How this instrument works
Free-space path loss describes how much a radio signal weakens from geometry alone — no walls, no rain, no foliage, just a spherical wavefront expanding outward from the antenna. Power radiated from a point source spreads over the surface of an ever-larger sphere as it travels, so the power density striking a fixed receiving area falls with the square of distance. FSPL restates that inverse-square falloff in decibels: the 20log₁₀(d) term is the distance penalty, and the 20log₁₀(f) term is a companion effect from the receiving antenna's effective aperture, which shrinks as wavelength shortens, so higher frequencies capture less of a given wavefront for the same physical dish or element.
The 92.45 constant is not arbitrary — it folds in the speed of light and the specific unit choice of kilometres and gigahertz, derived from the same 20log₁₀(4π/c) term that sits inside Harald Friis's 1946 transmission formula. Change the units and the constant changes with them: the more common 32.44 belongs to the kilometre-and-megahertz version of the same physics. Nothing here depends on transmit power, antenna gain, or receiver sensitivity — those are separate terms an engineer adds afterward in a link budget. FSPL is the one term fixed purely by where the two antennas sit and what frequency they use.
The formula is also a floor, not a forecast. It models a signal crossing a vacuum or perfectly clear air with an unobstructed line of sight, so it ignores rain attenuation, atmospheric gas absorption, multipath fading, and diffraction loss around terrain or buildings. A real measured link is always equal to or worse than what FSPL predicts, which is exactly why satellite engineers and point-to-point microwave planners use it as the starting number in a budget, then subtract every additional loss they can identify before deciding whether the link closes.
- Enter the line-of-sight distance between the two antennas into Distance, km — use slant range for a satellite or aircraft link, not the ground track.
- Enter the carrier frequency into Frequency, GHz — 2.4 or 5.8 for common Wi-Fi bands, or higher for a microwave or satellite uplink.
- Read Free space path loss, dB — the geometric loss alone, with no rain, foliage, or obstruction folded in.
- To budget a real link, subtract this figure from your transmitter's EIRP and add the receive antenna gain to estimate received power.
Worked example — a 2.4 GHz Wi-Fi bridge across 10 km
Take a 2.4 GHz outdoor Wi-Fi bridge spanning a clear 10 km line of sight. The distance term gives 20log₁₀(10) = 20.00 dB, and the frequency term gives 20log₁₀(2.4) = 7.604 dB. Add the 92.45 dB constant and the total is 20.00 + 7.604 + 92.45 = 120.054224834 dB, which rounds to 120.05 dB of free-space path loss — before any tree, wall, or rainstorm gets a vote.
Shrink the same link to 1 km and only the distance term changes, from 20.00 dB to 0 dB, so the total falls to 100.054224834 dB — exactly 20 dB less. That flat 20 dB-per-decade drop is the signature of an inverse-square law: cutting distance by a factor of ten always removes 20 dB, no matter the frequency, because the exponent inside the logarithm is fixed at two.
Now hold the distance at 10 km but retune to 5.8 GHz, the other common Wi-Fi band. The distance term is unchanged, but the frequency term climbs to 20log₁₀(5.8) = 15.269 dB, pushing the total to 127.718559871 dB — 7.66 dB worse than the 2.4 GHz case. That is the tradeoff a 5 GHz radio accepts for its wider, less congested channels: the same physical range now needs more antenna gain to close.
Questions
Does free-space path loss depend on transmit power or antenna gain?
No. FSPL is purely geometric and frequency-dependent, a function of distance and frequency alone. Transmit power, antenna gains, and receiver sensitivity are separate terms in the full link budget, where received power equals EIRP minus FSPL plus receive antenna gain. Two links at the same distance and frequency have identical path loss whether the transmitter runs 1 watt or 100 watts; only the power that eventually arrives changes.
Why does this formula use 92.45 instead of the more common 32.44?
The constant folds in a unit choice. The familiar 32.44 applies when distance is in kilometres and frequency in megahertz; switch frequency to gigahertz and the constant shifts to 92.45, because 20log₁₀(1000) = 60 dB gets added to cover that thousand-fold unit change. Both constants come from the same 20log₁₀(4π/c) term, just expressed with different unit conventions.
Is free-space path loss the same as the total signal loss on a real link?
No, it is a floor, not a total. FSPL models only the geometric spreading of the wavefront through a vacuum or clear air, so it ignores rain attenuation, foliage, atmospheric gas absorption, multipath fading, and diffraction around obstacles. Real link budgets add those as separate loss terms on top of FSPL, which is why measured path loss on an obstructed or rainy link is always equal to or worse than the free-space figure.
Why does doubling the frequency add about 6 dB of loss at a fixed distance?
Because 20log₁₀(2) is about 6.02 dB, and doubling f doubles the argument of that log term while distance stays fixed. Going from 2.4 GHz to 4.8 GHz over the same path adds roughly 6 dB of path loss. This frequency penalty is what engineers weigh against a higher band's extra available bandwidth when choosing a radio design.
What distance should I actually enter for a satellite or aircraft link?
The straight-line, line-of-sight distance between the two antennas — the slant range — not the horizontal ground distance shown on a map. For a low satellite pass near the horizon, slant range can run several times longer than the distance directly below the spacecraft, and using ground distance instead will understate the real path loss.
Can this same formula be used for sound instead of radio?
The underlying inverse-square spreading applies to any wave leaving a point source, but the 92.45 constant is specific to radio, built from the speed of light with distance in kilometres and frequency in gigahertz. Sound travels roughly a million times slower than light, so an acoustic version of this formula needs its own constant built from the speed of sound, not light's.