Frequency & Wavelength
Convert between frequency and wavelength in free space, coax or PCB, with quarter-wave and lumped-limit lengths.
Step-by-step
- Enter valid values to begin.
Wavelength uses c = 299,792,458 m/s and v = c × VF. The medium acts as a velocity factor on the wavelength; the frequency is the same in every medium. In wavelength mode the wavelength entered is the wavelength in the selected medium. VF values are typical, so check the cable or laminate datasheet; microstrip εeff depends on trace width, height and frequency. The λ/10 and λ/20 limits are rules of thumb, not standards. Band names follow the ITU designation by frequency.
Frequency and Wavelength: Why Cut Length Is Never the Free-Space Number
Core Engineering Principles
A radio wave covers one wavelength in one period, so λ = v / f. In free space v is c, 299,792,458 m/s, and at 145 MHz that gives 2.0675 m. Put the same wave on a cable or a board and it slows to v = c × VF, where VF = 1/√εeff. Solid-PE coax is about 0.66, foam about 0.80, and FR-4 microstrip near 0.55. The frequency never changes between media; the wavelength shrinks. That is why a quarter-wave stub cut from the free-space number is 50% too long on RG-58.
For antennas we use λ/4 and λ/2 as starting points, then cut shorter, because a real wire has end effect and thickness that make it resonate at about 95% of the free-space length. On a board we treat λ/10 as the limit where a trace is still electrically short, and λ/20 as the comfortable lumped-element limit. Past that, a trace needs controlled impedance and termination. At 1 GHz on FR-4 the λ/20 limit is only about 8 mm.
T = 1 / f • c = 299,792,458 m/s
Short limits: λ/10 (electrically short), λ/20 (lumped)
NEC & Standard References
ITU-R P.525 gives free-space attenuation, which grows with the square of frequency for fixed antenna gains and is why wavelength sets link loss. The ITU Radio Regulations define the band designations from ELF to EHF,. IEEE Std 145 defines antenna terms such as resonance, radiation resistance and effective length. Velocity factor comes from the cable or laminate datasheet; none of these documents fixes the VF of a particular product. Check the current edition before quoting.1. λ = 299,792,458 / 145,000,000 = 2.0675 m.
2. λ/2 = 1.0338 m; λ/4 = 51.69 cm; 5/8 λ = 1.2922 m.
3. λ/10 = 20.68 cm and λ/20 = 10.34 cm.
4. T = 1 / 145 MHz = 6.897 ns.
5. 145 MHz is in 30–300 MHz, so the band is VHF.
6. Trimmed vertical: 51.69 cm × 0.95 = 49.10 cm.
7. Quarter-wave stub in solid-PE coax: 51.69 × 0.66 = 34.11 cm.
- Don’t use the free-space length in coax. A stub, phasing line or balun sleeve must use the wavelength inside the cable, so multiply by VF.
- Allow for end effect. A bare wire resonates a few percent below λ/2 or λ/4; cut long and trim against an analyzer, because wire only gets shorter.
- Keep metal away. Gutters, masts and your own body detune an antenna and pull resonance down; tune it in its final position.
- Remember the harmonics. A quarter-wave stub is also a quarter-wave at 3f, so check that the filter you built does not pass the third harmonic.
- Trust the cable, not the table. The VF is printed on the jacket or datasheet, and it varies between brands and with foam density, so measure a sample length when it matters.