Antenna Wavelength Calculator: Find Length

This antenna wavelength calculator works out the physical length of a half-wave or quarter-wave antenna element for a given frequency, or the resonant frequency for a given element length. You enter the frequency in MHz (or the length in meters or feet), pick the wave fraction, and the calculator returns the element length in meters and feet, plus the corresponding full wavelength. The formulas are the standard dipole and monopole approximations used by radio amateurs and RF engineers.

Formula

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

λ = c / f

where λ is the wavelength in meters, c is the speed of light (approximately 300,000,000 m/s, or 300 million meters per second), and f is the frequency in hertz. When you work in megahertz (MHz), the formula simplifies to:

λ (meters) = 300 / f (MHz)

For an antenna element, the physical length is a fraction of that wavelength. The most common fractions are:

• Half-wave (0.5 λ) – the standard for a dipole antenna. The total length of the dipole (both elements) is half a wavelength.
• Quarter-wave (0.25 λ) – the standard for a vertical monopole or a ground-plane antenna. The radiating element is a quarter wavelength long.
• Full-wave (1.0 λ) – sometimes used for loops or Yagi driven elements, but rare for a simple straight wire.

In feet, the same relationship becomes λ (ft) = 984 / f (MHz), because 1 meter equals 3.28084 feet. Many ham radio references use 468 / f (MHz) for a half-wave dipole in feet, which includes a factor for the “end effect� (the velocity factor of a real wire). That 468 number is an approximation that accounts for the slight shortening caused by the wire’s capacitance and the insulators. The calculator here uses the pure physical length (300/f), so it gives the theoretical free-space length; in practice you will need to trim the antenna a few percent shorter.

Worked Example

Let’s use the default values: frequency = 145 MHz, half-wave dipole.

1. Compute the full wavelength: λ = 300 / 145 = 2.0689655 meters.
2. Multiply by the wave fraction: 2.0689655 × 0.5 = 1.0344828 meters.
3. Convert to feet: 1.0344828 × 3.28084 = 3.39397 feet, which rounds to 3.39 ft.

The calculator shows 1.034 m and 3.39 ft for the element length. That is the total length of a half-wave dipole at 145 MHz. If you build a dipole, you would cut the wire to 1.034 meters total, then trim it in small increments while checking the SWR (standing wave ratio) to get the best match at your desired frequency.

Why the 468 Formula Is Different

If you have seen the “468 / f (MHz)� rule for a half-wave dipole in feet, you might wonder why this calculator gives a different number. The 468 rule is a practical approximation that accounts for the end effect – the fact that a real wire has capacitance at the ends, which makes the antenna appear electrically longer than its physical length. To compensate, you cut the wire about 5% shorter than the theoretical half-wave. The calculator gives the theoretical length (300/f in meters, or 984/f in feet). For a half-wave dipole, the 468 rule would give 468/145 = 3.23 ft, while the theoretical length is 3.39 ft – a difference of about 5%. So if you use this calculator, remember to trim the antenna to resonance; the calculated length is a starting point, not the final cut.

How to Choose the Wave Fraction

Which fraction you use depends on the antenna type you are building:

• Dipole (half-wave) – Use 0.5. A dipole is a balanced antenna fed in the center, with each side being a quarter wavelength. The total length is half a wavelength.
• Vertical monopole / ground-plane (quarter-wave) – Use 0.25. The vertical element is a quarter wavelength; the ground plane acts as the other half of the dipole.
• Full-wave loop – Use 1.0. A full-wave loop is a closed loop of wire whose perimeter is one wavelength. It has a different radiation pattern than a dipole.
• Yagi elements – The driven element is usually a half-wave dipole, but the director and reflector elements are slightly shorter or longer than half-wave (typically 0.45λ and 0.5λ respectively). You would use those fractions directly.

For a simple wire antenna, the half-wave dipole is the most common because it offers a good match to 50-ohm coax (with a balun) and has a predictable radiation pattern.

Common Mistakes and How to Avoid Them

• Using the wrong frequency unit – Always enter the frequency in MHz. If you have a frequency in kHz, divide by 1000 first. If in GHz, multiply by 1000.
• Forgetting the end effect – The calculated length is the theoretical free-space length. Real wire antennas are shorter due to the velocity factor (about 0.95 for bare copper wire). Always trim to resonance.
• Mixing up total length vs. element length – For a dipole, the calculator gives the total length (both sides). Each side is half of that. For a quarter-wave vertical, the length is the vertical element only.
• Ignoring the environment – Nearby objects (ground, buildings, trees) detune the antenna. The calculated length is for free space; in practice you will need to adjust.
• Using the wrong speed of light – The 300 factor assumes the speed of light in a vacuum. In a transmission line or a dielectric, the velocity factor is lower, but for a wire antenna in air, 300 is correct.

Limits of the Formula

The formula λ = 300/f is exact for a plane wave in free space. For a wire antenna, it gives the electrical length, but the physical length is slightly shorter because of the end effect. The amount of shortening depends on the wire diameter, the insulation, and the height above ground. For a thin wire (diameter much smaller than the wavelength), the end effect is about 5% for a half-wave dipole. For thicker elements, the shortening is more. The formula also assumes a perfectly conducting wire with no losses; real copper wire has a small resistance, but that is negligible at HF frequencies.

The calculator does not account for the velocity factor of the wire insulation. If you use insulated wire (like THHN), the insulation slows the wave slightly, making the antenna electrically longer. In that case, you would need to cut the wire even shorter. A common rule of thumb for insulated wire is to use a velocity factor of 0.95, but it varies by insulation type.

Practical Antenna Building Tips

When you build an antenna using this calculator:

1. Cut the wire slightly longer than the calculated length – about 5% longer for a dipole.
2. Install the antenna in its final position, as high and clear as possible.
3. Connect a SWR meter or antenna analyzer and measure the resonant frequency.
4. Trim the wire in small increments (1-2% of the length) and re-measure until the SWR is lowest at your desired frequency.
5. Remember that the SWR bandwidth is narrow for a dipole – typically a few percent of the center frequency.

For a quarter-wave vertical, the ground plane (radials) also affects resonance. A typical ground plane has 3-4 radials, each a quarter wavelength long. The length of the radials is not critical, but they should be at least a quarter wave.

Frequently Asked Questions

What is the difference between a half-wave and quarter-wave antenna?
A half-wave antenna (like a dipole) is a balanced antenna fed in the center, with a total length of half a wavelength. A quarter-wave antenna (like a vertical monopole) is an unbalanced antenna that uses a ground plane as the other half. The quarter-wave vertical is shorter and often easier to mount, but it requires a good ground system.

Why does my antenna need to be trimmed shorter than the calculated length?
Because of the end effect – the capacitance at the ends of the wire makes the antenna appear electrically longer than its physical length. To compensate, you cut the wire about 5% shorter for a dipole. The exact amount depends on the wire diameter and insulation.

Can I use this calculator for a Yagi antenna?
You can use it for the driven element (half-wave), but the director and reflector elements are different lengths. A director is typically 0.45λ and a reflector is 0.5λ. Use the calculator with those fractions, but note that the spacing between elements also affects the tuning.

Does the height above ground affect the resonant frequency?
Yes. When an antenna is close to the ground (within a quarter wavelength), the ground acts as a reflector and detunes the antenna. The effect is more pronounced for horizontal antennas. The calculated length is for free space; in practice you will need to adjust for your specific installation.

What is the velocity factor?
The velocity factor is the ratio of the speed of a wave in a medium to the speed of light in a vacuum. For a wire antenna in air, the velocity factor is close to 1, but for insulated wire it is lower (around 0.95). The calculator assumes a velocity factor of 1, so for insulated wire you would multiply the length by the velocity factor.

Can I use this calculator for a loop antenna?
Yes, for a full-wave loop, use the fraction 1.0. The loop’s perimeter should be one wavelength. However, the shape (square, circle, delta) affects the radiation pattern, but not the resonant length significantly.

Related

• Velocity Calculation: Formula, Examples, and Units
• Resistor Calculation Sheet: Ohm’s Law and Power
• Mass Calculation Using Density and Volume

in f | Frequency | MHz | 145 | 0
sel frac | Wave fraction | Full wave=1, Half wave=0.5, Quarter wave=0.25
out len_m | Element length | m | (300 / f) * frac | 3
out len_ft | Element length | ft | ((300 / f) * frac) * 3.28084 | 2
out full_wl | Full wavelength | m | 300 / f | 3