Communication Systems
Free-Space Path Loss (Friis) Calculator
Free-space path loss from frequency and distance, and received power from transmit power, antenna gains, and losses.
About this calculator
In free space, radiated power spreads over an ever-larger sphere, so the power captured by a receiving antenna falls with the square of distance — and, for a fixed-gain antenna, with the square of frequency, because a higher-frequency antenna of the same gain has a smaller capture aperture. Between isotropic antennas the loss is FSPL = 20·log₁₀(4πd/λ) dB, the standard form of the Friis transmission equation.
Expanded into the familiar engineering constants, this is 32.45 + 20·log₁₀(f in MHz) + 20·log₁₀(d in km) — this calculator evaluates the exact expression with c = 299 792 458 m/s rather than the rounded constant, and one worked step shows how the two agree.
Add transmit power, antenna gains (in dBi, i.e. relative to isotropic), and miscellaneous losses, and the received power follows by dB arithmetic: P_rx = P_tx + G_tx + G_rx − FSPL − L_misc. This is the propagation term at the core of every link budget; the link budget calculator wraps it with feed losses and receiver sensitivity to give margin.
Remember what "free space" means: no ground reflections, no obstructions, no atmosphere. Real terrestrial links see multipath fading, diffraction, and clutter on top of FSPL — treat this as the best-case floor, not a prediction of coverage.
Assumptions
- Unobstructed free-space propagation: no ground reflection, diffraction, multipath, or atmospheric absorption.
- Far-field (Fraunhofer) conditions — distance much greater than the wavelength and the antenna aperture size.
- Antenna gains are boresight values in dBi with matched polarization between the two antennas.
When to use this calculator
Appropriate for
- Estimating idealized free-space path loss for a line-of-sight link at a given distance and frequency
- A baseline path-loss term in an early link budget before adding real-world margins
- Teaching the inverse-square and frequency dependence of radio propagation
Not suitable for
- Non-line-of-sight, terrestrial, or indoor links, where diffraction, reflection, and clutter dominate — use a terrain or empirical propagation model
- Links affected by atmospheric absorption, rain fade, or multipath, none of which free-space loss includes
- Final link design without appropriate fade margins and a site-specific propagation study
What this calculator does not cover
- Free space only — terrestrial links add ground-reflection (two-ray), diffraction, clutter, and fading terms that can exceed FSPL by tens of dB.
- No atmospheric effects: rain attenuation and gaseous absorption, significant above roughly 10 GHz, are not modeled.
- Near-field results are flagged but not corrected — inside the Fraunhofer distance the concept of a single path-loss number breaks down.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
Why does path loss increase with frequency if free space doesn't absorb power?
It doesn't, physically — the spreading loss is frequency-independent. The frequency term appears because FSPL is defined between isotropic antennas, and an isotropic (or any fixed-gain) antenna has an effective aperture that shrinks with the square of frequency. Fixed-size dishes, whose gain grows with frequency, can actually improve a link at higher frequency.
What is the 32.45 constant in the common FSPL formula?
It is 20·log₁₀(4π×10⁹/c), the exact 20·log₁₀(4πdf/c) expression regrouped so frequency is in MHz and distance in km. Variants like 32.44 or 92.45 (GHz·km) are the same equation with different units or rounding.
When is the free-space model actually valid?
When the first Fresnel zone is clear of obstacles and reflections are negligible — satellite links, short line-of-sight microwave hops, or lab conditions. For terrestrial mobile links it is a lower bound; measured loss is nearly always higher.
References
- Friis, H. T., “A Note on a Simple Transmission Formula,” Proceedings of the IRE, vol. 34, no. 5, 1946
- Rappaport, T. S., Wireless Communications: Principles and Practice, 2nd ed., Ch. 4 (free-space propagation)
- ITU-R Recommendation P.525, Calculation of free-space attenuation
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