Half Wavelength Calculator: Formula & Uses

This calculator works out the half wavelength of a signal from its frequency, or the frequency from a half wavelength, for a wave traveling in free space or a cable. You enter the frequency in MHz and a velocity factor (choose 1 for air/vacuum, or a typical cable value), and it returns the full wavelength and half wavelength in meters, feet, and inches. The first result is the half wavelength in meters, the quantity the page title asks for.

Formula

The fundamental relationship between wavelength and frequency is:

λ = v / f

where:

• λ = wavelength in meters (m)
• v = speed of wave in the medium in meters per second (m/s). In free space or air, v = 299,792,458 m/s (the speed of light). In a cable, v = c × velocity factor.
• f = frequency in hertz (Hz). Since we input MHz, the formula becomes λ (m) = 299.792458 / f (MHz).

The half wavelength is simply λ/2. For a frequency in MHz, the half wavelength in meters is:

λ/2 (m) = (299.792458 / f) × vf / 2

where vf is the velocity factor (1 for air, ~0.66 for solid polyethylene coax, ~0.82-0.85 for foam dielectric cables).

Worked Example

Using the default values: frequency = 146 MHz, velocity factor = 1 (air).

1. Full wavelength in meters: 299.792458 / 146 = 2.05337 m
2. Half wavelength: 2.05337 / 2 = 1.02669 m
3. Convert to feet: 1.02669 × 3.28084 = 3.3684 ft
4. Convert to inches: 1.02669 × 39.3701 = 40.421 in

The calculator shows 1.0267 m, 3.3684 ft, and 40.421 in. This matches a classic 2-meter band half-wave dipole, which is about 1 meter long.

Why Half Wavelength Matters

The half wavelength is a critical dimension in antenna design because a dipole antenna resonates when its total length is approximately half the wavelength of the operating frequency. At resonance, the antenna presents a purely resistive impedance (around 73 ohms for a thin wire dipole in free space), which simplifies matching to a 50-ohm transmission line. Similarly, a half-wave coaxial balun (a “choke balun�) uses a length of coax that is half a wavelength (electrical) to block common-mode current. In acoustics, a half-wavelength tube (closed at one end) resonates at its fundamental frequency, and in transmission lines, a half-wavelength section acts as a 1:1 impedance transformer.

How to Use the Calculator

To get the most accurate result, follow these steps:

• Enter the frequency in MHz. For example, for CB radio channel 19 use 27.185 MHz; for Wi-Fi 2.4 GHz use 2400 MHz.
• Select the velocity factor that matches your medium. For antennas in free space (or air), choose 1. For coax cables, choose the value from the cable datasheet. The calculator includes common values, but you can also compute using a custom vf if you know it.
• Read the half wavelength in meters, feet, and inches. The full wavelength is also shown for reference.

If you are cutting a dipole antenna, remember that the physical length is typically 95% of the electrical half-wavelength due to end effect (the capacitance at the wire ends makes the antenna appear longer). For a practical dipole, multiply the result by 0.95 to get the initial cutting length.

Common Mistakes and Misconceptions

One common error is forgetting the velocity factor when working with cables. In a coaxial cable, the wave travels slower than in air, so the physical length for a half wavelength is shorter. For example, a half wavelength at 146 MHz in air is 1.027 m, but in RG58 (vf=0.66) it is only 0.678 m. Another mistake is mixing up full and half wavelength: a half-wave dipole is not a full wavelength long. Also, when using the formula with frequency in MHz, do not convert to Hz; the constant 299.792458 already accounts for the mega prefix. Finally, the end effect mentioned above means the physical wire length is slightly shorter than the electrical half wavelength; ignoring this can cause the antenna to resonate at a lower frequency than intended.

Limits of the Formula

The formula assumes a lossless, uniform transmission medium and a sinusoidal steady-state signal. It does not account for:

• Antenna end effect (the need to shorten a dipole by ~5%)
• Proximity to ground or other objects, which changes the electrical length
• Wire thickness and insulation (which can affect the velocity factor)
• Attenuation in cables, which does not change the wavelength but does affect signal strength

For precise antenna construction, use an antenna analyzer to tune the length after initial cutting.

Alternatives and Related Calculators

If you need a full wavelength, just double the half wavelength result. For a quarter wavelength (common for ground-plane antennas), divide the half wavelength by 2. You can also use the calculator in reverse: enter a desired physical length and solve for frequency, but this calculator only accepts frequency as input. For more complex transmission line calculations (impedance, SWR), you would need a Smith chart or specialized software.

Frequently Asked Questions

What is the half wavelength of 2.4 GHz Wi-Fi?

Using the calculator with f = 2400 MHz and vf = 1, the half wavelength is (299.792458 / 2400) / 2 = 0.06246 m, or about 6.25 cm. This is the length of a typical 2.4 GHz half-wave dipole antenna element.

Why do I need to enter a velocity factor for coax?

In a coaxial cable, the electromagnetic wave travels slower than in air because the dielectric material (e.g., polyethylene) reduces the speed. The velocity factor is the ratio of the speed in the cable to the speed of light. For example, RG58 has a vf of 0.66, so the physical half wavelength in the cable is 66% of the free-space value.

How do I convert the result from meters to feet?

The calculator already shows feet and inches. If you need a manual conversion, multiply the meters by 3.28084 to get feet, or by 39.3701 to get inches. For example, 1.0267 m × 3.28084 = 3.3684 ft.

What is the end effect in a dipole antenna?

The end effect is the apparent lengthening of a dipole due to capacitance at the wire ends. This makes the antenna resonate at a lower frequency than the electrical half wavelength would suggest. To compensate, you cut the wire about 5% shorter than the calculated half wavelength, then trim to tune.

Can I use this calculator for sound waves?

No, this calculator uses the speed of light. For sound, you would need the speed of sound in the medium (e.g., 343 m/s in air at 20°C). The formula would be the same, but the speed constant changes.

What is the half wavelength of 50 MHz in free space?

Using the calculator with f = 50 MHz and vf = 1, the half wavelength is (299.792458 / 50) / 2 = 2.9979 m, or about 3 meters. This is common for the 6-meter amateur radio band.

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in f | Frequency | MHz | 146 | 0
sel vf | Velocity factor | Air=1, RG58=0.66, RG213=0.66, LMR-400=0.85, RG-8X=0.82 | 1
out half_m | Half wavelength | m | (299.792458 / f) * vf / 2 | 4
out full_m | Full wavelength | m | (299.792458 / f) * vf | 4
out half_ft | Half wavelength | ft | ((299.792458 / f) * vf / 2) * 3.28084 | 4
out half_in | Half wavelength | in | ((299.792458 / f) * vf / 2) * 39.3701 | 4