The Short Answer
Free space path loss, or FSPL, is the loss a radio signal suffers just from spreading out as it travels through empty space, before anything in the real world is added. In the free space model the medium contributes no attenuation by construction, and only the geometric spreading of the wave is considered. The power simply spreads over an ever larger sphere as the wave moves away from the antenna, so a fixed receiving antenna intercepts a smaller and smaller share of it with distance.
It is the cleanest, most predictable loss in radio, and it sets the floor of every link budget. Real path loss is always equal to or greater than free space path loss, because the real world only adds obstruction, diffraction, rain, gases and reflection on top. If a link will not close in free space, it will never close in practice, so FSPL is the first number an engineer works out.
The standard formula, with distance in kilometres and frequency in megahertz, is:
FSPL (dB) = 32.45 + 20 · log₁₀(d) + 20 · log₁₀(f)
Both distance and frequency arise from underlying squared relationships, which is why each appears as a 20 · log₁₀ term rather than a 10 · log₁₀ term. Double the distance and the loss rises by about 6 dB. Double the frequency and it rises by about 6 dB again. Those two facts carry most of the intuition you need.
FSPL comes from the inverse square spreading of power combined with the effective size of an isotropic receiving antenna. The exact expression, in consistent base units of metres and hertz, is:
FSPL (dB) = 20 · log₁₀(d) + 20 · log₁₀(f) + 20 · log₁₀(4π / c)
where d is the distance, f is the frequency, and c is the speed of light. The last term is just a constant. Folding it in and converting to the units engineers actually use gives the three forms worth memorising:
- Distance in km, frequency in MHz: FSPL (dB) = 32.45 + 20 · log₁₀(d) + 20 · log₁₀(f)
- Distance in km, frequency in GHz: FSPL (dB) = 92.45 + 20 · log₁₀(d) + 20 · log₁₀(f)
- Distance in metres, frequency in GHz: FSPL (dB) = 32.45 + 20 · log₁₀(d) + 20 · log₁₀(f) with d in metres and f in MHz, or equivalently the metre and hertz form above
The only difference between the variants is the constant, and the constant only changes because the units changed. The 32.45 figure is for kilometres and megahertz, and the 92.45 figure is exactly 60 dB higher because a gigahertz is a thousand megahertz and 20 · log₁₀(1000) is 60. Pick the form whose units match your inputs and the answer is identical.
It is worth being clear about what FSPL is not. It is a loss between two isotropic antennas, so it already assumes the gains are taken out separately. In a link budget you add the transmit and receive antenna gains back in as their own line items. FSPL is the spreading loss alone, and the antennas claw some of it back.
A Worked Example: 5 GHz Over 10 km
Take a point to point link at 5 GHz over a 10 km hop, the sort of backhaul a wireless ISP or a mine site might run. Using the kilometre and gigahertz form:
FSPL = 92.45 + 20 · log₁₀(10) + 20 · log₁₀(5)
20 · log₁₀(10) = 20 × 1 = 20 dB
20 · log₁₀(5) = 20 × 0.699 = 13.98 dB
FSPL = 92.45 + 20 + 13.98 = 126.4 dB
So the wave loses about 126 dB just getting there, with a clear line of sight and nothing in the way. Check it with the megahertz form to prove the units do not matter: 5 GHz is 5000 MHz and 10 km stays 10 km, so FSPL = 32.45 + 20 · log₁₀(10) + 20 · log₁₀(5000) = 32.45 + 20 + 73.98 = 126.4 dB. The same answer.
Now feed that into a budget. Suppose the transmitter puts out 20 dBm, each antenna has 28 dBi of gain, and the feeders cost 2 dB total:
Received power = 20 + 28 + 28 − 2 − 126.4 = −52.4 dBm
If the receiver needs −80 dBm to work, the link has a raw margin of about 28 dB before any fade margin or real world loss is taken out. That is a healthy starting point, and it shows why FSPL is the anchor of the whole calculation. The full method, with sensitivity, noise and fade margin, is set out in how to calculate an RF link budget.
Why FSPL Depends on Frequency, Even Though Space Absorbs Nothing
This is the part that trips people up, and it is the single most useful thing to understand about the formula. If empty space does not absorb energy, why does a higher frequency show more free space path loss for the same distance?
The answer is that the frequency term has nothing to do with absorption. It comes from the receiving antenna. The effective area, or aperture, of an antenna at a fixed gain shrinks as the wavelength shrinks, in proportion to the wavelength squared. A higher frequency means a shorter wavelength, which means a fixed gain antenna is physically smaller and captures a smaller slice of the spreading wavefront. Less captured power reads as more path loss.
Put another way, FSPL as defined by the Friis equation is the loss between two isotropic antennas, and an isotropic antenna at 10 GHz has a far smaller effective aperture than one at 1 GHz. The geometric spreading of the wave is itself frequency independent, governed only by distance, so the apparent frequency dependence in the Friis and FSPL formulation arises from the receiving antenna model rather than from any frequency dependent absorption in free space. The penalty is real in a link budget, but you recover it with antenna gain rather than by fighting the medium.
This matters in design, because you can claw the frequency penalty straight back with antenna gain. A dish of a given physical size produces more gain at a higher frequency, again because of that wavelength squared relationship, and the extra gain can offset and even overtake the higher FSPL. That is exactly why microwave and millimetre wave links use dishes: the antenna recovers what the formula appears to take away.
The 6 dB Rule
Because both distance and frequency enter the formula as 20 · log₁₀ terms, doubling either one adds 20 · log₁₀(2), which is 6.02 dB. That gives two rules of thumb worth keeping in your head:
- Double the distance, add 6 dB. Halve it, subtract 6 dB. A link at 20 km has 6 dB more free space loss than the same link at 10 km.
- Double the frequency, add 6 dB. Moving a link from 2.5 GHz to 5 GHz costs 6 dB of path loss before anything else changes.
The distance rule is just the inverse square law in disguise. Power density falls with the square of distance, and 10 · log₁₀ of a squared quantity is the same 20 · log₁₀ that doubling distance turns into 6 dB. It also lets you sanity check a calculator without reaching for a log table. If a tool tells you a 40 km hop has only 3 dB more loss than a 10 km hop, something is wrong, because two doublings of distance should cost about 12 dB.
These rules are also why long links and high frequencies are expensive in decibels, and why a small change in geometry can rescue or sink a marginal hop. Shortening a path or dropping a band is often the cheapest way to find link margin.
FSPL Is Not the Whole Path Loss
Free space path loss is a floor, not a forecast. It assumes a perfect line of sight, an unobstructed first Fresnel zone, no atmosphere and no ground. The real path adds loss on top of it from several mechanisms:
- Obstruction and diffraction. Hills, buildings and trees in or near the line of sight bend and block the signal. Even an apparently clear path loses margin if obstacles intrude into the Fresnel zone, which is the subject of path loss, Fresnel zones and the 80 percent rule.
- Atmospheric gases. Oxygen and water vapour absorb a small but real amount, which grows with frequency and matters above roughly 10 GHz.
- Rain. Above about 10 GHz, rain fade can dwarf every other loss during a downpour and is the deciding factor for link availability.
- Multipath and reflection. Signals bouncing off the ground, water or buildings arrive out of phase and can deepen fades well below the free space level.
This is why planners separate the clean, deterministic FSPL from the messy, statistical losses. In open environments with a path loss exponent near two, real loss tracks FSPL closely. In cluttered urban or indoor settings the loss grows much faster than free space, and a log distance model with a higher exponent fits far better. The log distance path loss calculator lets you set that exponent and see how quickly a built up environment pulls away from the free space curve.
Where FSPL Fits in a Link Budget
In a link budget, FSPL is the largest single subtraction on most paths, and it is the term every other line item is judged against. The received power is the transmit power plus the antenna gains, minus the feeder and connector losses, minus the path loss:
P_rx (dBm) = P_tx + G_tx + G_rx − L_feeder − FSPL
FSPL comes straight from the Friis transmission equation, which describes how power transfers between two antennas in free space. The Friis equation calculator works the same physics from the antenna point of view, while the FSPL formula isolates the spreading loss on its own. They are two faces of one relationship: Friis gives you received power directly, and FSPL gives you the loss term you drop into a budget table.
Once you have the received power, you compare it against the receiver sensitivity to find the raw margin, then set aside a fade margin to cover the statistical losses that FSPL ignores. Decide how many decibels of fade margin a link needs and you have turned a clean free space number into a design that survives bad weather and awkward geometry. That step is covered in what is fade margin and how much do you need.
Common FSPL Mistakes
- Mixing units. The constant in the formula depends entirely on the units. Using 32.45 with gigahertz, or 92.45 with megahertz, throws the answer out by 60 dB. Match the constant to the units every time.
- Forgetting the squared terms. Both distance and frequency carry a factor of 20, not 10. Treating either as a 10 · log₁₀ term halves the slope and badly underestimates the loss on long or high frequency links.
- Reading the frequency penalty as absorption. Higher FSPL at higher frequency is an antenna aperture effect, not the air soaking up the signal. The fix is antenna gain, which a larger or higher frequency dish supplies for free.
- Treating FSPL as the final path loss. Free space is the best case. A real link almost always loses more once obstruction, rain and multipath are counted, so designing to the bare FSPL number leaves no margin.
- Double counting antenna gain. FSPL is defined between isotropic antennas, so the gains are added separately in the budget. Building gain into the path loss term as well counts it twice.
Frequently Asked Questions
What is free space path loss in simple terms? Free space path loss is the signal a radio link loses purely because the wave spreads out as it travels, with nothing in the way to absorb or block it. Power spreads over a growing sphere with distance, so a fixed antenna captures less of it the further away it sits. It is the cleanest and most predictable loss in radio and the floor of every link budget.
What is the formula for FSPL? With distance in kilometres and frequency in megahertz, FSPL in decibels is 32.45 + 20 · log₁₀(d) + 20 · log₁₀(f). For gigahertz, the constant becomes 92.45. The exact form in metres and hertz is 20 · log₁₀(d) + 20 · log₁₀(f) + 20 · log₁₀(4π / c), where c is the speed of light.
Why does free space path loss increase with frequency? Empty space does not absorb more energy at higher frequencies. The frequency term comes from the receiving antenna, whose effective area at a fixed gain shrinks with the square of the wavelength. A higher frequency means a shorter wavelength, a smaller effective aperture and less captured power, which reads as more path loss. The penalty is recovered by using a higher gain antenna.
How much does path loss change if I double the distance? Doubling the distance adds about 6 dB of free space path loss, because distance enters the formula as a 20 · log₁₀ term and 20 · log₁₀(2) is 6.02 dB. Halving the distance subtracts about 6 dB. The same 6 dB rule applies to doubling the frequency.
Is free space path loss the same as total path loss? No. Free space path loss is the best case, assuming a clear line of sight and no atmosphere, rain or terrain. Real path loss is always equal to or greater than FSPL, because the real world only adds obstruction, diffraction, gaseous absorption, rain fade and multipath on top of the spreading loss.
Does FSPL include antenna gain? No. FSPL is defined as the loss between two isotropic antennas, so antenna gains are added back as separate line items in the link budget. Folding gain into the path loss term as well would count it twice.
Build it in noIM₃
The FSPL calculator works out the free space loss for any distance and frequency and keeps the units honest, so the 60 dB unit trap never bites. When you are ready to turn that into a received power and a margin, the link budget calculator drops FSPL into a full budget with antenna gains, feeder losses and sensitivity. For paths through clutter rather than open air, the log distance path loss calculator lets you raise the path loss exponent above the free space value of two, and the link planner carries the whole hop through terrain, Fresnel clearance and rain to a designed availability.
Key Takeaway
Free space path loss is the loss a radio signal suffers from spreading alone, the irreducible floor that every link budget is built on. The formula is simple once the units are pinned down, both distance and frequency cost 6 dB per doubling, and the frequency penalty is an antenna effect that gain recovers rather than something the air does to the signal. Work out FSPL first, treat it as the best case, then add the real world losses and a fade margin on top. Get the free space number right and everything else in the budget has something solid to stand on.
