Free Space Path Loss Calculator

Radio energy spreads over an expanding sphere, and the fraction a receiving antenna can catch falls with the square of distance. Enter the link distance and frequency, and this calculator returns the free-space path loss in decibels — the first and biggest line of every link budget.

Geometry's Tax on Radio

An isotropic radiator pours its power over a sphere of area 4πd²; a receiving antenna harvests the share its effective aperture (λ² ÷ 4π, for an isotropic receiver) intercepts — and the ratio of the two is the free-space path loss, FSPL = (4πd ÷ λ)², or in the engineer's working units, 20 log₁₀(d_km) + 20 log₁₀(f_MHz) + 32.44 dB. Nothing is absorbed; the energy is merely spread past catching — the "loss" is geometry's, and frequency enters because a higher frequency's smaller aperture catches less of the sphere (equivalently: at fixed antenna gain, aperture shrinks with λ²). This is Friis's transmission equation stripped to its universal term, the number every satellite pass, Wi-Fi plan and deep-space schedule starts by paying. The calculator evaluates it in the canonical km/MHz form and states its jurisdiction — free space — in its note, because the real world's reflections and absorptions are additions, not corrections. Even the "free space" of an anechoic chamber is audited against this formula before a single antenna is certified in it: the chamber's quiet zone is, by definition, the volume where measured loss matches Friis's within a decibel, so the calculator doubles as the calibration certificate's arithmetic for the rooms where antennas learn their own gains.

Worked Example: Wi-Fi Across Ten Kilometres

The defaults: 10 km at 2,400 MHz → 20 + 67.60 + 32.44 = 120.04 dB. Put flesh on it: a +20 dBm transmitter (100 mW) with modest +14 dBi antennas at both ends delivers 20 + 14 + 14 − 120 = −72 dBm at the receiver — comfortably above a Wi-Fi receiver's −90 dBm sensitivity floor, which is why point-to-point 2.4 GHz links span valleys on hobbyist budgets. Now the same link at 100 km: the distance term grows by 20 dB (ten times farther, the square law in logarithmic dress) and the margin shrinks to a whisper — long links are bought with antenna aperture (gain) or power, never with optimism. The calculator's two inputs are the fulcrum of every such negotiation.

Deep Space: The Formula at Its Most Heroic

Run the Voyager numbers mentally: at 15 billion km and 8,400 MHz, FSPL ≈ 20 log₁₀(1.5×10¹⁰) + 20 log₁₀(8400) + 32.44 ≈ 203.5 + 78.5 + 32.4 ≈ 314 dB — the received power from its 23 W transmitter arrives near 10⁻¹⁸ watts, a flux the Deep Space Network's 70 m dishes and cryogenic amplifiers exist to catch, bit by patient bit. That the same two-input formula prices a spacecraft's whisper and a router's shout is the decibel's finest advertisement and Friis's equation's claim to immortality. The calculator's fields accept the kilometres of interplanetary space as happily as the metres of a room (enter 0.01 for ten metres) — geometry's tax is scale-free, which is precisely why one page can levy it honestly.

The Moon Bounce and Other Heroics

Amateur radio's most romantic mode is EME — Earth–Moon–Earth — bouncing signals off the Moon: the path is 770,000 km of this page's spreading (at 144 MHz, FSPL ≈ 187 dB) plus the Moon's poor reflectivity (it returns some 6% of what strikes it, scattered), for a round-trip budget near 250 dB that nonetheless closes with big antennas, legal-limit power and weak-signal digital modes — contacts made, daily, by hobbyists off a celestial reflector. The calculator prices the free-space legs of that budget in two runs. Beside the interplanetary probes, the Moon bounce is FSPL's folk tradition: geometry's tax, paid gladly, for the pleasure of hearing one's own signal return two and a half seconds later with the Moon's accent on it.

The Inverse-Square Family Reunion

FSPL is the electromagnetic member of a family the hub keeps meeting: light's brightness, gravity's pull, sound's intensity and this radio spreading all fall as 1 ÷ d² for the same geometric reason — a fixed output painted over a sphere whose area grows as d². The family's unity is worth a paragraph because it converts intuition between domains: the photographer who knows two stops per doubling of distance (fourfold light, 6 dB in this page's currency) already owns the radio engineer's 6 dB-per-doubling rule, whether or not either has met the other's literature. The calculator's distance term is that shared inheritance, specialised to antennas — geometry charging the same tax in every currency of wave.

Related Tools

More from the Physics Calculators hub: the dB Gain Calculator — the arithmetic this loss must be budgeted in — and the Energy to Wavelength Calculator, for the λ inside this page's formula.

Frequently Asked Questions

Why does higher frequency lose more, if nothing absorbs it?

Because the receiving antenna's catch area, at fixed gain, shrinks as λ²: the same sphere of spreading power is sampled by a smaller net. Hold the physical dish size fixed instead and the verdict inverts — aperture antennas gain with frequency, which is why satellite links climb in frequency for their dish economics while free-space "loss" at fixed gain climbs too. The calculator quotes the fixed-gain convention (Friis's own), and this FAQ names the aperture convention, because half the arguments about FSPL in the wild are two conventions talking past each other under one formula's flag.

What does the real world add?

Everything else in the budget: ground-reflection interference (the two-ray model's nulls), diffraction over obstacles (knife-edge losses), atmospheric absorption (oxygen's 60 GHz wall, water vapour's lines), rain fade (severe above 10 GHz), foliage, walls (a brick wall can cost 10–20 dB at Wi-Fi frequencies) and multipath fading margins. Indoor and urban models (log-distance, COST, 3GPP's families) replace the exponent 2 with fitted values of 3–5. The calculator's free-space figure is the floor under all of them — the loss with every obstacle removed — and is labelled so, in its note, at every run.

How far can Wi-Fi actually reach?

With line-of-sight, high-gain dishes, legal power and this page's budget: tens of kilometres are routine for point-to-point links (the record under contest conditions runs to hundreds), because −90 dBm sensitivity against 120–140 dB of path loss leaves workable margins. The practical limits are the Fresnel zone's clearance (the path needs an ellipsoid of elbow-room, Earth curvature — this hub's page — claiming it at distance), interference, and regulation. The calculator sets the theoretical reach; the horizon calculator of this wave audits the geometry that usually binds first.

What is the 32.44?

The unit-conversion residue of the formula: 20 log₁₀(4π ÷ c) dressed in kilometres and megahertz — change the units and the constant changes (for metres and hertz it is −147.55 in the equivalent arrangement; for miles and MHz, 36.58). The calculator bakes the km/MHz form because link engineering quotes distance in kilometres and frequency in megahertz or gigahertz. Recognising the constant as bookkeeping, not physics, is the mark of a reader who owns the formula rather than renting it.

Do cables have path loss too?

Different mechanism, same dB ledger: a coaxial cable's loss per metre (from conductor resistance via the skin effect, and dielectric losses) is tabulated by manufacturers in dB per 100 m at stated frequencies, and enters link budgets as a plain subtraction beside the FSPL. Long antenna runs can eat a small antenna's entire gain — the calculator pair on this hub (this page for the air, the dB page for the sums) covers the ledger; the cable's own figure comes from its datasheet, the skin-depth page explaining why it worsens with frequency's square root before dielectric loss takes over.

Why do satellite TV dishes point once and work forever at 36,000 km?

Because the budget closes with room to spare at that fixed geometry: at 12 GHz over 36,000 km the path loss is about 205 dB, met by the satellite's transponder power and the dish's enormous aperture gain (a 60 cm dish at 12 GHz returns roughly 35 dBi), leaving a rain margin the link budgets of the dB page's kind juggle daily. Geostationary geometry trades the horror of the distance for the blessing of its constancy — no tracking, no Doppler drama, one Friis sum done once. The calculator prices that sum in the same two fields as a garden Wi-Fi link, the scale-invariance of the logarithm doing the honours.

How does this change for a link to a moving satellite?

The distance breathes — a low-orbit satellite's slant range swings from about 500 km overhead to nearly 3,000 km at the horizon within one pass, and the calculator's figure swings with it by 20 log₁₀ of the ratio, roughly 15 dB of variation the link must budget as margin or chase with power control — while the frequency acquires a Doppler shift the receiver must track (a separate account, kept by the hub's wave pages). Store-and-forward constellations are designed around exactly this breathing: the pass's worst geometry, priced by this formula, sizes the link.

Who was Friis?

Harald T. Friis (1893–1976), Danish-American engineer at Bell Labs, whose 1946 transmission formula organised radio link design into the gain-minus-loss bookkeeping every engineer since has used, and whose noise-figure work (the Friis formula for cascaded stages) accompanies it in every receiver text. The path-loss term this page computes is the opening move of his equation — the part that depends on nothing but distance, frequency and the geometry of spheres — and its durability across eighty years of radio revolutions is the equation's own best citation.