Electromagnetic Wave Propagation Engine
Free Space Path Loss (FSPL) Calculator
Calculate electromagnetic signal attenuation in dB across line-of-sight distance and carrier frequency with multi-band comparative analysis.
Free Space Path Loss (FSPL)
111.21 dB Linear Power Attenuation
1.32 × 10⁻¹¹ (132 fW/W) Wavelength (λ)
34.56 cm 1st Fresnel Radius
29.38 meters 60% Clearance Req.
17.63 meters Loss Per Decade
+20 dB / ×10 dist Step-by-Step Friis Equation Derivation
Step 1: Distance Term = 20 × log₁₀(10.00 km) = +20.00 dB
Step 2: Frequency Term = 20 × log₁₀(868.0 MHz) = +58.77 dB
Step 3: FSPL = 20.00 + 58.77 + 32.44 = 111.21 dB Path Attenuation
Step 2: Frequency Term = 20 × log₁₀(868.0 MHz) = +58.77 dB
Step 3: FSPL = 20.00 + 58.77 + 32.44 = 111.21 dB Path Attenuation
Worked Examples
Step-by-Step Free Space Path Loss Calculations
Review step-by-step mathematical examples computing electromagnetic path attenuation across microwave and sub-GHz carrier frequencies:
Example A: 5.8 GHz Microwave Backhaul (10 km) 5.8 GHz UNII
A point-to-point wireless bridge spans 10.0 kilometers across a clear line-of-sight valley path at 5,800 MHz.
System Inputs:
• Carrier Frequency (f): 5,800 MHz (5.8 GHz)• Link Distance (d): 10.0 km (10,000 meters)
• Speed of Light (c): 299,792,458 m/s
Step-by-Step Solution:
1. Distance Term: 20 × log₁₀(10) = 20.00 dB2. Frequency Term: 20 × log₁₀(5800) = 75.27 dB
3. Constant Offset: +32.44 dB
4. Total FSPL = 20.00 + 75.27 + 32.44 = 127.71 dB
Engineering Verdict: 127.71 dB represents a linear power reduction factor of 5.90 × 10¹². High-gain dish antennas are required on both ends to achieve an acceptable link margin on our RF Link Budget Calculator.
Example B: 868 MHz LoRaWAN IoT Telemetry (5 km) Sub-1GHz IoT
An agricultural sensor transmits telemetry to a central gateway over a 5.0 kilometer rural line-of-sight path at 868 MHz.
System Inputs:
• Carrier Frequency (f): 868 MHz• Link Distance (d): 5.0 km (5,000 meters)
• Speed of Light (c): 299,792,458 m/s
Step-by-Step Solution:
1. Distance Term: 20 × log₁₀(5) = 13.98 dB2. Frequency Term: 20 × log₁₀(868) = 58.77 dB
3. Constant Offset: +32.44 dB
4. Total FSPL = 13.98 + 58.77 + 32.44 = 105.19 dB
Engineering Verdict: At 868 MHz, FSPL is 22.52 dB lower than at 5.8 GHz over the same 5 km distance, enabling multi-kilometer connectivity with low-power batteries. Compare power levels with our dBm to Milliwatts Calculator.
Antenna Aperture Physics
The Physical Paradox: Why Does Path Loss Increase with Frequency?
A common misconception among engineers is that empty space absorbs high frequencies more than low frequencies:
1. Free Space Has Zero Frequency Absorption
In a pure vacuum, electromagnetic waves of all frequencies spread outwards according to the exact same inverse-square law (1 / R²). The power density (S = EIRP / 4πR²) in W/m² at a given distance is identical for 100 MHz and 100 GHz.
Calculate power flux with our dBm to Power Density Calculator.
2. The Shrinking Effective Aperture (A_e = λ² / 4π)
The frequency term appears in FSPL because an isotropic receiving antenna's effective capture area ($A_e$) is proportional to the square of its wavelength ($\lambda^2$). As frequency increases, wavelength shrinks, so a standard unity-gain antenna intercepts a smaller physical slice of the propagating wavefront.
Formula: P_RX = S × A_e = S × (λ² / 4π) • See our EIRP Calculator.
Microwave Line-of-Sight Engineering
1st Fresnel Zone Radius Clearance Solver
To achieve true free-space path loss conditions, line-of-sight links must maintain at least 60% obstacle clearance within the 1st Fresnel ellipsoidal zone:
Midpoint Fresnel Radius (r₁)
29.38 meters 60% Earth/Tree Clearance
17.63 meters Earth Curvature Bulge (d²/12.74)
1.96 meters Tower Height Sizing Recommendation:
To establish this 10.0 km link without multipath reflection fade, transmitter and receiver antennas should each be elevated at least 19.6 meters (64.3 ft) above surrounding vegetation and average terrain.
To establish this 10.0 km link without multipath reflection fade, transmitter and receiver antennas should each be elevated at least 19.6 meters (64.3 ft) above surrounding vegetation and average terrain.
Multi-Band Comparison
Propagation Attenuation Across Popular RF Bands
Compare how identical propagation distance impacts signal attenuation across different wireless spectrum bands:
| RF Spectrum Band | Frequency | FSPL at Current Distance | Delta vs. Sub-1GHz | Primary Use Case |
|---|---|---|---|---|
| VHF Broadcast / LMR | 150 MHz | 95.96 dB | −15.2 dB (Best Range) | FM Radio, Marine, Police Dispatch |
| Sub-1GHz IoT (LoRa / Sigfox) | 868 / 915 MHz | 111.21 dB | 0.00 dB (Baseline) | Smart Meters, Agricultural Sensors |
| 2.4 GHz ISM (Wi-Fi / BLE) | 2,412 MHz | 120.09 dB | +8.88 dB More Loss | Wi-Fi 4/6, Bluetooth, Zigbee |
| 5 GHz UNII (Wi-Fi / Backhaul) | 5,800 MHz | 127.71 dB | +16.50 dB More Loss | High-Speed Wi-Fi, Wireless ISPs |
| 5G mmWave (n257 / n258) | 28,000 MHz | 141.38 dB | +30.17 dB More Loss | Ultra-Dense Stadiums, Fixed Wireless |
Reference Table
Free Space Path Loss Comprehensive Benchmark Table
Calculated path attenuation across key telecommunications distances and frequencies:
| Distance | 433 MHz (LPD) | 915 MHz (LoRa) | 2.4 GHz (Wi-Fi) | 5.8 GHz (UNII) |
|---|---|---|---|---|
| 1.0 Meter | 25.17 dB | 31.69 dB | 40.05 dB | 47.70 dB |
| 10 Meters | 45.17 dB | 51.69 dB | 60.05 dB | 67.70 dB |
| 100 Meters | 65.17 dB | 71.69 dB | 80.05 dB | 87.70 dB |
| 1.0 Kilometer | 85.17 dB | 91.69 dB | 100.05 dB | 107.70 dB |
| 10 Kilometers | 105.17 dB | 111.69 dB | 120.05 dB | 127.70 dB |
| 100 Kilometers | 125.17 dB | 131.69 dB | 140.05 dB | 147.70 dB |
Knowledge Base
Frequently Asked Questions: Free Space Path Loss (FSPL)
Common questions about RF power conversions, negative dBm, and voltage calculations.
Using standard metric units (distance in km, frequency in MHz), the standard logarithmic formula is: FSPL (dB) = 20 × log₁₀(d_km) + 20 × log₁₀(f_MHz) + 32.44. In raw physics units (distance d in meters, wavelength λ in meters): FSPL = (4πd / λ)2.
Electromagnetic radiation itself does not lose energy in a vacuum. However, an isotropic receiving antenna's effective aperture (Aeff = λ2 / 4π) shrinks as frequency rises. Because shorter wavelengths capture less physical wavefront area, higher frequencies require higher directional antenna gains to maintain equal signal strength.
The 1st Fresnel Zone is an elliptical volume between the transmitter and receiver where indirect reflected waves travel within 180° (λ/2) of the direct line-of-sight path. To prevent destructive out-of-phase interference, at least 60% of the 1st Fresnel zone radius must remain completely free of obstacles.
Doubling propagation distance increases path loss by exactly +6.02 dB (20 × log₁₀(2)). In linear terms, doubling distance reduces received power to one-fourth (25%) of its previous value due to the inverse-square law.
Over 100 meters (0.1 km): 2.4 GHz experiences 80.05 dB of FSPL, whereas 5.8 GHz experiences 87.70 dB of FSPL. 5.8 GHz suffers roughly 7.65 dB higher free-space attenuation, requiring higher antenna gain.
By definition, pure Free Space Path Loss assumes an ideal lossless vacuum. In real atmospheric propagation, atmospheric oxygen, water vapor absorption, and rain fade introduce additional attenuation (especially severe above 10 GHz, such as Ku/Ka-band satellite and 28 GHz 5G mmWave).
When using distance in miles (dmi) and frequency in Gigahertz (fGHz): FSPL (dB) = 20 × log₁₀(d_mi) + 20 × log₁₀(f_GHz) + 96.58.
FSPL is the largest subtraction component in a link budget: P_RX (dBm) = P_TX (dBm) + G_TX (dBi) + G_RX (dBi) − L_cables (dB) − FSPL (dB).