Free Space Path Loss: Formula and Real Numbers

What Is Free Space Path Loss?

Free space path loss is the attenuation that a radio signal experiences as it travels through the air between a transmitter and receiver with nothing in the way. No walls, no trees, no reflections—just the transmitter radiating energy in all directions, and the receiver trying to capture a tiny fraction of it from some distance away.

It's one of the most fundamental concepts in RF engineering, and it's absolutely critical to get right. If you miscalculate path loss by just a few dB, your link budget collapses. Your satellite receiver stops working. Your IoT device drops off the network. Most engineers understand the formula intellectually, but fewer really grasp why it exists or how to avoid the traps that catch people in real designs.

Why It Matters

Every radio system—whether it's a WiFi access point, a cellular base station, a satellite uplink, or a hobby LoRaWAN gateway—has to account for path loss to determine whether the receiver will have enough signal to decode the transmission. You calculate transmit power, antenna gains, and receiver sensitivity, and somewhere in that link budget sits path loss, quietly eating your signal.

The worse part is that path loss gets worse the higher your frequency goes. Double the frequency, and path loss increases by 6 dB. That's why 5 GHz WiFi doesn't reach as far as 2.4 GHz. That's why millimeter-wave systems need directional antennas or they're dead on arrival.

Understanding path loss also helps you make smart trade-offs. Do you boost transmit power, add antenna gain, or accept a shorter range? Path loss tells you which lever to pull and how much it actually helps.

The Formula

Free space path loss in decibels is:

where $d$ is distance in meters, $f$ is frequency in Hz, and $c$ is the speed of light (3 × 10⁸ m/s).

That constant term simplifies to about 20 log₁₀(4π/c) ≈ −147.55 dB when frequency is in Hz and distance is in meters. So the practical formula most engineers use is:

If you want frequency in MHz and distance in kilometers, it becomes:

Both are correct; just make sure your units are consistent.

Where does this formula come from? It's Friis transmission equation. Imagine the transmitter radiates power $P_t$ uniformly in all directions. At distance $d$, that power is spread over a sphere of surface area $4\pi d^2$. The power density (watts per square meter) is $P_t / (4\pi d^2)$. The receiver antenna captures some of that based on its effective aperture, which depends on frequency and antenna gain. The ratio of received power to transmitted power is the path loss. The math works out to the formula above.

A Worked Example

Let's say you're designing a 2.4 GHz WiFi link 50 meters away. What's the path loss?

Using the practical formula with frequency in MHz and distance in km:

• $d_{km} = 50 \text{ m} = 0.05 \text{ km}$
• $f_{MHz} = 2400 \text{ MHz}$

First term: $20 \log_{10}(0.05) = 20 \times (-1.301) = -26.02$ dB

Second term: $20 \log_{10}(2400) = 20 \times 3.380 = 67.60$ dB

Third term: $32.45$ dB

So your signal loses about 74 dB just traveling through free space. If your transmitter puts out 20 dBm (100 mW) and your antenna has 2 dBi gain, the receiver sees 20 + 2 − 74 = −52 dBm. A typical WiFi receiver has a sensitivity of around −80 to −90 dBm, so you're fine. But if you go to 5 GHz at the same distance, path loss increases by about 8 dB (because frequency doubled), and now you're at −60 dBm received, which is still okay but tighter.

Try calculating this yourself with different distances and frequencies using the Free-Space Path Loss Calculator. Plug in 50 m and 2400 MHz and see what you get. Then change distance to 100 m and watch path loss increase by 6 dB (because you doubled distance, which is 20 log₁₀(2) ≈ 6 dB). This linear-in-dB relationship is why engineers think in logarithms.

The 6 dB Rule and Why It Matters

Path loss increases by 6 dB every time you double the distance or double the frequency. This isn't a coincidence; it falls straight out of the logarithm in the formula. $20 \log_{10}(2) = 6.02$ dB.

This is incredibly useful as a quick sanity check. If you're designing a system and someone claims they can double the range without changing anything else, they're wrong. Doubling range costs 6 dB of link margin. You have to either increase transmit power by 6 dB, add 6 dB of antenna gain, or accept a 6 dB reduction in receiver sensitivity (which usually means worse performance).

Similarly, moving from 2.4 GHz to 5 GHz costs about 8 dB of path loss (because 5/2.4 ≈ 2.08, and 20 log₁₀(2.08) ≈ 8 dB). That's why 5 GHz systems need better antennas or higher power to match 2.4 GHz range.

Common Mistakes and Gotchas

Mixing up your units. This is the most common trap. If you use frequency in MHz but distance in meters, your answer will be completely wrong. Always double-check. The formula with distance in km and frequency in MHz is the safest because those are the units most RF tools use. Forgetting that path loss is one-way, not round-trip. Path loss is the loss from transmitter to receiver. If you're doing a radar calculation or a two-way link, you might need to double it. But for most receiver calculations, it's just the one-way loss. Assuming free space when it doesn't apply. Free space path loss assumes nothing blocks or reflects the signal. In reality, buildings, trees, and ground reflections add extra loss. This is where empirical path loss models (like the Okumura-Hata model for cellular) come in. Free space is optimistic. Your actual link will be worse. Not accounting for antenna gains. Path loss is just the spreading loss. It doesn't include your antenna gains. A 2 dBi gain antenna on the transmitter and 2 dBi on the receiver means you recover 4 dB from path loss. Many engineers forget this and end up with overly pessimistic link budgets, or worse, they accidentally double-count antenna gains. Ignoring polarization mismatch. If your transmitter antenna is vertically polarized and your receiver is horizontal, you lose 20 dB or more due to polarization mismatch. This isn't path loss; it's a separate loss mechanism. But it's easy to forget, especially in outdoor systems where antenna orientation can drift. Getting the frequency wrong. Is your system at 2.4 GHz or 2.4 MHz? I've seen engineers work with the wrong frequency for weeks. Check the datasheet. Check twice. A 1000× error in frequency is a 60 dB error in path loss.

When Free Space Path Loss Breaks Down

Free space path loss assumes a clear line of sight with no obstructions or reflections. In the real world, this almost never happens. Buildings, terrain, vegetation, and even rain all add extra attenuation. The signal also bounces off the ground and nearby objects, creating multipath fading that can make received power fluctuate wildly.

For outdoor terrestrial links, empirical models like Okumura-Hata, COST-Hata, or the 3GPP models are more accurate than free space. For indoor links, you need ray tracing or measurements. For satellite, free space is closer to reality because there's less stuff in the way, but atmospheric absorption (especially at higher frequencies) still matters.

Free space path loss is best used as a baseline—a best-case scenario. Your actual link will be worse. How much worse depends on your environment. That's why link margin exists: you add extra dB to account for shadowing, fading, and other real-world losses.

Quick Reference Table

Here are some typical path loss values for common scenarios (free space only):

At 2.4 GHz, 10 m: ~60 dB At 2.4 GHz, 100 m: ~80 dB At 2.4 GHz, 1 km: ~100 dB At 5 GHz, 10 m: ~68 dB At 5 GHz, 100 m: ~88 dB At 5 GHz, 1 km: ~108 dB

These are useful anchors. If your calculation is wildly different, something's wrong.

Try It Yourself

Now that you understand the concept, use the Free-Space Path Loss Calculator to experiment. Try different frequencies, distances, and see how the path loss changes. Then think about your own system: what's your link budget? How much margin do you have? Path loss is just one piece of the puzzle, but it's the piece that drives everything else.

If you're building a full link budget, check out the RF Link Budget Calculator to see how path loss fits into the bigger picture, and the Link Margin Calculator to understand how much safety margin you have left after accounting for all losses.