Frequency to wavelength: the size a radio wave has to be
What this conversion does
It divides the speed of light in a vacuum — 299,792,458 metres per second — by the frequency, giving the distance the wave travels in one cycle. That distance is not an abstraction: it sets the size of the antenna that will radiate or receive the signal efficiently, which is why a Wi-Fi device can have an antenna printed on a circuit board while a broadcast tower is hundreds of metres tall.
Why the answer is often in millimetres
Wavelength shrinks as frequency rises, so the results at the top of the radio spectrum are small. A 2.4 GHz signal has a wavelength of about 125 millimetres, which is a comfortable size for a small antenna; a 5.8 GHz signal is around 52 millimetres. Writing those in metres would give two or three leading zeroes, so the converter scales them into millimetres, and into micrometres for the terahertz range.
Frequency to wavelength conversion table
Common radio frequencies with the wavelength each one corresponds to, from broadcast bands up to microwave links.
| Megahertz (MHz) | Wavelength (metres) |
|---|---|
| 1 | 299.8 m |
| 10 | 29.98 m |
| 100 | 2.998 m |
| 433 | 692.4 mm |
| 900 | 333.1 mm |
| 2400 | 124.9 mm |
| 5800 | 51.69 mm |
Why antenna size tracks the wavelength
An antenna works by coupling to the electric field of a passing wave, and that coupling is strongest when the antenna is a comparable size to one wavelength or a simple fraction of it. A half-wave dipole at 100 MHz is therefore about 1.5 metres, while the same design at 2.4 GHz is about 62 millimetres. This single relationship explains most of the visible difference between antennas for different services.
The approximation worth carrying around
Because the speed of light is close to 300 million metres per second, the wavelength in metres is roughly 300 divided by the frequency in megahertz. At 100 MHz that gives about 3 metres, which is accurate enough for a sanity check on any calculation the converter performs.
Frequently asked questions
How do I convert a frequency to a wavelength?
Divide the speed of light, 299,792,458 metres per second, by the frequency in hertz. A 100 MHz signal has a wavelength of about 2.9979 metres. The converter performs the division with the exact constant and scales the result.
What is the wavelength of 2.4 GHz?
About 124.9 millimetres. That is why Wi-Fi antennas are small enough to be etched onto a circuit board: a quarter-wave element at that frequency is only about 31 millimetres long.
Why does a higher frequency mean a shorter wavelength?
Because the wave travels at a fixed speed, so a signal that completes more cycles each second must fit each cycle into less distance. Doubling the frequency halves the wavelength, which is why the two quantities always move in opposite directions.
Does the converter use an exact value for the speed of light?
Yes. The metre is defined in terms of the speed of light, so the constant is exact by definition rather than measured, and the converter computes with the full value rather than a rounded one. Rounding it would introduce an error in the last digits of every result.
Does the wavelength change in a cable or a material?
Yes. In a medium other than vacuum the wave travels more slowly, so the wavelength shortens by the material's velocity factor — around two thirds for a typical coaxial cable. The converter calculates the free-space wavelength, which is the starting point for that adjustment.