Antenna Length to Frequency Calculator & Formula

This calculator converts between antenna electrical length and operating frequency for common half-wave and quarter-wave antennas. You enter the frequency (or the physical length and a velocity factor), and it returns the corresponding length (or frequency) for the antenna type you select.

Formula

The fundamental relationship between frequency and wavelength in free space is:

λ = c / f

where:

• λ (lambda) = wavelength in meters
• c = speed of light ≈ 299,792,458 meters per second (often rounded to 300,000,000 for quick mental math)
• f = frequency in hertz (Hz)

For an antenna, the physical length is a fraction of a wavelength. Most common are half-wave (0.5λ) and quarter-wave (0.25λ) antennas. Because the speed of radio waves in a conductor is slightly slower than in free space, you multiply by a velocity factor (typically 0.95 for a straight wire, 0.66 for coaxial cable, and around 0.98 for large-diameter tubing).

The full formula used here is:

Length = (c / f) × (fraction of wavelength) × velocity factor

In the calculator, frequency is entered in MHz, so the constant is adjusted: 299.792458 / f gives the wavelength in meters when f is in MHz.

Worked Example

Using the default values: frequency = 100 MHz, half-wave antenna (0.5), velocity factor = 0.95.

1. Wavelength = 299.792458 / 100 = 2.99792458 meters
2. Half-wave = 2.99792458 × 0.5 = 1.49896229 meters
3. Apply velocity factor = 1.49896229 × 0.95 = 1.42401418 meters
4. Convert to feet: 1.42401418 × 3.28084 = 4.672 feet

So a half-wave antenna for 100 MHz should be about 1.424 meters (4.67 feet) long. The calculator rounds to three decimals, showing 1.424 m and 4.672 ft.

How the Velocity Factor Affects Real Antennas

In free space, radio waves travel at the speed of light. But in a physical conductor, the wave slows down slightly. The velocity factor (VF) is the ratio of the actual speed to the speed of light. For a thin wire in air, VF is close to 0.95–0.98. For coaxial cable (used in some antenna designs like a coaxial collinear), VF is typically 0.66 or 0.80 depending on the dielectric. Ignoring VF can make your antenna resonate at a higher frequency than intended.

If you cut an antenna exactly to the theoretical free-space length, it will often be slightly too long. That is why many antenna builders cut a bit long and then trim while checking with an SWR meter or antenna analyzer.

Choosing the Right Fraction: Half-Wave vs Quarter-Wave

The most common antenna types are:

• Half-wave dipole – two equal elements, each a quarter-wave long, fed in the center. Total tip-to-tip length is half a wavelength.
• Quarter-wave vertical – a single element a quarter-wave long, often with ground radials. Common for mobile and base VHF/UHF antennas.
• Quarter-wave ground plane – a vertical radiator with four radials, each a quarter-wave long.

For a dipole, the total length is what the calculator gives for half-wave. For a quarter-wave vertical, use the quarter-wave setting. Some antennas use a 5/8-wave or 1/2-wave vertical, but those are less common for simple wire antennas.

Common Mistakes and How to Avoid Them

• Forgetting the velocity factor – Always include it for physical antennas. The free-space length is a starting point, not the final cut.
• Mixing units – If you measure in feet but calculate in meters, you will be off by a factor of 3.28. Convert carefully.
• Using the wrong fraction – A dipole is half-wave total, but each leg is quarter-wave. Make sure you know what your design calls for.
• Ignoring end effect – The velocity factor already accounts for most of this, but for very thick elements (like metal tubing), the effective length is slightly shorter than a thin wire.
• Rounding too early – Keep full precision in your calculations, then round the final answer.

Practical Tips for Building Antennas

1. Cut the antenna slightly longer than the calculated length (about 2–5% longer).
2. Install the antenna and measure the SWR (Standing Wave Ratio) at your target frequency.
3. If the SWR is lower at a lower frequency, the antenna is too long – trim a little.
4. If the SWR is lower at a higher frequency, the antenna is too short – you may need to add length or use a different design.
5. Re-check after each small trim (1–2% of length).

This iterative method is standard in amateur radio and professional antenna installation. The formula gives you a starting point, but the real world (nearby objects, height above ground, and local soil) can shift the resonant frequency.

Limitations of the Formula

This formula is accurate for simple wire antennas in free space or at moderate heights. It does not account for:

• Proximity to the ground or other conductive objects (which lowers the resonant frequency)
• Antenna thickness (very thick elements have a lower velocity factor)
• Loading coils or traps (which allow a physically shorter antenna)
• Dielectric loading (like a fiberglass radome)

For a simple dipole or vertical, the formula is usually within a few percent. For more complex designs, use antenna modeling software or published design data.

Frequently Asked Questions

Why is my calculated antenna length different from what I see in tables?

Most published tables use the free-space wavelength (velocity factor = 1) or a specific velocity factor like 0.95. Also, some tables give the length for a dipole as the total tip-to-tip length, while others give the length of each leg. Always check which convention is being used.

Does the antenna length change if I use a different feedline?

The feedline itself does not change the resonant length of the antenna element, but the feedline’s velocity factor matters if the feedline is part of the radiating structure (like a J-pole or a coaxial collinear). For a standard dipole fed with coax, the feedline length does not affect resonance.

What is the velocity factor for common materials?

For a bare copper or aluminum wire in air, use about 0.95. For insulated wire, it can be 0.80–0.90 depending on the insulation. For coaxial cable, it is typically 0.66 for solid polyethylene and 0.80 for foam dielectric. Check the cable’s datasheet.

Can I use this calculator for a 5/8-wave antenna?

Yes, but you would need to change the fraction in the formula. The calculator only offers half-wave and quarter-wave. For a 5/8-wave, multiply the free-space wavelength by 0.625 and then by the velocity factor. Many 5/8-wave verticals use a loading coil at the base, so the physical element is shorter than the electrical length.

Why do I need to cut the antenna longer than calculated?

Because the velocity factor is an approximation, and real-world effects (like nearby objects) tend to lower the resonant frequency. Cutting longer and then trimming is a safe way to avoid making the antenna too short, which is difficult to fix.

Does height above ground matter?

Yes, for a dipole, the resonant frequency changes slightly with height. At very low heights (less than 0.1 wavelength), the antenna can detune significantly. At heights above about 0.5 wavelength, the effect is minimal. For a vertical, the ground plane quality affects the feedpoint impedance, but the resonant length remains close to the calculated value.

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in f | Frequency | MHz | 100 | 0
sel type | Antenna type | Half-wave=0.5, Quarter-wave=0.25
in vf | Velocity factor | - | 0.95 | 0
out length | Antenna length | meters | (299.792458 / f) * type * vf | 3
out length_ft | Antenna length | feet | ((299.792458 / f) * type * vf) * 3.28084 | 3