Frequency Converter
Convert between Hz, kHz, MHz, GHz, THz, rpm and rad/s, and see the period and the wavelength of the same frequency. You can also enter a period or a wavelength and get the frequency back.
f = 1 ÷ T · λ = c ÷ f
Hz, kHz, MHz, GHz and THz
One hertz is one cycle per second. The larger units use the standard SI prefixes, and each step is a factor of 1,000. To go up a step, divide by 1,000. To jump two steps (Hz to MHz), divide by 1,000,000.
| Unit | In hertz | Power of ten |
|---|---|---|
| 1 kHz (kilohertz) | 1,000 Hz | 10³ |
| 1 MHz (megahertz) | 1,000,000 Hz | 10⁶ |
| 1 GHz (gigahertz) | 1,000,000,000 Hz | 10⁹ |
| 1 THz (terahertz) | 1,000,000,000,000 Hz | 10¹² |
| 1 mHz (millihertz) | 0.001 Hz | 10⁻³ |
Case matters: MHz (mega, a million cycles per second) and mHz (milli, one cycle every 1,000 seconds) differ by a factor of a billion. Likewise, kHz is written with a lower-case k and Hz with a capital H.
Frequency, Period and Wavelength
The period is how long one cycle takes, so it shrinks as the frequency rises: 50 Hz mains repeats every 20 ms, and a 4 GHz processor clock ticks every 0.25 ns. In that time, light covers only 7.5 cm.
The wavelength shown applies to radio waves and light in a vacuum. Air shortens it by only about 0.03%. In coaxial cable, glass or water it is noticeably shorter, because waves travel more slowly there. Sound needs a different calculation: its wavelength is the speed of sound (about 343 m/s in air at 20 °C) divided by the frequency, so a 440 Hz note is about 78 cm long.
Worked Example: An FM Station at 100.1 MHz
You want the wavelength of a 100.1 MHz FM station, to size a simple quarter-wave antenna.
Step 1: Convert to hertz
Step 2: Divide the speed of light by the frequency
Step 3: Take a quarter
The wavelength is about 3 m, so a quarter-wave antenna is about 75 cm. A real antenna is cut a few percent shorter, because the signal travels slightly slower along the conductor. The period of the same signal is 9.99 ns.
Radio, Wi-Fi and Light Frequencies
| Signal | Frequency | Wavelength |
|---|---|---|
| AM (medium wave) broadcast | 526.5–1,606.5 kHz (530–1,700 kHz in the Americas) | ≈ 300 m |
| FM broadcast | 87.5–108 MHz (88–108 MHz in the US) | ≈ 3 m |
| GPS L1 signal | 1,575.42 MHz | ≈ 190 mm |
| 2.4 GHz Wi-Fi and Bluetooth | 2.400–2.4835 GHz | ≈ 125 mm |
| Microwave oven | 2.45 GHz | ≈ 122 mm |
| 5 GHz Wi-Fi | 5.15–5.85 GHz | ≈ 54.5 mm |
| Visible light (red to violet) | about 400–790 THz | ≈ 545 nm |
Wavelengths are for a typical frequency in each band. Light is usually described by wavelength rather than frequency, so 380–750 nm is the same visible range as 400–790 THz. Exact radio band edges vary by country and are set by national regulators within the ITU Radio Regulations.
Sound, Mains Power and Rotation
| Source | Frequency |
|---|---|
| Lower limit of human hearing | about 20 Hz |
| Mains electricity (UK, Europe, most of Asia and Africa) | 50 Hz, period 20 ms |
| Mains electricity (North America, parts of South America) | 60 Hz, period 16.7 ms |
| Concert pitch A4 (ISO 16) | 440 Hz |
| Upper limit of human hearing (young adults) | about 20 kHz |
| Music at 120 bpm | 2 Hz |
| Engine idling at 750 rpm | 12.5 Hz |
Revolutions per minute and beats per minute are frequencies too: divide by 60 for hertz. An AC motor's synchronous speed follows the mains frequency, at 120 × f ÷ number of poles. A two-pole motor turns at 3,000 rpm on 50 Hz and 3,600 rpm on 60 Hz, and induction motors run a few percent below that.
Why Microwave Ovens Use 2.45 GHz
A common claim is that 2.45 GHz is the resonant frequency of water. It isn't: water absorbs microwaves across a wide range, and its absorption keeps rising well above 2.45 GHz. Ovens use 2.45 GHz because it falls in an ISM band (industrial, scientific and medical) that can be used without a licence. It also suits cooking: water absorbs it moderately, so the energy reaches a few centimetres into food instead of all being absorbed at the surface.
2.4 GHz Wi-Fi and Bluetooth share the same unlicensed band. That is why a leaky or running microwave oven can disrupt 2.4 GHz Wi-Fi, while 5 GHz Wi-Fi is unaffected.
Frequently asked questions
How do I convert MHz to GHz?
Divide by 1,000. 2,400 MHz is 2.4 GHz, and 5,500 MHz is 5.5 GHz.
How do I convert rpm to Hz?
Divide by 60. 3,000 rpm is 50 Hz, and 1 Hz is 60 rpm. For angular frequency in rad/s, multiply the hertz value by 2π.
What is the period of 60 Hz?
1 ÷ 60 = 0.0167 s, or 16.67 ms. For 50 Hz it is exactly 20 ms.
How do I get frequency from wavelength?
Divide the speed of light by the wavelength in metres. A 12.5 cm wavelength is 299,792,458 ÷ 0.125 ≈ 2.4 GHz. Choose a wavelength unit in the converter to do this automatically.
Is 1 Hz the same as 1 per second?
Yes for things that repeat in cycles. For random events such as radioactive decay, the SI uses becquerels instead, although both are 1/s.
Sources
- BIPM: The International System of Units (SI Brochure): the hertz, SI prefixes and the exact speed of light.
- ITU Radio Regulations: international allocation of broadcast and ISM frequency bands.
- GPS.gov interface specifications: the L1 carrier frequency of 1,575.42 MHz.
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