Free Space Path Loss Calculator
Path loss and received signal level for a radio link, from distance, frequency, power and antenna gains.
Results
What this tool does
Free space path loss is the best case a radio link will ever see: no obstacles, no reflections, no rain, nothing but the inverse square law and the size of the receiving aperture. Every real link does worse. It is still the right starting point for a budget, because it tells you immediately whether a path is plausible before you go up the mast.
Formula
FSPL(dB) = 20 log10(d km) + 20 log10(f MHz) + 32.44
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dd | Distance | km |
fr | Frequency | MHz |
pt | Transmit power | dBm |
gt | Transmitting antenna gain | dBi |
gr | Receiving antenna gain | dBi |
PL | Free space path loss | dB |
PR | Received power | dBm |
LK | Transmitted EIRP plus receive gain | dBm |
WL | Wavelength | cm |
Worked example
- Distance5 km
- Frequency2400 MHz
- Transmit power20 dBm
- Transmitting antenna gain12 dBi
- Receiving antenna gain12 dBi
- Free space path loss114.0236 dB
- Received power-70.0236 dBm
- Transmitted EIRP plus receive gain44.00 dBm
- Wavelength12.491 cm
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
Why does doubling the distance cost 6 dB?
Because the same power spreads over the surface of a sphere, and that surface grows with the square of the radius. Twice as far means a quarter of the power density, and a quarter is 6 dB. The same logic explains the frequency term: a higher frequency means a smaller antenna aperture for the same gain figure, so it collects less of the passing wave.