Frequency Converter
Convert a frequency between hertz multiples, rotation speeds (RPM, rad/s), beats per minute and period. The wavelength is shown too, for sound in air or water or for radio waves and light.
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Pick a period unit in From to convert a cycle time (seconds per cycle) into frequency.
How to use the Frequency Converter
- Enter a frequency (or a period, such as 20 ms).
- Choose the From and To units. Period units work in both directions.
- Pick the wave type for the wavelength: sound in air or water, or radio waves and light.
- Read all the other units, the wavelength and the angular frequency in the results.
- Copy the results or download the reference table.
Frequency formulas
- Hertz multiples: 1 kHz = 1,000 Hz, 1 MHz = 106 Hz, 1 GHz = 109 Hz, 1 THz = 1012 Hz.
- Per-minute rates:
Hz = RPM ÷ 60andHz = BPM ÷ 60. - Angular frequency:
ω = 2π × f, sof = ω ÷ 2π. 1 rad/s ≈ 0.159155 Hz. - Period:
T = 1 ÷ f. Doubling the frequency halves the period. - Wavelength:
λ = v ÷ f, where v is the speed of the wave in its medium.
Example: a 60 Hz power line has a period of 1 ÷ 60 = 16.67 ms, an angular frequency of 2π × 60 = 376.99 rad/s, and the same rate as a motor spinning at 3,600 RPM.
Wave speeds used for the wavelength
| Wave and medium | Speed | Wavelength at 1 kHz | Wavelength at 100 MHz |
|---|---|---|---|
| Radio / light in a vacuum | 299,792,458 m/s (exact) | 299.8 km | 2.998 m |
| Radio / light in air | ≈ 299,705,000 m/s (n ≈ 1.000293) | 299.7 km | 2.997 m |
| Sound in air, 20 °C | ≈ 343 m/s | 34.3 cm | 3.43 µm |
| Sound in fresh water, 20 °C | ≈ 1,482 m/s | 1.482 m | 14.82 µm |
The speed of sound in air rises by about 0.6 m/s for every 1 °C, so wavelengths in a cold room are slightly shorter. Light in air is only about 0.03% slower than in a vacuum.
Where each unit is used
- Hz and kHz: audio, music notes, mains electricity (50 or 60 Hz), sample rates.
- MHz and GHz: radio stations, Wi-Fi, mobile networks and processor clock speeds.
- THz: infrared and visible light (green light is about 545 THz).
- RPM and rad/s: engines, motors, fans, drills and turntables; rad/s is the SI form used in physics.
- BPM: music tempo and heart rate.
- Period: oscilloscopes, timers and animation frame times (60 fps = 16.67 ms per frame).
Frequently asked questions
How do I convert Hz to kHz, MHz and GHz?
Each step is a factor of 1,000: divide hertz by 1,000 for kHz, by 1,000,000 for MHz and by 1,000,000,000 for GHz. For example 2,450,000,000 Hz = 2,450 MHz = 2.45 GHz.
How do I convert RPM to Hz?
Divide by 60, because RPM counts revolutions per minute and hertz counts cycles per second. 3,600 RPM ÷ 60 = 60 Hz. Multiply Hz by 60 to get RPM.
How are frequency and period related?
They are reciprocals: period T = 1 ÷ f and f = 1 ÷ T. A 50 Hz signal repeats every 1 ÷ 50 = 0.02 s (20 ms); a 1 kHz tone repeats every 1 ms.
How do I convert rad/s to Hz?
One full cycle is 2π radians, so f = ω ÷ 2π. For example 314.16 rad/s ÷ 6.2832 = 50 Hz. In reverse, ω = 2πf.
How do I find the wavelength from the frequency?
Divide the wave speed by the frequency: λ = v ÷ f. Sound in air at 20 °C travels about 343 m/s, so a 440 Hz tone has a wavelength of 0.78 m. Radio waves travel at the speed of light, 299,792,458 m/s, so 100 MHz FM has a wavelength of about 3 m.
Is BPM the same as RPM?
Numerically yes: both count events per minute, so 120 BPM and 120 RPM are both 2 Hz. BPM is used for heartbeats and music tempo, RPM for rotating machines.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.