How to use the wavelength and electrical length calculator
- Choose Wavelength and lengths or Electrical length.
- Enter the frequency and choose hertz, kilohertz, megahertz or gigahertz.
- Enter the velocity factor: 1 for free space, or the value for your cable or line.
- For lengths, set the end effect factor; for electrical length, enter the physical length. Read the table of lengths.
Formula
Wavelength = c x velocity factor / frequency, with c = 299,792,458 m/s
Half-wave dipole length = (free-space wavelength / 2) x end effect factor
Quarter wave = wavelength / 4; 5/8 wave = 5 x wavelength / 8
Electrical length (degrees) = physical length / wavelength in the line x 360
The velocity factor slows the wave in a cable. A wire antenna in air uses the free-space wavelength, not the cable value.
Two meters, 40 meters and a cable
At 146 MHz the free-space wavelength is 2.05337 m. A half-wave dipole with an end effect factor of 0.95 is 0.975352 m, or 3.2 ft. At 7.1 MHz the wavelength is 42.2243 m and the half-wave dipole is 20.0565 m, about 65.8 ft.
A cable with a velocity factor of 0.66 at 144 MHz carries a wave of 1.37405 m, so a quarter-wave section of it is 34.35 cm. A 3 m length of line at 100 MHz in free space is 1.00069 wavelengths long, or 360.249 degrees.
Wavelength and velocity factor
A radio wave travels at the speed of light in free space and more slowly in a cable, by a fraction called the velocity factor. Solid polyethylene coax is often around two thirds, and foam or air-spaced lines are higher, but the right number is on the data sheet of your cable. A line cut to a fraction of a wavelength has to be cut using the wavelength in the line, which is shorter than in air.
The quarter-wave and half-wave lengths show up everywhere in antennas and in matching sections, stubs and filters. For the cut length of a half-wave dipole, with a shortening factor you can set, see the dipole antenna length calculator. To convert wavelength to the energy of a photon, use the photon energy and wavelength converter.
Electrical length
Electrical length compares the physical length of a line to the wavelength, in degrees: 90 degrees is a quarter wave, 180 a half wave, 360 a full wave. A quarter-wave line turns a short circuit at one end into an open circuit at the other, and a half-wave line repeats the impedance at its end. These properties are used to make matching sections and phase shifters.
The end effect factor, 0.95 by default, is an example for a wire dipole: the wave does not stop exactly at the wire end, so a real antenna cuts shorter than the free-space half wave. Thickness, height and nearby objects change it, so use the result as a first cut and tune it with an analyzer. The speed of sound calculator gives the equivalent speed for sound waves.
Assumptions and limits
- The speed of light in free space is 299,792,458 m/s.
- The velocity factor is between 0.01 and 1 and is the same at all frequencies.
- The end effect factor is an example you can change; it applies to the dipole lines only.
- Feet are shown as 3.280839895 feet per meter.
Frequently asked questions
How do I find the wavelength?
Divide the speed of light by the frequency. In a cable, multiply by the velocity factor as well.
What is the velocity factor?
The speed of the wave in a cable as a fraction of the speed of light. It depends on the insulation.
Why is a dipole shorter than a half wavelength?
Because of end effects, so the best length for a wire antenna is a few percent under the free-space half wave.
What does 90 degrees of electrical length mean?
A quarter of a wavelength in the line.