# Dipole Calculator

Created by Davide Borchia
Last updated: Jul 30, 2022

If you are planning to build a radio set-up but don't remember how to calculate a dipole antenna's length, you are in the right place. With our dipole length calculator, you will find the optimal size of a half-wave antenna for any given frequency in a few seconds.

• What is a dipole antenna, and why does its length matter ;
• The formula for the length of a dipole antenna (calculate the length from frequency and wavelength);
• The dependency of the antenna length on the diameter of the conductor; and
• How to use our dipole calculator.

Tune in with the basics of radio technology with Omni! Be sure to check the solenoid magnetic field calculator or RLC circuit calculator to learn more about other elements of electronics.

## What is a dipole antenna?

Antennas are the interface between the propagation medium (air, vacuum, water — you name it) and the electric device receiving or transmitting the signal.

The most common type of antenna is the dipole antenna. A dipole antenna is composed of two identical conductors separated by an insulator. In its basic configuration, a dipole antenna has a T-shape, but there's flexibility to this rule.

Keeping it short, the length of a dipole antenna determines the optimal frequency at which the antenna operates (dipole antennas are, in their simplest form, resonant antennas) — with some caveats. Thanks to the symmetry of a sinusoidal wave, the optimal operating frequency can match the value of half the resonating frequency. Once you build your set-up with that frequency in mind, you will pick up that particular wave with the highest possible gain.

🙋 If you have a TV set at home, and no outdoor antenna, the classic-looking bunny ears antenna is a perfect example of a dipole antenna. The two arms are not aligned (it's not necessary), but their length still matters. Use our dipole calculator to find out the best value to pick up your favorite station!

## How to calculate the length of a dipole antenna?

The length of a dipole antenna is roughly equal to half the free-space wavelength of the target radio wave.
This relationship, however, doesn't hold for real-world situations. To calculate the antenna length, this formula comes in handy:

$L = \frac{142.65}{f}$

Where:

• $L$ is the length of the antenna; and
• $f$ the frequency in megahertz.

🙋 Our tool's calculations refer to Hertz antennas (also known as half-wave dipoles). There is another type of basic dipole antenna, the short dipole: its applications are, however, slightly more limited.

The formula to calculate the antenna length from the frequency can be easily rewritten to use the wavelength instead:

$L = 142.65\frac{\lambda}{1,\!000,\!000}$

The wavelength $\lambda$ here is in meters: the factor $1,000,000$ is needed since the constant $142.65$ was calculated from a frequency measured in $\text{MH}$. To obtain this formula for the length of a dipole antenna, we simply plugged in the relation between frequency and wavelength.

Why $142.65$? The value of the constant comes from experimental measurements performed a century ago: most of the time, science doesn't go stale!

However, the formula for the length of an antenna we use in our dipole calculator is a slightly modified version of the one we presented above.

## The dependence the calculated antenna length on the diameter of the conductor

The diameter of the conductor your antenna is made of has consequences on calculating the dipole length. The formula you've seen in the previous section can be, in fact written again as:

$L = \frac{1}{2}k\frac{c}{f} = \frac{1}{2}k\cdot \lambda$

Now you can see a couple of things:

• The constant $142.65$ disappeared: in turn, you got a factor $2$, the parameter $k$ and $c$, the speed of light.
• If you ignore $k$, you can see that the length of the dipole antenna depends on half the wavelength; and

$k$ is determined using a fit of an experimentally measured curve. Its formula is rather ugly:

$k\! =\!0.9787\! -\! \frac{11.86497}{(1\!+\!(\frac{R}{0.000449})^{1.7925})^{0.3}}$

$R$ has formula:

$R=\frac{\frac{\lambda}{2}}{d}$

Where $d$ is the diameter of the conductor. More often than not, this quantity is measured in terms of wavelength, with formula $d = n\cdot \lambda$ (e.g., $d=0.0001\cdot \lambda$). We can write the formula for $k$ as:

$k\! =\!0.9787\! -\! \frac{11.86497}{(1\!+\!(\frac{1}{2\cdot n \cdot 0.000449})^{1.7925})^{0.3}}$

This way, we can express the diameter as a dimensionless quantity and maintain a connection to the radio set-up.

🙋 In our dipole calculator, $k$ has default value $0.9517$: this is the correction from the ideal half-wave antenna.

## How to use our dipole calculator

In its simplest mode, our dipole calculator allows you to input one of these quantities:

• Frequency;
• Wavelength;
• Half-wavelength and quarter wavelength;
• Antenna length; and
• Antenna's leg length.

We need only one of these to calculate the others. If you click on advanced mode, the diameter and the value of $k$ will appear too. We calculated the diameter already, starting from the default value of $k$: change it as needed to fit your design!

Davide Borchia
Frequency
MHz
Results
Antenna length (L)
ft
Dipole leg length (l)
ft
Wavelength
ft
½ wavelength
ft
¼ wavelength
ft
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