Friis Transmission Calculator converts transmitter power, antenna gains, distance, and frequency into received power for RF engineers and satellite teams planning link budgets.
Calculate Received Power Between Two Antennas with the Friis Transmission Calculator
The Friis Transmission Calculator converts transmitter power, antenna gains, distance, and frequency into the actual power arriving at a receiver’s feedpoint. RF engineers, wireless ISPs, and satellite link designers use it to confirm a receiver will see enough signal above its noise floor before a link is built.
How to Use
Enter transmitter power (Ptx) in dBm, W, or mW; transmitter gain (Gtx) and receiver gain (Grx) in dBi; transmission distance (Dr) in m, km, ft, or mi; and operating frequency (f0) in Hz, kHz, MHz, or GHz. The calculator returns received power (Prx), free-space path loss, and antenna aperture size.
Formula
Per the Friis transmission equation (H.T. Friis, “A Note on a Simple Transmission Formula,” Proceedings of the IRE, vol. 34, 1946), received power in linear terms is:
$$\frac{P_{rx}}{P_{tx}} = G_{tx} \, G_{rx} \left(\frac{\lambda}{4\pi d}\right)^2$$
In logarithmic form, this becomes a simple addition of gains minus free-space path loss:
$$P_{rx(dBm)} = P_{tx(dBm)} + G_{tx(dBi)} + G_{rx(dBi)} – FSPL_{(dB)}$$
Worked example:
at $P_{tx} = 13$ dBm, $G_{tx} = G_{rx} = 10$ dBi, $d = 10$ km, and $f_0 = 2.4$ GHz, FSPL works out to 120.05 dB, giving $P_{rx} = 13 + 10 + 10 – 120.05 = -87.05$ dBm. The most common input mistake is plugging dBi gain values directly into the linear form of the equation above — $G_{tx}$ and $G_{rx}$ must first be converted to linear ratios ($10^{G_{dBi}/10}$) before multiplying; only the logarithmic version accepts gain in dB directly.
The Friis equation also assumes far-field propagation. For links shorter than the Fraunhofer distance, $2D^2/\lambda$ (where $D$ is the larger antenna’s largest dimension), the antennas sit in each other’s near field and the equation understates actual coupling — a frequent source of confusion when this calculator is applied to short-range RFID or wireless-power links instead of the long-range communication links it was derived for.
Reference Table
| Constant | Value | Source |
|---|---|---|
| Speed of light in vacuum (c) | 299,792,458 m/s (exact) | SI Brochure (BIPM) / CODATA |
| Impedance of free space (η0) | 376.730 Ω | CODATA recommended values |
| Free-space path loss constant (d in km, f in GHz) | 92.45 dB | ITU-R P.525 |
FAQ
What does the Friis equation actually calculate?
It predicts the power arriving at a receiving antenna’s terminals given the transmitter’s power, both antennas’ gains, the distance between them, and the operating frequency, assuming free-space propagation with no obstructions.
What is antenna effective aperture?
Effective aperture (Ae) is the equivalent physical area an antenna presents to an incoming wave, related to gain by $A_e = G\lambda^2/(4\pi)$. Higher gain and longer wavelength both increase the area over which an antenna can capture incident power.
Why is my received power so much lower than the transmitted power?
Free-space path loss grows with the square of both distance and frequency, so even short links at gigahertz frequencies can lose over 100 dB — a factor of 10 billion in power — before antenna gain is added back in.
Does the Friis equation account for atmospheric or rain loss?
No. It models free-space propagation only. Real outdoor links need separate margins added for rain attenuation, atmospheric absorption, and multipath fading on top of the Friis result, per the relevant ITU-R propagation recommendations.
Can this calculator be used for RFID or near-field wireless power links?
Not reliably at very short range. The Friis equation assumes far-field conditions; inside the Fraunhofer distance, coupling behaves differently and this calculator’s output will not match measured results.