# How to Calculate a Monopole Length

By Steven J. Wamback

The monopole is one type of radio antenna known for its simplicity of construction and high efficiency in terms of the amount of radio signal effectively transmitted or received. Also known as a ground plane vertical antenna, the monopole is easy to design, and it is the antenna of choice for most radio broadcast stations, as well as for many commercial and amateur radio communications stations. Calculate the length (eventual height) of a wire monopole antenna by simply deciding what frequency you intend to transmit on and enter that information into an equation to figure the length of wire required.

## Step 1

Determine what frequency in megahertz (MHz) you intend to operate on and whether you have the space for and the ability to erect a quarter wavelength monopole antenna.

## Step 2

Choose where you will mount your antenna. If you will be mounting it on the ground, you will need a highly conductive moist soil. Swamps and beaches are excellent locations. Otherwise, install wire ground radials the same length as the height of your antenna. If you mount your antenna on a building or a pole, you will need to construct an artificial ground plane from at least four quarter-wavelength wire radials, whose lengths are calculated the same as the length of the monopole.

## Step 3

Calculate the length of wire you will need to construct a quarter wavelength monopole antenna for the frequency upon which you intend to operate. Use the formula: Length (feet) = 234 / Frequency (MHz). For example, if you intend to operate on 14.2 Megahertz (in the 20-Meter amateur radio band): 234 / 14.2 = 16.5 feet (rounded to nearest 0.1 foot). Your 14.2 MHz quarter wavelength wire monopole ham radio antenna needs to be 16.5 feet in length.

## Step 4

Calculate the length of wire you will need to construct a quarter wavelength monopole antenna for another frequency upon which you intend to operate. Use the formula: Length (feet) = 234 / Frequency(MHz). For example, if you intend to operate on 27.5 Megahertz: (in the CB-Radio Citizens Band) 234 / 27.5 = 8.5 feet (rounded to nearest 0.1 foot). Your 27.5 MHz quarter wavelength wire monopole CB antenna needs to be 8.5 feet in length.

## Step 5

Calculate the length of wire you will need to construct a quarter wavelength monopole antenna for the FM broadcast band at 100 MHz. Again, use the formula: Length (feet) = 234 / Frequency (MHz) to get 234 / 100 MHz = 2.3 feet. That is why most portable FM broadcast radio receivers (boomboxes) have an adjustable antenna of about 2.5 feet in length. When the antenna properly matches the frequency, it is said to be resonant. Resonance is the key to antenna function and efficiency.

## Step 6

Calculate the length of a quarter wavelength monopole antenna for an ordinary 4G cell phone in the 2500 Megahertz band (for example). Use the formula: Length (feet) = 234 / Frequency(MHz). 234 / 2500 = 0.09 feet (rounded to nearest 0.1 foot.) Your 4G cell phone 2500 MHz quarter wavelength wire monopole antenna needs to be 0.09 feet or about 1 inch in length. That is why many cell phones have such tiny antennas or appear to have no antenna at all. Observe how with increasing frequency, wavelength and monopole antenna length both decrease proportionally.

References

Writer Bio

Steven J. Wamback is a natural resources scientist, writer and editor. He holds a Bachelor of Science in biology and a Bachelor of Arts in geology, both from SUNY Fredonia. Wamback's writings and editorial projects include books, chapters, articles, essays, editorials, reports and research publications on such diverse topics as wetlands, wildlife, groundwater, rocks, fossils, sexuality, health, the environment and radio-wave propagation.