# Frequency Calculator: Calculating frequency of radio waves

Radio Frequency or RF is one of the most fundamental concepts in mobile communications. Our mobile phones communicate with the mobile network using radio waves that are also called RF waves. These radio waves are electromagnetic radiations that travel through the air at specific frequencies.

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

Mobile networks use a range of different cellular technologies to connect us to the mobile networks, including 5G New Radio (NR), 4G LTE, 3G UMTS, CDMA2000 and a few others. In all cellular technologies, once the mobile signal is ready to be sent from the antennas of a mobile network to the mobile phones, it is transmitted in the air interface in the form of electromagnetic radiation.

The mobile phones communicate back with the mobile network in the same way through electromagnetic radiation. These radiations are sent at very specific frequencies in a highly controlled manner to ensure that they do not interfere with other radio waves operating at similar frequencies. The frequency of a radio wave is the number of wave cycles it generates in one second.

If you look at the highly simplified diagram below, you may note that there is a link between the base station of a 4G LTE network and a mobile phone that is receiving the 4G signal. This link is the radio wave that operates between the network and the mobile phone at specific frequencies.

## How do you calculate the frequency of a radio wave?

The frequency of a radio wave is the number of wave cycles generated by the transmitting antenna in one second. The mathematical way to calculate frequency is by dividing the speed of the radio wave (in metres/sec) by the length of one complete wave (wavelength in metres).

Since the frequency of a wave is the number of cycles per second, the unit of frequency is “one cycle per second” or “1/sec”, which is generally expressed as Hertz or Hz. 1 Herz equals one cycle per second. In mobile networks, the frequencies are described in Megahertz (e.g. 900 MHz in GSM) and Gigahertz (e.g. 3.4 GHz in 5G).

The formula for calculating the frequency of a radio wave:

Frequency = f = c/λ;

where λ is the wavelength in metres and c = 299792458 m/s.

Have a look at the simplified diagram below showing a low-frequency wave with a low number of cycles per second. The information-carrying signals, e.g. a sound wave, operate at low frequencies. In mobile communications, the information-carrying signal is modulated with a radio signal that can carry the information signal over a mobile network. As a result, the frequencies of the radio signals are referred to as carrier frequencies.

The frequencies employed by GSM networks were in the order of 890 MHz and upwards. The latest 5G networks use frequencies in different bands, including the sub 1G Hz band and high bands like 6 GHz+.

Radio waves travel through the air at the speed of light, which is 3 x 108 metres per second or 299 792 458 meters per second, to be exact. It means that a radio wave can cover almost 300 million meters or 300 thousand kilometres in one second, which is quick. However, when radio waves are deployed in mobile networks, the coverage range of a regular radio base station, called a macro base station, is in tens of kilometres. The range of a radio wave depends on many factors, including transmission power.

Wavelength (λ) is the length of one complete wave cycle from start to finish. It is the distance between the beginning and end of the cycle and is expressed in metres. If you are using our frequency calculator above, you can enter a value in metres, e.g. 2m and the calculator will give you a value in Hertz (cycles per second) for theoretical reasons and in megahertz (MHz) for more real-life situations.

## How are radio frequencies used in mobile networks?

One of the critical parts of a mobile network is the radio access network that is responsible for wireless connectivity.

A radio network consists of base stations and other interrelated equipment allowing the mobile network to transmit and receive signals over the air interface. The communication between the base station and the mobile phones takes place at radio frequencies, also known as carrier frequencies.

Radio frequencies are the most fundamental part of mobile communications and are necessary for the existence of mobile networks. The radio frequency spectrum is the most scarce resource for mobile network operators, and they invest heavily in buying radio frequencies to offer cellular coverage.

The ability of a mobile operator to provide connectivity to their customers depends on how much radio frequency spectrum they own and how efficiently they can use the radio resources to serve their customers.

For example, the frequency band 890 MHz to 960 MHz is used by second-generation GSM mobile networks. In GSM, the frequency band is first split into two so that one part of the band can be used for downlink communication (base station to the phone) and the other part for uplink communication (phone to the base station). There are frequency channels of 200 kHz bandwidth within these bands, which are further divided into timeslots. The communication between the mobile phone and the mobile network takes place through these timeslots.

The other more advanced networks, like 4G LTE and 5G New Radio (NR), are more complex and use the available frequency much more efficiently. 4G LTE and 5G NR networks use much bigger bandwidths to deliver much higher bit rates than the GSM networks.

One important point to note is that even though today’s mobile networks, including GSM, UMTS, LTE and 5G NR, are all digital, the radio communication part that employs the radio frequencies is always analogue.

When a base station antenna transmits a signal to the mobile phone antenna, the signal is analogue. Both mobile phones and base stations have analogue-to-digital and digital-to-analogue converters. As soon as the data enters the mobile phone or the base station, the information is converted into a digital format.