Free Space Path Loss Calculator

Created by Luciano Mino
Last updated: Aug 30, 2022

Our free space path loss calculator can help you obtain the attenuation of signal strength through free space between an emitter and a receiver.

We've paired this FSPL calculator with a short text describing:

  • Antenna gain;
  • Free space path loss definition;
  • The free space path loss formula; and
  • How to calculate free space path loss.

Let's dive right in!

Antenna gain

An antenna's gain compares its ability to radiate in a specific direction to that of an isotropic source (a theoretical antenna that emits uniformly in all directions).

Gain GG combines an antenna's directivity η\eta and radiation efficiency DD:

G=ηDG = \eta D

We use gain to find the ratio between the power at the receiver antenna and the power radiated by an antenna. This is what we call free space path loss.

Let's see how to calculate free space path loss now.

Free space path loss formula

We can derive the free space path loss formula from the Friis transmission equation, developed by Harald T. Friis. Here is what the formula looks like:

PrPt=GtGr(λ4πd)2\frac{P_{r}}{P_{t}} = G_{t} G_{r} (\frac{\lambda}{4\pi d})^{2}

where:

  • PrP_{r} is the power at the receiving antenna;
  • PtP_{t} is the transmitted power;
  • GrG_{r} is the receiver antenna's gain;
  • GtG_{t} is the transmitter antenna's gain;
  • λ\lambda is the wavelength of the signal; and
  • dd is the distance between the antennas.

🙋 Like many others in physics (the gravitational force, for example), this equation follows the inverse square law. In this case, it means that the radiation at any distance from its source is inversely proportional to the square of the distance.

It is convenient to express free space path loss in decibels (dB). To do that, we should use the following formula instead:

FSPL(dB) = 20 * log10(d) + 20 * log10(f) + 20 * log10(4π / c) - GT - GR

where again:

  • d is the distance between the antennas;
  • f is the signal's frequency; and
  • GT and GR are the transmitter and receiver antennas' gain, respectively.

Feel free to experiment with our FSPL calculator! Input these parameters, and our tool will automatically find the free space path loss between the antennas for you.

Luciano Mino
Distance (d)
mi
Frequency (f)
GHz
Transmitter gain (Gᴛ)
dB
Receiver gain (Gʀ)
dB
Free space path loss (FSPL)
dB
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