The free space path loss calculator above gives the single most important number in any radio link budget: how much signal strength disappears simply by spreading out between the transmitting antenna and the receiving one. Nothing is absorbed and nothing is reflected in this model. The power is still all there; it is just spread over a sphere that grows as the wave travels, and only the fraction that lands on the receiving antenna is captured.
Arb Digital builds free tools that pick one job and finish it properly. This page reports the loss in decibels, then carries it through to received power, link margin and the maximum distance at which the receiver would still hear anything. Those last three are what actually tell you whether a link will work.
What This Free Space Path Loss Calculator Does
It implements the standard free space attenuation formula and the surrounding link budget arithmetic. You give it a frequency, a distance, the transmitter output, the antenna gains at each end and the feeder losses, and it returns the path loss and the power arriving at the receiver input. Against the receiver's stated sensitivity it also reports the margin you have left and, by inverting the formula, the distance at which that margin reaches zero.
Frequency and distance units are handled explicitly. Frequency can be entered in kilohertz, megahertz or gigahertz, and distance in metres, kilometres, statute miles or nautical miles. The tool converts everything internally to hertz and metres before calculating, which removes the single most common source of error in hand-worked path loss figures.
What it does not model is everything that makes real radio hard: terrain, buildings, foliage, rain, ground reflections, multipath fading and antenna misalignment. Free space loss is the best case. It is still the right starting point, because every other effect is quoted as an additional loss on top of it.
How to Use It
- Enter the frequency in its natural unit. 2400 MHz and 2.4 GHz give identical answers here, so use whichever the datasheet quotes.
- Give the real distance, not the map distance. For an elevated link the slant range between antennas is slightly longer than the ground distance, and at short ranges with tall masts the difference matters.
- Use conducted power at the radio, then subtract feeder loss separately. Do not enter effective radiated power in the transmit power box, or the antenna gain will be counted twice.
- Take sensitivity from the datasheet at the data rate you plan to use. A receiver that manages −100 dBm at the lowest rate may only reach −75 dBm at the highest.
- Judge the link on the margin, not the received power. A margin of 20 dB or more is a comfortable outdoor link; under 10 dB and normal weather or a passing vehicle will drop it.
The Formula: How Free Space Path Loss Is Calculated
The physical form is FSPL = (4πd ÷ λ)², where d is the separation and λ is the wavelength. Expressed in decibels that becomes FSPL(dB) = 20 × log10(d) + 20 × log10(f) + 20 × log10(4π ÷ c), with d in metres, f in hertz and c the speed of light. ITU-R Recommendation P.525, Calculation of free-space attenuation, is the standards document that defines this quantity.
Collapse the constant term for a particular pair of units and you get the versions people memorise. For distance in kilometres and frequency in megahertz, that constant is 32.44. For kilometres and gigahertz it is 92.45, and for metres and megahertz it is −27.55. The constant is the only thing that changes, and mixing up which one belongs to which unit pair is where most errors come from.
The link budget wrapped around it is simply addition and subtraction in decibels: received power = transmit power + transmit antenna gain + receive antenna gain − feeder losses − path loss. Margin is the received power minus the receiver sensitivity, and because both are already in dBm the margin comes out directly in decibels.
Work the defaults. At 2,400 MHz over 1 km, 20 × log10(1) is 0 and 20 × log10(2400) is 67.60, so the path loss is 67.60 + 32.44 = 100.05 dB. The calculator carries the exact speed of light rather than the rounded 32.44 constant, which is why the two agree to within a hundredth of a decibel. With 20 dBm of transmit power, 3 dBi at each antenna and 1 dB of feeder loss, the received power is 20 + 3 + 3 − 1 − 100.05 = −75.05 dBm. Against a −90 dBm sensitivity that leaves 14.95 dB of margin, and inverting the formula puts the zero-margin range at about 5.6 km.
Why Higher Frequencies Lose More Without Absorbing Anything
The formula says loss rises with frequency, which sounds like the atmosphere is eating the signal. It is not, at least not in this term. Free space contains nothing to absorb anything. The frequency dependence comes entirely from the receiving antenna.
A wave spreading from a point source obeys the inverse square law, and that part of the loss depends only on distance. But the effective aperture of an antenna of fixed gain is proportional to the square of the wavelength. A 3 dBi antenna at 900 MHz physically intercepts about seven times more of the passing wavefront than a 3 dBi antenna at 2.4 GHz, because it is a bigger object. Holding gain constant while raising frequency therefore shrinks the collector, and the extra 20 dB per decade of frequency in the formula is exactly that shrinkage.
This has a practical consequence that surprises people. If you hold the physical antenna size constant instead of the gain, higher frequency links actually improve, because a dish of fixed diameter has more gain at higher frequency. That is why satellite and microwave backhaul links keep climbing in frequency. It is only in the fixed-gain, omnidirectional case that higher frequency is a straight penalty.
Free Space Loss Is a Floor, Not a Forecast
Real links are always worse than this number, often by a very large amount. Free space assumes an unobstructed straight line with no reflecting surfaces anywhere near it, which almost never exists near the ground. The wider framework that free space loss sits inside is set out in ITU-R Recommendation P.341, The concept of transmission loss for radio links, which separates the free space component from the additional losses a real path adds.
The first thing that breaks it is the Fresnel zone. Even a completely clear line of sight is not enough; the ellipsoid of space around that line has to be substantially clear too, and an obstruction that never touches the direct ray can still cost several decibels. Ground reflections are the second issue: at longer ranges over flat terrain the reflected ray arrives out of phase with the direct one and the loss starts increasing with the fourth power of distance rather than the square, which is 40 dB per decade instead of 20.
Indoors, add roughly 3 to 5 dB per plasterboard wall and considerably more for concrete, brick or foil-backed insulation. Outdoors above about 10 GHz, rain becomes a real absorber and heavy rainfall can add tens of decibels over a few kilometres. Foliage is worse than most people expect, particularly when wet. None of these are in the free space figure, which is why a sensible design carries 20 dB or more of margin rather than the bare minimum.
Reading dBm, dBi and dB Without Mixing Them Up
Three similar-looking units do three different jobs here. dBm is an absolute power, referenced to one milliwatt, so 0 dBm is 1 mW, 20 dBm is 100 mW and −90 dBm is one thousand-millionth of a milliwatt. dBi is an antenna gain relative to an isotropic radiator. Plain dB is a ratio with no reference, which is what path loss, feeder loss and link margin all are.
The reason the whole link budget is done in decibels is that multiplication becomes addition. Every gain and loss along the chain is a multiplying factor in linear terms, and stacking them in logarithms turns the entire calculation into arithmetic you can do on paper. Two useful anchors: 3 dB is a factor of two in power, and 10 dB is a factor of ten. A 6 dB gain is therefore four times the power, and a 30 dB loss is one thousandth.
Note also that doubling the distance costs 6 dB, and that this is why range extension is expensive. Recovering a doubling of range requires 6 dB found somewhere else, which means four times the transmit power or a meaningfully larger antenna at one end. The inverse square law calculator covers the same spreading behaviour in its general form, for light and sound as well as radio.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the 32.44 constant with the wrong units — it belongs to kilometres and megahertz only. Kilometres with gigahertz needs 92.45, and metres with megahertz needs −27.55.
- Entering radiated power and antenna gain both — effective radiated power already includes the antenna, so adding the gain again inflates the budget by the gain figure.
- Treating the free space figure as the expected loss — it is the best case. Terrain, walls, foliage, rain and ground reflection all add on top.
- Quoting sensitivity at the wrong data rate — receiver sensitivity degrades sharply as the modulation gets denser, sometimes by 25 dB across a radio's rate range.
- Assuming line of sight is enough — the Fresnel zone around the direct ray also has to be clear, and an obstruction that never touches the line can still cost several decibels.
Related Free Tools From Arb Digital
The wavelength this calculation depends on is what the wavelength calculator gives from frequency and propagation speed, and it also sets the physical size of any antenna for the band. Unit changes between hertz, kilohertz, megahertz and gigahertz are handled by the frequency converter, and the reciprocal relationship between a frequency and its period is in the frequency and period calculator. For long terrestrial links the horizon matters as much as the loss, and the Earth curvature calculator shows how far apart two antennas of a given height can see each other. The general spreading law behind all of this is in the inverse square law calculator, and the full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
In decibels it is 20 times the log of the distance plus 20 times the log of the frequency plus a constant that depends on the units. For kilometres and megahertz that constant is 32.44, for kilometres and gigahertz it is 92.45, and for metres and megahertz it is minus 27.55.
Because the effective aperture of an antenna of fixed gain shrinks with the square of the wavelength. The spreading of the wave depends only on distance; the frequency term is the receiving antenna becoming a physically smaller collector as frequency rises.
Exactly 6 dB, because the loss goes with the square of distance and a factor of four in power is 6 decibels. Recovering that needs four times the transmit power or an equivalent gain at one of the antennas.
No, it is the best case and real links are always worse. Terrain, buildings, foliage, rain above about 10 GHz and ground reflections all add losses on top, which is why designs normally carry 20 dB or more of margin.
Twenty decibels or more is comfortable for an outdoor fixed link. Below about 10 dB the connection becomes sensitive to weather, moving obstructions and antenna drift, and it will drop intermittently rather than fail cleanly.
dBm is an absolute power referenced to one milliwatt, so 0 dBm is 1 mW. dBi is antenna gain relative to an isotropic radiator. Plain dB is a ratio with no reference, which is what path loss, feeder loss and margin all are.
No. The Fresnel zone, an ellipsoid of space surrounding the direct ray, also has to be substantially clear. An obstruction that never touches the straight line between antennas can still cost several decibels.
This tool is provided for educational and planning use. Real propagation depends on terrain, obstructions and weather that this model does not include, and nothing on this page is radio licensing or safety guidance.
