Friis Transmission & Path Loss Calculator
Enter power, antenna gains, losses, distance and frequency to get path loss, received power, link margin and maximum range.
Step-by-step
- Enter valid values to begin.
Free-space (line-of-sight) model: ITU-R P.525 free-space attenuation and the Friis transmission equation, valid in the far field with matched, polarisation-aligned antennas. Real links add ground reflection, terrain and obstruction loss, atmospheric absorption (oxygen peaks near 60 GHz, water vapour near 22 GHz), rain fade and multipath. Treat a margin below about 10 dB as fragile and verify with a site survey. Receive voltage assumes a 50 Ω input.
Friis and Path Loss: Counting the Decibels Between Two Antennas
Core Engineering Principles
Free-space loss is geometry, not absorption. A transmitter spreads its power over a sphere of area 4πd², so the power density falls with the square of distance, and the receiving antenna’s effective area is λ²/4π times its gain. Combine those and you get Friis: Pr = PtGtGr(λ/4πd)². In decibels the path loss is 20 log(4πd/λ), or 32.44 + 20 log dkm + 20 log fMHz. Doubling the distance costs 6 dB, and so does doubling the frequency, because the same antenna aperture collects less at a shorter wavelength.
A link budget just adds and subtracts: transmit power, minus cable loss, plus antenna gain gives EIRP; subtract path loss and every other loss, add the receive gain, subtract receive cable loss, and you have the signal at the receiver. Compare that with sensitivity and the difference is margin. We want 10 dB or more because real links fade. Add ground reflection, trees, buildings, rain, multipath and gaseous absorption, with oxygen peaking near 60 GHz and water vapour near 22 GHz, and the free-space number stops being the truth. Keep the first Fresnel zone, at least 60% of it, free of obstructions, or an optimistic budget turns into a dropped link.
Pr = EIRP − FSPL − losses + Gr − Lrx • Margin = Pr − sensitivity
rF1 = 8.657 √(Dkm / fGHz) m at midpoint
NEC & Standard References
ITU-R P.525 gives the free-space attenuation formula used here. ITU-R P.530 covers terrestrial line-of-sight system design, ITU-R P.676 gas absorption and ITU-R P.838 rain attenuation. IEEE Std 145 defines gain, EIRP and related terms. Regulators such as the FCC (Part 15) and ETSI limit the radiated power in EIRP terms, not the conducted power, so antenna gain uses up your allowance.1. EIRP = 20 − 1 + 15 = 34.00 dBm (2.51 W).
2. FSPL = 32.44 + 0 + 67.60 = 100.04 dB; the exact-c form gives 100.05 dB.
3. Pr = 34.00 − 100.05 − 3 + 15 − 1 = −55.05 dBm, about 3.1 nW.
4. Margin = −55.05 + 90 = 34.95 dB, healthy.
5. Free-space range at zero margin is 55.9 km, or 17.7 km keeping 10 dB.
6. First Fresnel radius at midpoint = 8.657 × √(1/2.4) = 5.59 m.
- Don’t mix dBi and dBd. A dipole’s gain is 2.15 dBi, so an antenna quoted in dBd is 2.15 dB smaller than the same number in dBi.
- Maximum range is an upper bound. Earth curvature and terrain stop the link long before the free-space limit; 55.9 km needs very tall masts.
- Polarisation mismatch costs real dB. A cross-polarised link can lose 20 dB or more.
- Near-field breaks Friis. Under about 10 wavelengths, or inside 2D²/λ for large dishes, the formula is optimistic.