# Free Space Path Loss Calculator

## This calculator calculates the free space loss, given the distance, frequency, and gain, between two antennas.

(dB)
(dB)

(dB) decibel

### Equations

$$FSPL = 20 log_{10} (d) + 20 log_{10} (f) + 20 log_{10} (\frac{4 \pi}{c}) - G_{t} - G_{r}$$

Where:

$$d\ is\ the\ distance$$

$$f\ is\ the\ frequency$$

$$G_{t}\ is\ the\ transmitter\ gain$$

$$G_{r}\ is\ the\ receiver\ gain,\ and$$

$$c\ is\ the\ speed\ of\ light$$

#### Applications

The free space path loss is used to predict the strength of a RF signal at a particular distance. This is a theoretical value, as in the real world; there are many obstacles, reflections and losses which need to be accounted for when estimating the signal at a location. However the FSPL is a good approximation for estimating the loss of signal when propagating through free space.

The free space path loss calculator takes into account the gain on both the receiving and transmitting antennas. The gain of the antennas offsets the loss by a certain decibel value. If you ignore the gain at either end i.e the transmitting and receiving end, then the FSPL would just be a factor of the frequency and distance. We have also assumed that the rf signals will be propagating in air. If they were propagating in another medium this calculator would not give the correct result.