Guide
Free-space path loss: how far a radio signal weakens in clear air
Radio waves spread out as they travel, so the signal at the receiving antenna is a tiny part of what left the transmitter, even in perfectly clear air with nothing in the way. That loss grows with distance and frequency and is the starting point of every link design. The page computes it from frequency and distance, or works backwards to find the range that corresponds to a given loss.
The formula
Free-space path loss in decibels, for distance d in kilometres and frequency f in megahertz, is 20·log10(d) + 20·log10(f) + 32.44. The two logarithmic terms show the whole behaviour: each doubling of distance adds 20·log10(2) = 6.02 dB, and each doubling of frequency adds exactly the same. A tenfold increase in either adds 20 dB. The constant 32.44 absorbs the speed of light and the unit conversions. The model assumes isotropic antennas, which radiate equally in all directions, so antenna gains are handled separately in a link budget.
Three modes
The default mode, “Path loss from distance”, takes the frequency in MHz (the placeholders mention 2437 MHz for Wi-Fi channel 6 and 5180 MHz for channel 36), the distance and its unit. “Distance from path loss” inverts the formula to give the range at which a given loss occurs at that frequency. Presets load 2.4 GHz at 100 m, 5 GHz at 1 km and 915 MHz with 80 dB of loss. Below the answer, a table lists the loss at 10 m, 50 m, 100 m, 500 m, 1 km, 5 km and 10 km for your frequency.
What the figure leaves out
Free space means a clear line of sight with nothing nearby. Walls absorb a few dB to tens of dB each depending on material, rain and foliage matter above about 10 GHz, and the ground reflects part of the signal and can cancel it. Long links also need the first Fresnel zone to be mostly clear. Indoors, practical models add 20 to 40 dB or more over free space. Treat the result as a floor on the loss, and add margin for everything real.
A worked example
At 2437 MHz and 100 m the loss is 20·log10(0.1) + 20·log10(2437) + 32.44 = −20 + 67.74 + 32.44 = 80.18 dB. The table beside it follows the 6 dB rule: 60.2 dB at 10 m, 74.2 dB at 50 m, 80.2 dB at 100 m, 94.2 dB at 500 m, 100.2 dB at 1 km, 114.2 dB at 5 km and 120.2 dB at 10 km. Doubling the frequency to roughly 4874 MHz at the same distance would add 6.02 dB.
Limits
The result is a theoretical minimum. It does not include antenna gain, cable and connector loss, obstacles, atmospheric absorption or multipath, and it is not a coverage map. Use the Link Budget Calculator to combine path loss with transmit power, gains and receiver sensitivity, and the Wi-Fi Signal Calculator to interpret readings.
Related tools
- Link Budget Calculator turns the loss into a received level and fade margin.
- Wi-Fi Signal Calculator converts dBm readings to power and quality.
- Fibre Loss Budget Calculator is the optical counterpart.
- PoE Power Calculator sizes the switch budget for the access points you place.
Checked against the current version of the FSPL Calculator on .