Hong Life CalculatorsUnderstanding the free space path loss and link budget calculator — concept and principle
Free space path loss (FSPL) is how much a radio signal weakens between two antennas with nothing in between but empty space. This calculator gives FSPL from distance and frequency, then adds transmit power and both antenna gains to estimate the received power. It is the first step in planning Wi-Fi bridges, telemetry, satellite and amateur radio links.
How it is calculated
- FSPL (dB) = 20 log₁₀(d) + 20 log₁₀(f) + 32.45, with d in kilometres and f in megahertz.
- Received power (dBm) = P_t + G_t + G_r − FSPL.
P_t is transmit power in dBm, G_t and G_r the antenna gains in dBi (relative to an isotropic antenna). Because everything is in decibels, the link budget is simple addition and subtraction. The constant 32.45 is 20 log₁₀(4π × 10³ × 10⁶ / c), which absorbs the unit conversions (more precisely 32.44).
The principle
The formula comes from the Friis transmission equation. Power leaving an isotropic antenna spreads over a sphere of area 4πd², so power density falls with the square of distance. A receiving antenna captures power in proportion to its effective area, which for an isotropic antenna is λ²/4π; shorter wavelengths have smaller capture areas. Together these give a loss of (4πd/λ)² = (4πdf/c)². That is why the loss grows by 6 dB every time distance or frequency doubles, and by 20 dB per tenfold increase.
Worked example
- 20 log₁₀(10 km) = 20.00 dB.
- 20 log₁₀(2400 MHz) ≈ 67.60 dB.
- FSPL = 20.00 + 67.60 + 32.45 ≈ 120.05 dB.
- Gains: P_t + G_t + G_r = 20 + 10 + 10 = 40 dBm.
- Received power = 40 − 120.05 ≈ −80.05 dBm.
| Distance (km) | FSPL (dB) |
|---|---|
| 2.5 | 108.013025 |
| 5 | 114.0336249 |
| 7.5 | 117.5554501 |
| 10 | 120.0542248 |
| 12.5 | 121.9924251 |
| 15 | 123.57605 |
| 20 | 126.0748247 |
How to read the result
Compare the received power with the receiver's sensitivity at the data rate you need; the difference is the fade margin. Planners commonly keep 10 to 20 dB of margin for weather, multipath and misalignment. At −80 dBm, a Wi-Fi link at 2.4 GHz will usually connect only at modest data rates. To gain margin, raise antenna gain on both ends (each 3 dB doubles effective power), shorten the path, or use a lower frequency.
Common mistakes
- Entering distance in metres or frequency in GHz while keeping the 32.45 constant (it applies only to km and MHz).
- Forgetting cable and connector losses between radio and antenna.
- Ignoring the Fresnel zone; trees, terrain or roofs inside it add loss even with visual line of sight.
- Treating FSPL as absorption; it is purely geometric spreading, and air absorption is extra.
Frequently asked questions
Why does higher frequency have more path loss?
The spreading is the same, but a receiving antenna of fixed gain has a smaller effective area at shorter wavelength, so it captures less power.
How much does doubling the distance cost?
About 6 dB, meaning one quarter of the received power.
What constant do I use for metres and hertz?
With d in metres and f in hertz the constant is about −147.55 dB.
Sources: Friis, H. T., A Note on a Simple Transmission Formula, Proceedings of the IRE, 1946 · ITU-R Recommendation P.525, Calculation of free-space attenuation