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Free-Space Path Loss Calculator

Calculate free-space path loss (FSPL) in dB using the Friis equation. Enter frequency and distance for wireless link budget analysis. Free, instant results.

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Formula

FSPL(dB)=20⋅log10(4πdf/c)FSPL(dB) = 20·log₁₀(4πdf/c)
FSPL— Free-space path loss (dB)
d— Distance between antennas (m)
f— Signal frequency (Hz)
c— Speed of light (3×10⁸) (m/s)
λ— Wavelength (c/f) (m)

How It Works

Free-Space Path Loss (FSPL) calculates the signal attenuation between two antennas with unobstructed line-of-sight — essential for satellite links, microwave backhaul, and point-to-point wireless design. RF engineers use FSPL to determine required transmit power and antenna gains before accounting for real-world losses.

The formula derives from the Friis transmission equation (IEEE Antennas and Propagation Society standard): FSPL(dB) = 20·log₁₀(d) + 20·log₁₀(f) + 20·log₁₀(4π/c), which simplifies to 32.44 + 20·log₁₀(d_km) + 20·log₁₀(f_MHz). At 2.4 GHz and 1 km, FSPL is 100.0 dB; doubling distance adds exactly 6.02 dB (inverse-square law). ITU-R P.525-4 provides the international reference for these calculations, used in spectrum coordination worldwide.

Path loss increases with frequency: at 5.8 GHz, FSPL is 7.7 dB higher than 2.4 GHz for the same distance. This explains why 5G mmWave (28 GHz) requires cell sites every 200–500 m while LTE (700 MHz) covers 10+ km. For distances under 100 m, atmospheric absorption is negligible (<0.01 dB); beyond 10 km, add 0.01–0.02 dB/km for oxygen/water vapor per ITU-R P.676.

Worked Example

Design a 10 km Wi-Fi backhaul link at 5.8 GHz (per IEEE 802.11ac outdoor deployment)

Given: f = 5800 MHz, d = 10 km

FSPL = 32.44 + 20·log₁₀(10) + 20·log₁₀(5800) = 32.44 + 20 + 75.27 = 127.7 dB

Link budget check (typical commercial equipment):
  • Transmit power: 30 dBm (1 W, FCC Part 15.247 limit with antenna)
  • TX antenna gain: 23 dBi (0.6 m dish)
  • RX antenna gain: 23 dBi
  • FSPL: −127.7 dB
  • Received power: 30 + 23 + 23 − 127.7 = −51.7 dBm

With receiver sensitivity of −75 dBm (64-QAM, 20 MHz channel), fade margin = 23.3 dB — sufficient for 99.99% availability per ITU-R P.530 rain fade statistics in temperate climates.

Practical Tips

  • ✓Add 3–6 dB fade margin minimum for 99% link availability; 10–15 dB for 99.99% per ITU-R P.530 recommendations
  • ✓Use exact c = 299,792,458 m/s (SI definition) for precision calculations; 3×10⁸ introduces 0.07% error
  • ✓Above 10 GHz, add atmospheric absorption: 0.2 dB/km at 22 GHz (water vapor), 15 dB/km at 60 GHz (oxygen) per ITU-R P.676
  • ✓For Earth-space links, add 0.5–2 dB ionospheric scintillation below 3 GHz (GPS L1 affected during solar maximum)

Common Mistakes

  • ✗Using FSPL for indoor/NLOS: real indoor path loss exponent is 2.5–4.0 (not 2.0), adding 10–30 dB over FSPL at 50 m
  • ✗Confusing near-field vs far-field: FSPL only valid beyond d > 2D²/λ (Fraunhofer distance). For a 1 m dish at 10 GHz, far-field starts at 67 m
  • ✗Ignoring cable losses: 30 m of RG-58 at 2.4 GHz loses 7.8 dB — equivalent to quadrupling the free-space distance
  • ✗Applying FSPL to surface reflections: multipath adds constructive/destructive interference of ±6 dB or more; use two-ray ground reflection model below 1 GHz

Frequently Asked Questions

Free-space path loss is the reduction in power density of an electromagnetic wave as it propagates through space, caused by the natural spreading of the wave's energy over an increasing area.
Higher frequencies experience greater path loss, meaning signal strength decreases more rapidly with distance compared to lower frequency signals.
No, free-space path loss assumes perfect vacuum conditions. Real-world environments introduce additional losses from obstacles, atmospheric conditions, and terrain.
Free-space path loss at 2.4 GHz is FSPL = 40 + 20·log10(d_meters) dB (approximately). At 100 m: ~80 dB FSPL. A typical WiFi transmitter at 20 dBm with 3 dBi antennas gives received power of 20+3+3−80 = −54 dBm — well above the −70 dBm sensitivity threshold. In practice, walls add 3–15 dB per barrier, so 100 m through a building is often marginal. Outdoor line-of-sight 802.11ac can reach 300+ m with directional antennas.
Free-space path loss follows an inverse-square law: power density decreases as 1/r². Doubling the distance quarters the received power, which is a 6 dB reduction (10·log10(4) = 6.02 dB). This is baked into the Friis equation: FSPL increases by 20·log10(2) = 6 dB per doubling of distance. At 10× the distance, FSPL increases by 20 dB.
No — free-space path loss assumes no obstacles. Inside buildings, use the log-distance path loss model: PL(d) = FSPL(d₀) + 10·n·log10(d/d₀) + X_σ, where n is the path loss exponent (2 for free space, 3–4 for indoor environments, up to 6 in cluttered areas) and X_σ is a zero-mean Gaussian random variable representing shadowing. For link budget purposes, add 15–30 dB of building penetration loss depending on construction materials.

Methodology & References

References

  • ITU-R P.525-4 — Calculation of free-space attenuation link
  • A Note on a Simple Transmission Formula — Harald T. Friis, Proc. IRE 34(5), pp. 254–256 (1946)
  • Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 14.1

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