What is the frequency?
Type a period, a wave speed and wavelength, or an angular frequency. The frequency calculator gives the frequency in hertz and kilohertz, the period, the angular frequency and the cycles per minute.
- Frequency (Hz)
- 50
The frequency is 50 Hz, one cycle every 0.02 s.
- Frequency (kHz)
- 0.05
- Period (s)
- 0.02
- Angular frequency (rad/s)
- 314.159
- Cycles per minute
- 3,000
Frequency (Hz): 50. The frequency is 50 Hz, one cycle every 0.02 s.
How to calculate
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.
Example with the default inputs (Find the frequency from Period, Period 20 ms): The frequency is 50 Hz, one cycle every 0.02 s.
Method: f = 1 ÷ T; f = v ÷ λ; f = ω ÷ 2π.
- 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
Each example is checked against the calculator on every build.
- Find the frequency from Period, Period 0.02 gives Frequency (Hz) 50, Cycles per minute 3,000, Angular frequency (rad/s) 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
- Find the frequency from Wave speed and wavelength, Wave speed 343 m/s, Wavelength 0.78 m gives Frequency (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
- Find the frequency from Period, Period 2 gives Frequency (Hz) 0.5, Cycles per minute 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
- Find the frequency from Angular frequency, Angular frequency (rad/s) 314.159265 gives Frequency (Hz) 50, Period 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
How it works
Pick what you know:
- Period T: f = 1 ÷ T.
- Wave speed v and wavelength λ: f = v ÷ λ.
- Angular frequency ω (rad/s): f = ω ÷ 2π.
From the frequency the page also shows kilohertz (f ÷ 1,000), the period T = 1 ÷ f in seconds, the angular frequency ω = 2π f (the typed ω itself in that mode), and the cycles per minute f × 60.
Unit sizes: 1 ms = 0.001 s; 1 min = 60 s; 1 h = 3,600 s; 1 km/h = 1/3.6 m/s; 1 mph = 0.44704 m/s; 1 ft/s = 0.3048 m/s; 1 cm = 0.01 m; 1 mm = 0.001 m; 1 µm = 10⁻⁶ m; 1 nm = 10⁻⁹ m; 1 km = 1,000 m; 1 ft = 0.3048 m; 1 in = 0.0254 m.
Exact arithmetic. Each value is read as the exact decimal you typed, in its unit, so f = 1 ÷ T and f = v ÷ λ are exact fractions until they are rounded for display. The angular mode divides by 2π, a 64-bit float.
Output format. Every value shows 6 significant figures; values of 10¹⁵ or more, or below 10⁻⁶, show in scientific form.
Assumptions
- The motion repeats at a steady rate.
- Period 10⁻¹⁵ to 10⁹ s; wave speed 10⁻⁶ m/s up to the speed of light; wavelength 10⁻¹⁵ to 10⁹ m; angular frequency 10⁻⁹ to 10¹⁸ rad/s.
Worked examples by hand
A period of 20 ms. f = 1 ÷ 0.02 = 50 Hz; × 60 = 3,000 per minute; ω = 2π × 50 = 314.159 rad/s.
Sound at 343 m/s, wavelength 0.78 m. f = 343 ÷ 0.78 = 439.744 Hz.
A pendulum with a 2 s period. f = 1 ÷ 2 = 0.5 Hz = 30 per minute.
ω = 100π rad/s. f = 100π ÷ 2π = 50 Hz; T = 1 ÷ 50 = 0.02 s.
Other questions people ask
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.