# Free Space Path Loss Calculator

Created by Purnima Singh, PhD
Reviewed by Steven Wooding
Last updated: Oct 31, 2022

Use the free space path loss calculator to predict the strength of a radio frequency signal emitted by an antenna at a given distance. Just enter the distance between the transmitting and receiving antennas, their gain, and the signal's frequency. The FSPL calculator will give you the loss in signal strength during transmission.

Continue reading to know what free space path loss is and the formula to calculate it. You will also find an example of how to calculate free space path loss using our FSPL calculator.

## What is free space path loss?

In telecommunication, path loss refers to the attenuation of the power radiated by the transmitter with an increase in distance. When a signal travels from a transmitter to a receiver through free space (vacuum) without any obstacles between the two (i.e., clear line of sight), the reduction in signal strength is referred to as the free space path loss (FSPL).

To understand the effect, we will consider the free space propagation of electromagnetic waves. When electromagnetic waves travel through free space or vacuum, their intensity decreases with increasing distance from the source.

The situation is analogous to the ripples of waves in a pond when you drop a stone into it. As the ripples move outwards, their intensity decreases. Similarly, the signal strength of electromagnetic waves falls as the wavefront moves away from the radiation source.

The decrease in intensity is inversely proportional to the square of the distance from the source.

Estimating the signal characteristics and associated losses during transmission is very important for designing wireless communication systems.

## Free space path loss formula

According to the free space propagation model developed by Friis, the signal strength at the receiving antenna, i.e., the received RF power is given by:

$\scriptsize P_\text R = P_\text T \ G_\text T \ G_\text R \left ( \frac{\lambda}{4 \pi d} \right )^2$

or

$\scriptsize P_\text R = P_\text T \ G_\text T \ G_\text R \left ( \frac{c}{4 \pi d f} \right )^2$

where:

• $P_\text T$ — Transmitted signal power;
• $G_\text T$ — Gain of the transmitting antenna;
• $G_\text R$ — Gain of the receiving antenna;
• $d$ — Distance between the antennas;
• $λ$ — Wavelength of the signal;
• $f$ — Frequency of the signal; and
• $c$ — Speed of light in vacuum.

For practical purposes, it is more convenient to express the free space path loss in decibels, i.e., dB (check out the decibel calculator for further information).

To calculate free space path loss in dB, we will use the formula:

$\scriptsize \begin{split} FSPL(\text{dB}) & = -10 \log_{10} \left( \frac{P_\text R}{P_\text T} \right ) \\ & = 20 \log_{10}(d) + 20 \log_{10}(f) \\ & + 20 \log_{10} \left (\frac{4 \pi}{c} \right ) - G_\text T - G_\text R \end{split}$

For isotropic antennas (one that radiates equally in all directions), the antenna gain is 0 dB. Hence, the above equation can be simplified as:

$\scriptsize \begin{split} FSPL(\text{dB}) = 20 \log_{10}(d) &+ 20 \log_{10}(f) \\ &+ 20 \log_{10} \left (\frac{4 \pi}{c} \right ) \end{split}$

The above set of formulae are only applicable for unobstructed line of sight signal paths.

## How to calculate free space path loss?

Let us see how we can calculate the free space path loss for a 4 GHz signal from a satellite in a geosynchronous orbit at an altitude of 35,863 km from the Earth.

Suppose the antenna gains of the satellite and ground-based antennas are 44 dB and 48 dB, respectively.

Using the free space path loss formula, we can write:

$\scriptsize \begin{split} FSPL(\text{dB}) & = 20 \log_{10}(35863) \\ &+ 20 \log_{10} (4 \times 10^6) \\ & + 20 \log_{10} \left (\frac{4 \times 3.14}{3 \times 10^8} \right ) \\ & - 44 - 48\\ & = 103.58\ \rm dB \end{split}$

## How to use the free space path loss calculator?

Now we will solve the same problem using our free space path loss calculator:

1. Input the distance between the transmitter and receiver antennas (35,863 km).

2. Type the frequency of the signal (4 GHz). You can use the frequency calculator to determine the frequency if you know the wavelength

3. Enter the gains of the transmitting and receiving antennas (44 dB and 48 dB). For an isotropic antenna, set the gain as 0 dB.

4. The FSPL calculator will display the free space path loss (103.58 dB).

## FAQ

### What causes free space path loss?

Free space path loss is a direct consequence of the fact that the intensity of all electromagnetic waves decreases with an increase in distance from the radiator. As the radiated wavefront travels away from the transmitter antenna, it spreads out. This results in an increase in the surface area, and the transmitted energy per unit area is reduced.

### How does the free space path loss change with distance?

The attenuation of signal intensity with distance follows the inverse square law. Hence, the free space path loss increases with increasing distance between the transmitter and receiver.

In wireless communication, shadowing refers to the signal power attenuation due to obstacles between the transmitter and receiver. In shadowing, signal loss occurs due to the absorption, reflection, scattering, and diffraction of the electromagnetic waves when they encounter a physical obstruction.

### How do I calculate free space path loss for isotropic antennas?

To calculate free space path loss for isotropic antennas, follow the given instructions:

1. Take the square of the wavelength of the carrier wave.
2. Multiply the distance between the transmitter and receiver antennas by , and take the square of the result.
3. Divide the value from step 1 with that of step 2.
4. Congrats! You have calculated the free space path loss for isotropic antennas.
Purnima Singh, PhD
Distance (d)
mi
Frequency (f)
GHz
Transmitter gain (Gᴛ)
dB
dB
Free space path loss (FSPL)
dB
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