Free Space Path Loss Calculator (with Formula and Examples)

The FSPL calculator provides the attenuation or loss of a signal as it propagates through free space. In this post we have also provided an example of how to use the calculator.

Calculator

To calculate the FSPL, enter the following:

  • Frequency of operation f
  • Distance d
  • Transmit Antenna Gain GTx
  • Receive Antenna Gain GRx

Formula

FSPL = 20*Log10(d) + 20*Log10(f) + Lc + 20*Log10(4π/c) – GTx – GRx

💡 This formula only applies when the distance (d) between the antennas is large enough that the antennas are in the far field of each other. In other words d >> λ where λ = c/f. It is sufficient if the distance is at least 10 times larger than the wavelength.

Background

FSPL stands for Free Space Path Loss. It is a term used in wireless communication and radio frequency (RF) engineering to describe the loss of signal strength as electromagnetic waves propagate through free space, such as air or a vacuum, without any obstructions or reflections.

The Free Space Path Loss is primarily determined by the following factors:

  1. Distance: FSPL increases with the square of the distance between the transmitter and receiver. This means that as you move farther away from the source of the signal, the signal strength decreases significantly.
  2. Frequency: FSPL is also influenced by the frequency of the electromagnetic waves. Higher frequency signals tend to experience greater path loss compared to lower frequency signals when traveling the same distance.
  3. Antenna Gain: As the receive or transmit antenna gain is increased, the path loss decreases.

FSPL is an important concept in wireless communication system design, as it helps radio system engineers determine the expected signal strength at a given distance and frequency. This information is important for designing wireless networks, estimating coverage areas, and ensuring reliable communication between devices.

Definition of Terms

Below is a list of the terms used in the calculator and what each of them mean.

Frequency of operation

This is the frequency at which the communication system operates.

Transmit Antenna Gain

This depends on the type of antenna used and is expressed in dBi (dB relative to isotropic antenna).

Receive Antenna Gain

Depends on antenna used and is expressed in dBi. In cases where the signal is from a particular direction, a high gain antenna (8 dBi for instance) can be used. This allows focusing of energy instead of receiving from all directions. It can be calculated from the Antenna Factor and frequency of operation.

💡 The free space path loss equations assume an ideal operating environment i.e. an unobstructed propagation path between transmitter and receiver.

Example Free Space Path Loss Calculation

At a frequency of 100 kHz and a distance of 100 km, the attenuation or FSPL = 52.45 dB.

Limitation

At a frequency of 100 kHz and distance of 100 meters, the FSPL = -7.55 dB which is clearly an erroneous result as the attenuation cannot be negative.

To understand this, let’s take into consideration the requirement that for the equation to be valid the distance d has to be at least 10*λ = 2998 meters (using the frequency to wavelength calculator).

The calculator is therefore applicable at distances greater than 29980 meters or 30 km for a frequency of 100 kHz.

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