Path Loss and Link Budget — RF System Planning
Every time you make a radio contact, there is an invisible accounting going on in the background. Power leaves your transmitter, travels through a feedline, launches from your antenna, spreads across space, arrives at a distant antenna, passes through another feedline, and finally reaches the receiver. At every step, some energy is added (by antennas) or lost (to cable attenuation, free space spreading). The net result — the signal level at the receiver — determines whether the contact works.
A link budget is simply this accounting written down in dB values, step by step, from transmitter to receiver. It lets you answer definitively: "Will this link work?" before you build it, buy it, or point your antenna at it. Understanding link budgets is what separates the engineer from the guesser — and in amateur radio, it is the skill that lets you predict whether your 5-watt simplex link to a repeater will work, whether your 2m setup is adequate for EME, or whether a 50-watt HF station can support a reliable NVIS link at 500 km.
- What path loss is and why it exists (the inverse square law)
- Free space path loss — the FSPL formula and what the 32.44 constant means
- Additional real-world losses beyond free space
- EIRP (Effective Isotropic Radiated Power)
- Building a complete link budget step by step
- Link margin and why it matters
- Worked example: 144 MHz FM link, 50 km, 50 W, 5 dBd antenna
- Both the FSPL calculator and the full link budget calculator
A complete RF link budget: transmitter power minus feedline loss plus antenna gain gives EIRP. Subtract FSPL plus real-world losses, then add receive antenna gain minus receive feedline loss. Compare the result to receiver sensitivity to find link margin.
View LargerWhat Path Loss Is
Path loss is the reduction in signal power as it travels through space from the transmitter to the receiver. Even in a perfect vacuum with no absorbing or scattering material between the two antennas, signal power would still decrease with distance. This is not because energy is being absorbed — it is because the energy is spreading out in three dimensions, and a distant receiver only intercepts a tiny fraction of the total energy radiated.
Imagine throwing a bucket of water upward. A person nearby gets soaked — a large fraction of the water hits them. A person far away barely gets wet — the water has spread out in all directions and only a tiny fraction of the drops reach them. Radio waves behave the same way. The transmitting antenna radiates energy in a three-dimensional pattern, and the power density (watts per square meter) at any point in space decreases as that energy spreads over an ever-larger sphere. This spreading loss is the fundamental reason why radio signals become weaker with distance.
The Inverse Square Law
The power density from an isotropic (perfectly omnidirectional) point source decreases with the square of the distance. This is the inverse square law, and it applies to all radiating sources — light, sound, radio waves, and gravity.
Power density S = PT / (4πd²) (W/m²)
Where:
PT = transmitted power (W)
d = distance from transmitter (m)
4πd² = surface area of a sphere of radius d
If you double the distance, the power density drops to one-quarter (6 dB loss).
If you increase distance by 10×, power density drops to 1/100 (20 dB loss).
The inverse square law gives us the 20 log(d) term in the path loss formula. Every time distance doubles, path loss increases by 6 dB. Every decade of distance (10×) adds 20 dB of loss. A link at 100 km has 6 dB more loss than a link at 50 km. A link at 1,000 km has 20 dB more loss than a link at 100 km. This rapid growth of path loss with distance is why long-range communication requires either high power, high-gain antennas, low receiver noise figures, or some combination of all three.
Free Space Path Loss Formula
The complete free space path loss formula combines the inverse square law with the effect of frequency on the effective receiving aperture of an isotropic antenna:
FSPL (dB) = 20 × log10(dkm) + 20 × log10(fMHz) + 32.44
Where:
dkm = distance in kilometers
fMHz = frequency in MHz
32.44 = constant (derived from the wavelength formula and unit conversions)
Alternative form using meters and Hz:
FSPL (dB) = 20 × log10(dm) + 20 × log10(fHz) − 147.55
The 32.44 constant comes from the unit conversions in the full free space path loss derivation. When distance is in kilometers and frequency is in MHz, the constants combine to give +32.44 dB. This constant represents the baseline free space loss at 1 km and 1 MHz (which equals 32.44 dB).
Why does frequency appear in the path loss formula if we said the inverse square law is the cause of path loss? The frequency term comes from the definition of antenna effective aperture. An isotropic antenna has an effective aperture proportional to the square of the wavelength (λ²/4π). Higher frequency means shorter wavelength means smaller effective aperture. A 433 MHz antenna captures less power from a given power density than a 144 MHz antenna of the same physical size. In a link budget, this effect is usually treated as part of the antenna gain, but the standard FSPL formula bundles it into the path loss for convenience.
144 MHz, 50 km:
FSPL = 20 × log(50) + 20 × log(144) + 32.44
= 20 × 1.699 + 20 × 2.158 + 32.44
= 33.98 + 43.16 + 32.44 = 109.6 dB
144 MHz, 100 km:
FSPL = 20 × log(100) + 20 × log(144) + 32.44
= 40 + 43.16 + 32.44 = 115.6 dB (exactly 6 dB more than 50 km — distance doubled)
432 MHz, 50 km:
FSPL = 20 × log(50) + 20 × log(432) + 32.44
= 33.98 + 52.71 + 32.44 = 119.1 dB (9.5 dB more than at 144 MHz for same distance)
Real-World Losses Beyond Free Space
The FSPL formula gives the minimum possible path loss in a perfect vacuum. Real-world paths add additional losses that must be included in a realistic link budget:
Atmospheric absorption: Water vapor and oxygen absorb microwave energy at specific frequencies. At frequencies below 1 GHz, atmospheric absorption is negligible for most amateur paths. Above 10 GHz, it becomes significant — the 22 GHz water vapor absorption band and the 60 GHz oxygen absorption band set practical limits for very long paths at those frequencies. For most 2m and 70cm links, atmospheric absorption adds less than 0.5 dB.
Rain attenuation: Heavy rain absorbs and scatters signals above about 5 GHz. For the amateur 10 GHz (3 cm) band, a heavy rain shower along the path can add 10–30 dB of attenuation per kilometer of rain. This is why 10 GHz links over longer distances need generous link margins to survive rain events.
Multipath and terrain diffraction: In a real environment, signals reflect off buildings, hills, and other surfaces, creating multiple paths between transmitter and receiver. At some frequencies and positions, these multipath reflections combine destructively (out of phase), creating deep fades — sometimes 20–40 dB below the expected signal level. This is why mobile VHF/UHF signals fade rapidly as you drive — the multipath geometry changes with position, alternating between constructive and destructive interference.
Vegetation attenuation: Trees and dense vegetation absorb VHF and UHF signals. A path through dense forest at 144 MHz might add 10–30 dB of excess loss compared to the same path over open ground. At 432 MHz and above, vegetation attenuation is even higher.
Knife-edge diffraction: A signal passing over a hilltop or building edge can be partially diffracted — bent around the obstacle. Diffraction adds loss (typically 6–20 dB) but it is often better than complete blockage, which would be the result if diffraction did not occur.
EIRP — Effective Isotropic Radiated Power
Before calculating received signal level, you need the EIRP — the effective power delivered by the transmitting system, referenced to an isotropic radiator. EIRP accounts for the transmitter output power, any feedline losses, and the antenna gain.
EIRP (dBm) = PTX (dBm) − LTX cable (dB) + GTX antenna (dBi)
Or equivalently with ERP (using dBd):
ERP (dBm) = PTX (dBm) − LTX cable (dB) + GTX antenna (dBd)
EIRP = ERP + 2.15 dB
EIRP is expressed in dBm (dB relative to 1 milliwatt) when used in link budgets. A 50-watt (47 dBm) transmitter with 2 dB feedline loss and a 6 dBi antenna has an EIRP of 47 - 2 + 6 = 51 dBm. This 51 dBm EIRP is what you use as the starting point for the received signal level calculation.
The EIRP concept is important because it separates the transmitter system from the propagation path. Two transmitters with the same EIRP but different power/antenna combinations produce identical received signal levels at any given distance, regardless of how the EIRP was achieved. 1 watt into a 20 dBi antenna has the same EIRP as 100 watts into a 0 dBi antenna — both give 50 dBm EIRP. This equivalence is fundamental to RF system design.
Building the Link Budget
A complete link budget follows this path of calculations from transmitter to receiver:
RSL (dBm) = EIRP (dBm) − FSPL (dB) − Additional losses (dB) + GRX antenna (dBi) − LRX cable (dB)
Simplified for typical line-of-sight VHF/UHF links with minimal additional losses:
RSL = PTX (dBm) − LTX cable + GTX ant − FSPL + GRX ant − LRX cable
Each term in this equation contributes to the final received signal level. A gain term (antenna gain) adds to the RSL. A loss term (feedline loss, path loss) subtracts from it. The beauty of working in dBm and dB is that all of these factors combine with simple addition and subtraction rather than complex multiplication and division.
Link Margin
Once you know the received signal level, you compare it to the receiver sensitivity to find the link margin:
Link Margin (dB) = RSL (dBm) − Receiver Sensitivity (dBm)
A positive link margin means the link works.
A negative link margin means the link fails.
Practical minimum margins:
• Voice (FM or SSB): +10 to +20 dB minimum for reliable operation
• Digital data: +6 to +10 dB minimum
• Safety-critical links: +20 dB or more recommended
The link margin is the safety buffer above the minimum required signal. You need this buffer because the FSPL formula calculates the best possible case — line of sight, no rain, no multipath fades. In practice, path conditions vary. A 20 dB link margin means that even if conditions deteriorate by 20 dB (rain, multipath, antenna misalignment), the link still works. A 5 dB margin is likely to fail whenever conditions are less than ideal.
For amateur radio applications, a rule of thumb is to aim for at least 20 dB of margin on voice links where reliability matters. If your link budget shows less than 10 dB margin, you need to improve the system — add power, improve antennas, reduce feedline losses, or accept that the link will be marginal.
Worked Example: 144 MHz FM Link
A 144 MHz FM repeater system links a mobile station to a mountain-top repeater 50 km away. Here are the parameters and the full link budget:
Mobile TX power: 50 W = +47 dBm
Mobile antenna (5/8 wave vertical): 5 dBi gain, 1 dB feedline loss
Mobile EIRP = 47 − 1 + 5 = 51 dBm
FSPL at 144 MHz, 50 km: 109.6 dB (calculated above)
Additional loss (some terrain): 3 dB
Total path loss: 112.6 dB
Repeater receive antenna: 10 dBi collinear, 1 dB feedline loss
RSL at repeater receiver = 51 − 112.6 + 10 − 1 = −52.6 dBm
Repeater receiver sensitivity: −120 dBm (typical for a good repeater)
Link margin = −52.6 − (−120) = 67.4 dB
Result: PASS with 67.4 dB margin — an extremely strong link. This is typical for a 50-km VHF link from a 50W mobile to a mountaintop repeater.
Repeater TX power: 50 W = +47 dBm
Repeater antenna: 10 dBi collinear, 1 dB feedline loss
Repeater EIRP = 47 − 1 + 10 = 56 dBm
Total path loss: 112.6 dB
Mobile receive antenna: 5 dBi, 1 dB feedline loss
RSL at mobile = 56 − 112.6 + 5 − 1 = −52.6 dBm
Mobile receiver sensitivity: −118 dBm (typical for a good FM radio)
Link margin = −52.6 − (−118) = 65.4 dB
Result: PASS with 65.4 dB margin.
This example is deliberately a strong, easy link. Now let us look at a more challenging case:
HT TX power: 5 W = +37 dBm
HT rubber duck antenna: 0 dBi, no appreciable feedline loss (short internal lead)
HT EIRP = 37 − 0 + 0 = 37 dBm
FSPL + terrain: 112.6 dB
Repeater receive: 10 dBi, 1 dB feedline loss
RSL = 37 − 112.6 + 10 − 1 = −66.6 dBm
Repeater sensitivity: −120 dBm
Link margin = −66.6 − (−120) = 53.4 dB
Result: Still PASS with 53.4 dB margin — the link works even with the modest HT.
Free Space Path Loss Calculator
Free Space Path Loss Calculator
Calculates FSPL in dB using the formula: FSPL = 20×log10(d_km) + 20×log10(f_MHz) + 32.44
Full Link Budget Calculator
Link Budget Calculator
Enter your transmit and receive system parameters to calculate received signal level and link margin. You can enter FSPL directly or auto-calculate it from distance and frequency.
Frequently Asked Questions
Why does path loss increase with frequency if frequency does not affect how energy spreads?
This is a subtle but important point. The inverse square spreading of power density is the same at all frequencies. However, the effective aperture of a receiving antenna — the area it presents to the incoming wave for the purpose of collecting energy — is proportional to the square of the wavelength. An isotropic receiving antenna at 432 MHz captures less energy from a given wave than the same antenna at 144 MHz. In the FSPL formula, this aperture effect is bundled into the path loss number. You could equally well leave frequency out of FSPL and instead include the frequency-dependent aperture in the receive antenna gain, but the standard convention includes it in FSPL.
What is a typical receiver sensitivity for ham radio equipment?
Receiver sensitivity varies widely by frequency and mode. For a good 2m all-mode transceiver with a preamp, sensitivity for SSB is typically -125 to -135 dBm. For FM mode, sensitivity (for 12 dB SINAD) is typically -118 to -125 dBm. HF transceivers are typically -120 to -130 dBm for SSB. Commercial DMR and P25 digital radios may specify sensitivity at -116 to -120 dBm for 5% bit error rate. When doing link budgets, always use the sensitivity appropriate for your mode of operation.
How do I convert dBd antenna gain to dBi for a link budget?
Add 2.15 dB. A 5 dBd antenna has 5 + 2.15 = 7.15 dBi gain. This conversion is needed because EIRP is defined relative to an isotropic radiator (dBi reference), while many antenna specifications use a dipole reference (dBd). If you use dBd in an EIRP calculation, the EIRP you calculate is actually ERP (Effective Radiated Power), which is 2.15 dB less than EIRP. For casual link budgeting the difference is minor, but for precise work always convert to dBi.
Does FSPL apply to HF ionospheric paths?
Not directly. FSPL describes the spreading loss for a line-of-sight path in free space. An HF path via the ionosphere is not line-of-sight — the signal travels at an angle, reflects off a layer at 300 km altitude, and returns. The actual path length is longer than the surface distance, and there are additional losses from imperfect ionospheric reflection (typically 5–10 dB per hop) and D-layer absorption. For HF prediction, the VOACAP model is more appropriate than a simple FSPL calculation.
How much link margin is enough?
The required margin depends on the application and the variability of the path. For a fixed point-to-point VHF link with a clear line of sight over flat terrain, 15–20 dB is generally sufficient. For a mobile link where the vehicle may be parked in a valley or behind a building, 30+ dB is preferred. For satellite and EME paths with predictable, stable losses, 10–15 dB may be sufficient. Safety-critical communications (search and rescue, emergency management) should use at least 20 dB margin with additional margin added for the worst expected conditions.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.