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Tool 04 · Available

Free-Space Path Loss

Calculate the isotropic free-space reference loss from positive frequency and distance.

Typical inputs
Positive frequency and distance with explicit unit scales.
Calculated output
Free-space basic transmission loss and wavelength.
Model status
Release A · documented and numerically tested
Engineering question

What is the geometric free-space transmission loss between two isotropic reference antennas?

Isotropic free-space reference

ITU-R P.525-5 (11/2024). This reference loss represents geometric spreading and conventional aperture—not absorption or a complete channel model.

Free-space basic transmission loss60.231105 dBExact-form equation using exact SI speed of light
Linear path ratio
1.05465518e+6
incident/reference power ratio
Wavelength
122.364 mm
Double distance
66.251705 dB
+6.020600 dB
Double frequency
66.251705 dB
+6.020600 dB

Calculation path

  1. λ=cf\lambda = \frac{c}{f}
  2. LFS=20log⁡10(4πdλ)L_{\mathrm{FS}} = 20\log _{10}(\frac{4\pi d}{\lambda })
  3. Doubling either frequency or distance adds 6.020600 dB when the other quantity is fixed.
Model

What this calculator is doing

The model compares isotropic power flux at distance d with isotropic receive aperture. It represents geometric spreading, not every propagation mechanism.

Decision

How to read the result

Use FSPL as one link-budget term. Add obstruction, atmospheric, feeder, polarization, and fade terms only when required.

Equations & conventions

  • LFS=20log⁡10(4πdλ)L_{\mathrm{FS}} = 20 \log _{10}(\frac{4\pi d}{\lambda })
  • λ=cf\lambda = \frac{c}{f}
  • LFS is the positive basic transmission loss in decibels.
  • d is separation in metres; f is frequency in hertz.
  • λ = c/f with exact c = 299,792,458 m/s.

Independently checked example

Checked example: 2.45 GHz over 10 m gives 60.231105 dB using exact c and the ITU-R P.525-5 exact form.

Common mistakes

  • Reading FSPL as absorbed power rather than a transmission ratio.
  • Mixing the MHz/km shortcut constant with other units.

Assumptions, validity & omissions

  • Perfect vacuum/free-space reference.
  • Distance is in the region where the link model applies.
  • No obstruction, atmosphere, fading, or antenna gain is included.

Sources & model provenance

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