Free Space Path Loss Calculator

Free-space path loss: the signal attenuation between two isotropic antennas in unobstructed line-of-sight. Use this as a first-pass path loss estimate for any wireless link — WiFi, GNSS, point-to-point backhaul, or drone telemetry.

Free Space Path Loss

Frequency
Distance
ParameterValue
Wavelength λ—
Free-Space Path Loss—
Optional: received power estimate

Enter transmit power to estimate received signal level. Antenna gains default to 0 dBi (isotropic) if left blank.

Transmit Power
Antenna Gains
ParameterValue
Received Power (dBm)—
Received Power (W)—

⚠ This estimate assumes unobstructed free-space line-of-sight. Real links have additional losses from terrain, buildings, rain, and multipath. Use as a first-pass sanity check only.

Formula & Theory

Free-space path loss is the attenuation between two isotropic antennas in free-space line-of-sight. From ITU-R P.525-4 (2019):

  • Exact (SI): FSPL (dB) = 20·log₁₀(4π·d·f / c), where c = 299,792,458 m/s
  • Practical (GHz, km): FSPL = 20·log₁₀(fGHz) + 20·log₁₀(dkm) + 92.45
  • Practical (MHz, km): FSPL = 20·log₁₀(fMHz) + 20·log₁₀(dkm) + 32.45
  • Wavelength: λ = c / f
  • With gains (Friis): Pr (dBm) = Pt (dBm) + Gt (dBi) − FSPL + Gr (dBi)

This calculator uses the canonical form FSPL = 20·log₁₀(d_m) + 20·log₁₀(f_hz) − 147.55 internally. The constant 92.45 is derived from 20·log₁₀(4π × 10⁹ × 10³ / c) ≈ 92.45.

References: ITU-R P.525-4 (2019) §3; Friis, H.T. (1946) "A Note on a Simple Transmission Formula," Proc. IRE 34(5), 254–256.

Worked Example

2.4 GHz WiFi at 100 m:

  • λ = 299,792,458 / 2,400,000,000 = 0.125 m (12.5 cm)
  • FSPL = 20·log₁₀(100) + 20·log₁₀(2.4×10⁹) − 147.55 = 40 + 187.60 − 147.55 = 80.05 dB
  • With +20 dBm Tx, +3 dBi Tx antenna, isotropic Rx: Pr = 20 + 3 − 80.05 + 0 = −57.05 dBm

GPS L1 (1575.42 MHz) from orbit at 20,200 km:

  • λ = 0.190 m
  • FSPL = 20·log₁₀(20,200,000) + 20·log₁₀(1,575,420,000) − 147.55 = 182.6 dB
  • Published GPS received power at ground: approximately −130 dBm into a 0 dBi antenna — consistent with this result and published satellite EIRP specs.

Assumptions & Limitations

  • Far-field only — valid when d ≫ λ and d ≫ antenna aperture. This calculator warns when d < 10λ.
  • Unobstructed line-of-sight — no terrain, buildings, foliage, or Fresnel-zone obstruction modelled
  • Lossless medium — no atmospheric absorption, rain attenuation, or ionospheric effects. At f > 10 GHz over distances > 10 km, add atmospheric absorption (see ITU-R P.676).
  • Isotropic baseline — optional power section adds antenna gains (dBi); omitting them is equivalent to 0 dBi at both ends
  • No cable or connector losses — add manually or use the RF Link Budget Calculator for a full accounting
  • No polarization mismatch — add up to 3 dB manually for cross-polarized antenna pairs

Common Mistakes

  • Using FSPL for indoor or obstructed paths: Indoor propagation adds 10–30 dB beyond FSPL depending on wall materials and frequency. Use empirical models (e.g., ITU-R P.1238) for indoor budgets.
  • Confusing power ratio with voltage ratio: 80 dB of FSPL is a power ratio of 10⁸. Voltage ratio is √(10⁸) = 10,000× — a different number. Always verify which domain your spec refers to.
  • Forgetting antenna gain: A 15 dBi directional antenna at both ends recovers 30 dB of FSPL. Every 6 dB of total antenna gain doubles the usable range.
  • Applying FSPL in the near field: Below roughly 10 wavelengths, the field has not fully formed as a propagating plane wave and the 1/r² spreading law does not apply. The calculator flags this case.
  • Ignoring cable and connector losses: 1 dB of cable loss at each end cuts effective EIRP by 2 dB — equivalent to shrinking transmit power by 37%. Use the RF Link Budget Calculator to account for the full signal path.
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Frequently Asked Questions

What is free-space path loss (FSPL)?

Free-space path loss is the reduction in signal power between two isotropic antennas separated by a distance d in an unobstructed, line-of-sight environment. It is a geometric spreading effect, not absorption. FSPL (dB) = 20·log₁₀(4πd·f/c). At 2.4 GHz and 100 m, FSPL ≈ 80 dB.

Why does FSPL increase with frequency?

A higher frequency means a shorter wavelength and a smaller effective capture area for an isotropic receive antenna. The receive aperture scales as λ², so doubling frequency (halving λ) reduces captured power by 6 dB. A directional antenna with fixed physical size compensates — its gain rises 6 dB per octave of frequency.

What is the FSPL formula?

The canonical form is FSPL (dB) = 20·log₁₀(4π·d/λ), where λ = c/f (c = 299,792,458 m/s). In practical units: FSPL = 20·log₁₀(f_GHz) + 20·log₁₀(d_km) + 92.45, or equivalently 20·log₁₀(f_MHz) + 20·log₁₀(d_km) + 32.45. Reference: ITU-R P.525-4 (2019).

When should I not use this calculator?

FSPL assumes free-space, unobstructed, far-field line-of-sight. Do not use it for: links with terrain or building obstruction; distances below about 10 wavelengths (near-field effects); frequencies above 10 GHz at distances over 10 km (add atmospheric absorption); ground-reflection paths (use the two-ray ground reflection model instead). For a complete link budget with antenna gains, cable losses, and fade margin, use the RF Link Budget Calculator.

What is a typical FSPL value for WiFi?

At 2.4 GHz and 30 m (typical indoor AP-to-client distance), FSPL ≈ 68 dB. At 100 m, FSPL ≈ 80 dB. A typical 802.11n AP at +20 dBm with +3 dBi antenna, and a client sensitivity of −90 dBm, gives: 20 + 3 − 80 + 0 = −57 dBm received — 33 dB margin. At 500 m outdoors, FSPL ≈ 94 dB, leaving about 19 dB margin.