What this calculator does
Free space path loss (FSPL) is the reduction in signal strength a radio wave experiences simply from spreading out as it travels, in ideal conditions with no obstructions, reflections or atmospheric absorption. It applies to any radio link, from Wi-Fi and mobile signal to satellite communication, and grows with both distance and frequency.
FSPL is not the only loss a real signal experiences, since buildings, terrain, weather and antenna characteristics all add further losses or gains on top of it. It is, however, the theoretical floor: the minimum loss that would occur even in a perfectly clear, obstruction-free line of sight, which makes it the standard starting point for link-budget calculations.
The formula
FSPL in decibels equals 20 times the base-10 logarithm of the distance in kilometres, plus 20 times the base-10 logarithm of the frequency in megahertz, plus a constant of 32.44 that folds in the speed of light and the unit conversions. Both distance and frequency contribute logarithmically, so doubling either one adds roughly 6 dB of loss.
| Term | Meaning |
|---|---|
| FSPL | Free space path loss, in decibels: the signal power lost purely to distance, with no obstructions in the way. |
| Distance | The straight-line distance between transmitter and receiver, in kilometres. |
| Frequency | The radio frequency in use, in megahertz. Higher frequencies suffer more free space loss over the same distance. |
The inputs explained
| Field | What to enter |
|---|---|
| Distance (km) | The straight-line distance between the two ends of the radio link, in kilometres. |
| Frequency (MHz) | The operating frequency of the radio link, in megahertz (2,400 MHz for the 2.4 GHz Wi-Fi band, for example). |
When to use it
Planning a wireless link budget
FSPL is the baseline loss figure that gets combined with transmitter power, antenna gains and receiver sensitivity to check whether a proposed radio link, such as a point-to-point wireless bridge, will actually work.
Comparing frequency bands for the same distance
Higher frequency bands carry more data but suffer noticeably more free space loss over the same distance, which is one reason lower frequencies are favoured for longer-range coverage.
Estimating range for a fixed power budget
Rearranging the relationship between loss and distance gives a rough sense of how much further a link could reach, or how much closer it would need to be, at a different frequency.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How free space path loss changes with frequency at 1 km
A fixed 1 km distance, across a range of common radio frequencies.
| Frequency | Free space path loss |
|---|---|
| 100 MHz | 72.44 dB |
| 433 MHz | 85.17 dB |
| 900 MHz | 91.52 dB |
| 2,400 MHz | 100.04 dB |
| 5,000 MHz | 106.42 dB |
| 10,000 MHz | 112.44 dB |
How free space path loss changes with distance at 2.4 GHz
A fixed 2,400 MHz frequency, across a range of distances.
| Distance | Free space path loss |
|---|---|
| 0.1 km | 80.04 dB |
| 0.5 km | 94.02 dB |
| 1 km | 100.04 dB |
| 2 km | 106.06 dB |
| 5 km | 114.02 dB |
| 10 km | 120.04 dB |
Questions
Why does loss increase with frequency as well as distance?
A higher-frequency wave has a shorter wavelength, and a receiving antenna of a given physical size effectively captures less of a shorter wavelength than a longer one, which shows up mathematically as extra loss in the free space path loss formula.
Is free space path loss the total loss a real signal will experience?
No. It is the theoretical minimum loss in perfectly clear, unobstructed space. Real links also lose signal to buildings, foliage, terrain, rain and other obstructions, so the actual loss on a real-world link is normally higher than the free space figure.
Why does doubling the distance only add about 6 dB, not double the loss?
Decibels are a logarithmic scale, and the formula uses 20·log10(distance). Doubling a value inside a base-10 logarithm multiplied by 20 adds 20·log10(2), which is approximately 6.02 dB, regardless of the starting distance.
Can this formula be used for sound or light instead of radio waves?
The same inverse-square spreading behaviour underlies loss for any wave travelling outward through free space, but this specific formula and its constant are set up for radio frequency links measured in megahertz and kilometres.
For converting the resulting signal power between RF units, see the dBm to watt calculator.