hz = 0.5, perMinute = 30. Source: OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (f = 1 ÷ T; ω = 2πf), https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion.
4. from = angular, w = 314.159265 gives hz = 50, T = 0.02. Source: OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (f = 1 ÷ T; ω = 2πf), https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion.

## FAQ

### How do you calculate frequency from the period?

Frequency is one divided by the period: f = 1 ÷ T. A period of 20 ms (0.02 s) gives 1 ÷ 0.02 = 50 Hz, the frequency of the power grid in much of the world.

### How do you calculate frequency from wavelength?

Divide the wave speed by the wavelength: f = v ÷ λ. Sound at 343 m/s with a wavelength of 0.78 m has a frequency of 343 ÷ 0.78 = 439.7 Hz, close to the note A4 (440 Hz).

### What is a hertz?

One hertz (Hz) is one cycle per second. 1 kHz = 1,000 Hz, 1 MHz = 1,000,000 Hz.

### What is angular frequency?

Angular frequency ω is the frequency in radians per second: ω = 2π f. A 50 Hz signal has ω = 2π × 50 = 314.16 rad/s, and f = ω ÷ 2π turns it back.

### How do frequency and rpm relate?

For something that turns, one cycle is one turn, so the cycles per minute are the rpm: f × 60. A part at 50 Hz turns 3,000 times a minute.

## Sources

- OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (f = 1 ÷ T; ω = 2π f). https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion (retrieved 2026-10-03)
- OpenStax, University Physics Volume 1, §16.1 Traveling Waves (v = λ ÷ T = λ f). https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves (retrieved 2026-10-03)