Tool 03 · Available

Friis Transmission Equation

Estimate received available power and keep every gain, loss, and polarization term visible.

Typical inputs: Transmit power, directional antenna gains, frequency, separation, polarization loss, and other named loss.
Calculated output: Received available power, FSPL, wavelength, net gain, and a complete dB ledger.
Model status: Release A · documented and numerically tested

Engineering question

Under ideal free-space far-field conditions, what available power reaches the receiver?

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Free-space receive estimate

Select absolute-power and antenna-gain conventions explicitly. Losses are positive magnitudes; the ledger subtracts them.

Transmit power

Power unit

Transmit antenna gain

Transmit gain convention

Receive antenna gain

Receive gain convention

Frequency

Frequency unit

Separation

Distance unit

Polarization mismatch lossdB

Other named lossdB

Received available power-32.447783 dBmReceiving-antenna terminal under free-space, far-field, matched-port assumptions

Received power: 569.143 nW
Received level: -62.447783 dBW
Power ratio Pr/Pt: 5.69143366e-4
Free-space loss: 32.447783 dB
Wavelength: 299.792 mm
Net gain / named loss: 0.0000 dB

Calculation path

$L_{\mathrm{FS}}=20\log_{10}\left(\frac{4\pi d}{\lambda}\right)=32.447783\,\mathrm{dB}$
$P_r=P_t+G_t+G_r-L_{\mathrm{FS}}-L_{\mathrm{pol}}-L_{\mathrm{other}}$
Fixed gain is not fixed physical aperture: changing frequency while holding gain constant answers a different comparison than holding aperture constant.

Model

What this calculator is doing

Friis relates available powers through the spherical spreading factor (λ/4πd)². The dB form adds gains and subtracts positive loss magnitudes.

Decision

How to read the result

Treat the answer as an unobstructed far-field reference. Differences from measurement can come from patterns, polarization, obstruction, multipath, atmosphere, and reference planes.

Equations & conventions

$P_{r} = P_{t}G_{t}G_{r}(\frac{\lambda }{4\pi d})^{2}$
$P_{r}[\mathrm{dBm}] = P_{t} + G_{t} + G_{r} - L_{\mathrm{FS}} - L_{\mathrm{other}}$

Pt and Pr are available powers at the stated antenna reference planes.
Gt and Gr are directional gains, displayed in dBi.
d is separation in metres and λ is free-space wavelength.

Independently checked example

Checked example: 0 dBm through 0 dBi antennas at 1 GHz and 1 m gives −32.4478 dBm with no added losses.

Common mistakes

Applying Friis in the antenna reactive near field.
Subtracting antenna gain or entering a positive loss as a negative number.

Assumptions, validity & omissions

Far-field, unobstructed, free-space propagation.
Gains apply in the mutual antenna directions.
Ports are matched unless a named mismatch loss is entered; polarization is aligned unless an explicit loss is entered.
Indoor, terrain, foliage, atmospheric, multipath, and near-field behavior are excluded.

Sources & model provenance

Recommendation ITU-R P.525-5 (11/2024) (opens in a new tab) — In-force free-space attenuation model. Accessed 2026-09-05.

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