# Wavelength Calculator: Calculating wavelength of radio waves

Mobile networks employ radio waves (RF waves) for all communication between the mobile network base station and the cell phone. The radio waves travel through the air at particular radio frequencies, and as the frequency of a radio wave goes up, the length of the wave goes down. It means lower frequencies have bigger wavelengths and, therefore, wider range.

The wavelength of a radio wave is calculated by dividing the velocity of the radio wave (speed of light, c =299 792 458 m/s) by frequency (f). The frequency is the number of cycles generated by the radio wave in one second. Mathematically, Wavelength λ = c/f.

## What is the wavelength of a radio wave (RF wave)?

The wavelength of a radio wave depends on the frequency at which it travels. For example, at a frequency as high as 300 GHz, the wavelength of a radio wave is approximately 1 millimetre. On the other hand, at a frequency as low as 30 Hz, the wavelength is about 10000 kilometres.

All mobile networks use electromagnetic radiations that enable communication between the cell towers (base stations) of a mobile cellular network and the cell phone. These radiations travel through the air at specific radio frequencies, and these radiations are called radio waves. One of the most precious resources of a mobile operator is the frequency spectrum based on these radio frequencies, also known as carrier frequencies. The frequencies are generally expressed in GigaHertz (GHz) or MegaHertz (MHz) in modern networks.

The length of a radio wave is inversely proportional to the frequency, which means the higher the frequency, the shorter the wave. In modern mobile networks, 5G uses a much broader frequency spectrum than earlier networks. It means 5G can employ frequencies in the sub 1 GHz band, but it can also use frequencies above 6 GHz. Since wavelength is inversely proportional to frequency, the wavelength of the 6 GHz frequency band in 5G will be very short. Therefore, mobile networks with lower frequencies can efficiently work with larger cells, whereas networks that employ very high frequencies benefit from a network architecture with smaller cells.

For reference, GSM mobile networks use these frequency bands: 850 MHz, 900 MHz, 1800 MHz and 1900 MHz. At these frequencies, the wavelength is between 15.7 and 35.2 cm. 5G New Radio technology in the UK uses frequency bands ranging from 3.4 -3.8 GHz, which results in wavelengths of approximately 8 cm. Have a look at our dedicated post on GSM frequency bands in different regions.

## How do you calculate the wavelength of radio (RF) waves?

The wavelength of a radio wave is the length of one full wave cycle from start to finish, as shown by the red lines in the diagram below. It is the distance between the start and end of the wave cycle and is expressed in metres. The endpoint of a full-wave cycle is the starting point of another wave cycle.

When you read a theoretical document, you may come across ‘peaks’ and ‘troughs’ when explaining wavelength, which can be confusing. You don’t have to worry about the peaks and troughs of a wave when measuring wavelength. You can pick any two random points on a wave that have the same position on the wave. For example, look at the green line below, which starts at a random point A and ends at a random point B. For mathematical calculations, you don’t need to look at any diagrams; all you need is the frequency in Hertz and the speed of light, which is 299 792 458 meters per second. The wavelength (λ) of a radio wave can be calculated by dividing the speed of light (c = 299 792 458 m) by the frequency of the radio wave.

The formula for calculating the wavelength of a radio wave:

Wavelength = λ = c/f;

where f is the frequency in Hertz and c = 299792458 m/s.

## What is the application of wavelength in mobile radio networks?

When working with the antenna technologies for the mobile networks, all characteristics of a radio signal are critical. The wavelength of the radio waves determines the size of the antenna it is designed for. At high frequencies, the wavelength is small, and so is the size of the antenna.

If you are a telecoms student, it may be natural to wonder why you are looking at this wavelength formula and if you will ever need this in your career. Let’s take an example of the application of wavelength in mobile radio networks to bring this concept to life. MIMO or Multiple Input Multiple Output is an antenna technology used by 4G LTE and 5G NR networks to improve the data rates and signal quality. The basic plot of MIMO is to utilise multiple antennas to transmit the signal and multiple antennas to receive the signal to provide benefits like spatial diversity and spatial multiplexing. Mobile network vendors (e.g. Ericsson, Huawei etc.) are the ones who design antennas for mobile radio networks. 5G networks use a type of MIMO called Massive MIMO, which has tens or hundreds of antenna elements. If these vendors had to build tens or hundreds of large antenna elements to create one big 5G radio antenna, the size would be impractical, and the cost of the hardware and implementation would be high also. That is is where the wavelength plays a crucial role in deciding the required size of the antenna. The wavelength of a signal is directly proportional to the length of the antenna, which means the longer the radio wave, the longer the required antenna. We also know that wavelength and frequency are inversely proportional, which means the higher the frequency, the shorter the wavelength (use the wavelength calculator above to try). So, if a network were to use higher frequencies, the required length of the antenna would be small. 5G networks use frequencies in various ranges, including high frequencies above 6 GHz. The antenna size would be very small for those frequencies, making the Massive MIMO antenna design feasible for 5G networks.

## Here are some helpful downloads

Thank you for reading this post. I hope it helped you in developing a better understanding of cellular networks. Sometimes, we need extra support, especially when preparing for a new job, studying a new topic, or buying a new phone. Whatever you are trying to do, here are some downloads that can help you:

Students & fresh graduates: If you are just starting, the complexity of the cellular industry can be a bit overwhelming. But don’t worry, I have created this FREE ebook so you can familiarise yourself with the basics like 3G, 4G etc. As a next step, check out the latest edition of the same ebook with more details on 4G & 5G networks with diagrams. You can then read Mobile Networks Made Easy, which explains the network nodes, e.g., BTS, MSC, GGSN etc.

Professionals: If you are an experienced professional but new to mobile communications, it may seem hard to compete with someone who has a decade of experience in the cellular industry. But not everyone who works in this industry is always up to date on the bigger picture and the challenges considering how quickly the industry evolves. The bigger picture comes from experience, which is why I’ve carefully put together a few slides to get you started in no time. So if you work in sales, marketing, product, project or any other area of business where you need a high-level view, Introduction to Mobile Communications can give you a quick start. Also, here are some templates to help you prepare your own slides on the product overview and product roadmap.

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