When to use: Use to calculate free space path loss (FSPL) — the signal attenuation due to distance in an unobstructed line-of-sight environment. This is the starting point for every RF link budget. Higher frequencies and longer distances result in greater path loss. Select a preset frequency or enter a custom value. The result feeds directly into the Link Budget Calculator. In-building applications should add penetration and shadowing losses on top of FSPL.
The Free Space Path Loss (FSPL) Calculator computes signal attenuation due to propagation distance in an unobstructed line-of-sight environment using the standard ITU formula, covering public safety (P25 700/800 MHz), LTE, and Wi-Fi frequencies. It is the required first step in any RF link budget and coverage radius calculation.
Free space path loss is calculated using the Friis transmission formula: FSPL (dB) = 20·log10(d_km) + 20·log10(f_MHz) + 32.44, where d is distance in kilometers and f is frequency in MHz. This formula accounts for the geometric spreading of the wavefront as an electromagnetic wave propagates outward from a point source — the power per unit area decreases as the inverse square of distance (the inverse-square law).
Key relationships: doubling the distance adds 6 dB of path loss (20·log10(2) = 6.02 dB). Doubling the frequency also adds 6 dB. Increasing distance by 10× adds 20 dB. At 800 MHz and 100 m, FSPL = 72.5 dB; at 800 MHz and 1 km, FSPL = 92.5 dB. Free-space path loss represents the theoretical minimum — actual propagation adds shadowing, multipath, and building penetration losses on top of FSPL.
The FSPL formula is derived from ITU-R P.525 (Calculation of free-space attenuation). For public safety radio coverage calculations, TIA-TSB-88 references free-space path loss as the foundation for all coverage planning. NFPA 1221 in-building calculations use the log-distance model with FSPL at a 1-meter reference distance as the starting point. FCC licensing for point-to-point microwave links (Part 101) requires path loss calculations using FSPL plus site-specific fade margins per ITU-R P.530.
FSPL is the lower bound on path loss — real-world propagation in any environment involves additional losses. For outdoor macro-cell planning, the Okumura-Hata model adds an urban excess loss of 10–30 dB to FSPL depending on height above average terrain and urban density. For in-building coverage, add 10–25 dB of building penetration loss to FSPL calculated at the building exterior, then add floor penetration losses (15–25 dB per floor for concrete construction) for multi-floor propagation. The two-ray ground reflection model applies for near-ground propagation at distances beyond the crossover distance d_c = 4·h_tx·h_rx / λ, where the path loss exponent transitions from 2 to 4.
Select a frequency preset from the dropdown — common P25 public safety frequencies (700 and 800 MHz), LTE bands, and Wi-Fi frequencies are included. For custom frequencies, select "Custom frequency" and enter the value in MHz. Enter the distance and select the unit (m, km, or ft). The calculator returns FSPL in dB at the specified distance, plus a table showing FSPL at 10, 30, 100, 300, and 1,000 m for the selected frequency. Use this FSPL value directly as the "Free Space Path Loss" input in the Link Budget Calculator.
Free-space path loss increases with frequency because the effective aperture of a receiving isotropic antenna decreases as frequency increases. The effective aperture A_eff = λ²/(4π), so a higher frequency antenna captures less power from the same wave. Doubling the frequency halves the effective aperture and adds 6 dB of path loss. This is why 5 GHz Wi-Fi has shorter range than 2.4 GHz Wi-Fi, even at the same transmit power and antenna gain (in dBi).
FSPL (exponent n = 2) is valid only in open, unobstructed, LOS environments. The log-distance path loss model generalizes this with an exponent n > 2 for environments with obstructions: PL(d) = FSPL(d0) + 10·n·log10(d/d0). For indoor NLOS environments, n = 3 to 4; for dense urban, n = 3.5 to 5. FSPL provides the absolute floor; the log-distance model with n > 2 provides realistic estimates for obstructed environments.
For in-building applications, compute FSPL at the distance from the antenna to the test point, then add building penetration loss (if calculating from an outdoor source) and indoor shadowing margin (8–10 dB for 90% location probability in NLOS indoor environments). For DAS systems where the antenna is already inside the building, use the log-distance model with the indoor path loss exponent n = 3 to 4 instead of FSPL.
The crossover distance where ground reflections become significant is d_c = 4·h_tx·h_rx / λ. For P25 at 800 MHz with antennas at 5 m height, d_c = 4 × 5 × 5 / (0.375) ≈ 267 m. Beyond this distance, path loss follows a 40 dB/decade (1/d^4) slope rather than 20 dB/decade. This matters for near-ground mobile communications but not for high-antenna microwave links.
At 1 km: 155 MHz = 78.3 dB, 450 MHz = 85.5 dB, 769 MHz = 90.3 dB, 851 MHz = 91.0 dB, 1900 MHz = 98.0 dB. Each doubling of frequency adds 6 dB, so a 1900 MHz LTE system experiences 17.7 dB more path loss than a 155 MHz VHF system at the same distance. This explains why P25 VHF systems cover larger geographic areas than 800 MHz systems with equivalent transmitter power.
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