Free Space Path Loss Calculator

Frequently Asked Questions

Why does doubling the distance add only 6 dB loss?

When a radio transmitter radiates, its power spreads outward over an ever-expanding sphere. The surface area of a sphere is 4πr², so doubling the radius quadruples the area. A fixed-aperture receiver intercepts the same physical area regardless of distance, so it captures 1/4 as much power when the distance doubles. A factor of 4 in power corresponds to 10 × log10(4) = 6.02 dB. This is the 6 dB per octave (doubling) or 20 dB per decade (10x) rule that appears in both FSPL and in electrostatic and gravitational field strength - all inverse square law phenomena obey this rule.

Does FSPL apply inside buildings?

No - inside a building, the dominant propagation mechanisms are reflection, diffraction, and scattering from walls, floors, ceilings, and furniture, not free-space geometric spreading. The FSPL formula will give you a number, but it will typically underestimate actual loss by 20-40 dB compared to measurements. Indoor propagation follows empirical models such as the ITU indoor path loss model (which adds a frequency-dependent floor attenuation factor) or the COST 231 model. WiFi engineers use measured data or site surveys rather than FSPL to predict indoor coverage. FSPL is most valid outdoors for line-of-sight links where Fresnel zone clearance is maintained - roughly, the link path should have no obstacles within the first Fresnel zone radius to achieve near-free-space propagation.

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How This Calculator Works

Free space path loss describes how the power of a radio signal weakens as it travels through empty space between a transmitter and a receiver. It assumes a clear line of sight with no obstructions, reflections, or atmospheric absorption. The loss grows with both distance and frequency because higher frequencies spread their energy over a smaller effective aperture and a longer path lets the wavefront expand further before it reaches the receiver.

The Formula

This calculator uses the standard form expressed in decibels with distance in kilometers and frequency in megahertz. The constant of 32.44 folds in the unit conversion and the fixed terms of the underlying physics. Doubling the distance adds about six decibels of loss, and doubling the frequency adds the same six decibels.

Tips

Free space path loss is a best case figure; real links lose more to terrain, foliage, and rain.

Add transmit power and antenna gains, then subtract this loss, to estimate received signal strength.

Use it early in a link budget to check whether a connection is even feasible.

Free-Space Path Loss in Link Budgets

FSPL is the foundation of any wireless link budget, but it is important to understand exactly what it does and does not represent. FSPL assumes a perfect vacuum with no obstructions, no ground reflection, no multipath, and no atmospheric effects. In practice, it represents the absolute minimum propagation loss that any real system can achieve - every real link will have higher total path loss. Outdoor line-of-sight microwave links in clear air come closest to FSPL; adding terrain, vegetation, and buildings rapidly increases the effective path loss beyond the free-space prediction.

Practical correction factors to add on top of FSPL: indoor WiFi links through walls and floors add 20-30 dB of building penetration loss; suburban mobile radio adds 10-15 dB of excess loss compared to free space; a link in dense urban canyon conditions may add 20-40 dB beyond FSPL. In contrast, a clear-sky line-of-sight microwave link at 6 GHz between two towers may come within 1-2 dB of the free-space prediction on a calm day. FSPL is useful as a best-case baseline, and the difference between FSPL and your actual measured path loss reveals how much margin you need to add for the environment.

FSPL grows with distance squared (20 dB per decade, or 6 dB per doubling) and also with frequency squared (another 20 dB per decade). This second-order frequency dependence is one reason that lower frequencies are preferred for long-range communication: a link at 900 MHz loses 10 dB less to path loss than the same link at 2.4 GHz, all else being equal. It is also why cellular networks have historically reserved 700-900 MHz spectrum for coverage and used 1.7-2.6 GHz for capacity.

Why Frequency Matters

The frequency-squared dependence in FSPL can seem counterintuitive. A photon at 5 GHz carries more energy than one at 2.4 GHz, yet the 5 GHz signal suffers more path loss. The explanation lies in antenna aperture rather than photon energy. A receiving antenna with a fixed physical size intercepts a smaller fraction of the wavefront as frequency increases, because the effective aperture of an isotropic antenna (the theoretical reference) shrinks as wavelength squared. If you fix the antenna gain instead of its physical size, the frequency dependence in FSPL cancels out, and range depends only on distance. This is why satellite dish designers speak of G/T rather than absolute aperture: a smaller dish at higher frequency can achieve the same gain as a larger dish at lower frequency, because the wavelength is shorter.

Extending FSPL to Real Propagation Models

Free-space path loss is the starting point; real engineering requires more detailed models. The Friis transmission equation extends FSPL to include antenna gains on both ends: P_received = P_transmitted + G_tx + G_rx - FSPL. This is the complete free-space link budget. For terrestrial links, additional models account for the terrain and atmosphere. The two-ray ground reflection model adds the contribution of the direct path and the ground-reflected path, and predicts that at short ranges FSPL applies while at longer ranges path loss transitions to a 40 dB per decade slope due to destructive interference between the two rays - this is why flat terrain is not always better for radio propagation.

The ITU-R recommendation family provides standardized models for different environments: ITU-R P.525 for free-space propagation, ITU-R P.452 for terrestrial and Earth-space paths including troposcatter and diffraction, and the Okumura-Hata model for urban and suburban cellular coverage prediction. Above about 10 GHz, atmospheric effects become significant: water vapor has an absorption peak near 22 GHz (about 0.2 dB/km), oxygen absorbs strongly near 60 GHz (about 15 dB/km, making 60 GHz nearly unusable beyond a few hundred meters), and rain causes frequency-dependent attenuation that can reach 10+ dB/km in heavy rain at Ka-band. These effects make frequency selection critical for long-distance links at microwave and millimeter-wave frequencies.

Practical Applications by Frequency Band

Understanding how FSPL varies across frequency bands puts real system design in context:

900 MHz IoT and LoRa: At 1 km range, FSPL is about 91 dB. LoRa systems with -137 dBm receiver sensitivity and 14 dBm transmit power can achieve LOS ranges of 5-15 km in rural areas, limited more by terrain and Fresnel zone clearance than FSPL alone.

2.4 GHz WiFi: At 50 m indoors, FSPL is about 80 dB, but wall and furniture losses add another 20-30 dB. Effective indoor range is limited to 30-50 meters through typical construction materials. Outdoor LOS at 300 m adds about 6 dB more FSPL.

5 GHz WiFi: About 6 dB more FSPL than 2.4 GHz at the same distance, plus greater wall penetration loss. This limits indoor range but the band benefits from much less interference and higher available bandwidth.

28 GHz 5G millimeter wave: FSPL at 100 m is approximately 121 dB. Combined with building penetration loss of 20-40 dB, mmWave 5G is limited to 100-200 m urban deployments and requires dense cell site placement. Large antenna arrays are essential to provide enough gain to close the link.

C-band satellite (4-8 GHz): At 35,786 km geostationary orbit altitude, FSPL is about 196-200 dB. Satellite terminals require modest dish sizes because the frequency is low enough that FSPL is manageable and rain fade is minimal.

Ka-band satellite (26-40 GHz): FSPL at GEO orbit is about 210-215 dB. Rain fade at Ka-band can exceed 20 dB during heavy rain, requiring link margin or adaptive coding to maintain service. The higher frequency enables smaller dishes and higher bandwidth.

GPS L1 (1575.42 MHz): At 20,200 km orbit altitude, FSPL is about 183 dB. GPS receivers work with signals at -130 dBm, which requires correlation processing across a long integration window to extract signal from below the noise floor.

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