Frequency is how often something repeats: cycles of an alternating current, vibrations of a string, revolutions of a shaft, beats of a song or oscillations of a radio carrier. The SI unit is the hertz (one cycle per second), but rotating machinery is rated in revolutions per minute, physics uses radians per second and music uses beats per minute. This converter switches between all of them and adds the numbers that usually come next — period, angular frequency, wavelength and, for audible tones, the closest note on a piano.
How to use the frequency converter
- Enter a frequency or speed and choose its unit in From (hertz with any prefix, rpm, rev/s, rad/s, degrees per second, bpm or cycles per hour).
- Choose the unit you want in To.
- Read the converted value and the extra rows: the period of one cycle, the angular frequency, the wavelength as a radio wave, the wavelength as sound in air (for frequencies up to 100 kHz) and the nearest musical note (for 16 Hz to 20 kHz).
Frequency formulas
Every unit here counts cycles per unit time, so conversion is a single factor. The related quantities are:
where T is the period, ω the angular frequency in rad/s, λ the wavelength and v the wave speed: 299,792,458 m/s for electromagnetic waves (exact by the SI definition of the meter) and about 343 m/s for sound in dry air at 20 °C.
| From | To | Multiply by |
|---|---|---|
| Hz | rpm | 60 |
| rpm | Hz | 1/60 = 0.016667 |
| Hz | rad/s | 6.283185 |
| rad/s | rpm | 9.549297 |
| bpm | Hz | 1/60 |
| kHz → MHz → GHz | next prefix up | 0.001 |
Worked example
US household power alternates at 60 Hz.
As rpm: 60 × 60 = 3,600 rpm — the synchronous speed of a two-pole AC motor on a 60 Hz supply (a four-pole motor runs near 1,800 rpm).
Period: 1 ÷ 60 = 0.016667 s = 16.67 ms per cycle.
Angular frequency: 2π × 60 = 376.99 rad/s.
Second case: Wi-Fi at 2.4 GHz is 2,400 MHz, and its wavelength is 299,792,458 ÷ 2.4 × 10⁹ = 0.1249 m, about 12.5 cm — which is why a quarter-wave 2.4 GHz antenna is only about 3 cm long.
Frequencies you will meet
| Thing | Frequency | Period |
|---|---|---|
| Resting heart, 60 bpm | 1 Hz | 1 s |
| Mains power (Europe / US) | 50 / 60 Hz | 20 / 16.67 ms |
| Concert pitch A4 | 440 Hz | 2.273 ms |
| Upper limit of human hearing | about 20 kHz | 50 µs |
| FM radio band (US) | 88–108 MHz | about 10 ns |
| Wi-Fi bands | 2.4, 5 and 6 GHz | under 0.42 ns |
Musical notes
In twelve-tone equal temperament each semitone multiplies the frequency by the twelfth root of 2 (about 1.05946), and an octave doubles it. With A4 tuned to 440 Hz, the note n semitones away is 440 × 2^(n/12). The calculator rounds to the nearest note and reports the remainder in cents, hundredths of a semitone; a tuner showing “+12 cents” means the tone is slightly sharp.
Pitfalls
- rpm is not angular velocity in radians. Physics formulas such as P = τω need rad/s; multiply rpm by 0.10472 first.
- Sample rate is not tone frequency. A 44.1 kHz audio sample rate can only represent tones below half of it (22.05 kHz), the Nyquist limit.
- Prefix case matters. mHz is millihertz, a thousand times smaller than a hertz, while MHz is megahertz, a million times larger.
For a wavelength-first calculation with any wave speed, use the wavelength calculator. To scale other SI prefixes, try the metric prefix converter.
Frequently asked questions
How do I convert rpm to Hz?
Divide by 60. One revolution per second is 1 Hz and there are 60 seconds in a minute, so 3,600 rpm is 60 Hz and 1,500 rpm is 25 Hz. Multiply Hz by 60 to get rpm.
What is the difference between Hz and rad/s?
Hertz counts complete cycles per second; radians per second measures angular frequency, the angle swept per second. One cycle is 2π radians, so ω = 2π × f. 1 Hz equals 6.2832 rad/s, and 1 rad/s equals 9.5493 rpm.
How do I find the period from a frequency?
Take the reciprocal: T = 1 ÷ f. A 60 Hz power line has a period of 1/60 s = 16.67 ms; a 2.4 GHz Wi-Fi carrier has a period of about 0.417 nanoseconds.
How is wavelength related to frequency?
Wavelength equals wave speed divided by frequency. For radio and light, use the speed of light, 299,792,458 m/s; for sound in air at 20 °C, use about 343 m/s. The same 440 Hz tone is 78 cm long in air but 681 km long as a radio wave.