Free Space Path Loss (FSPL) Calculator
Free space path loss is radio signal attenuation caused by geometric spreading in free space — the fundamental formula behind every wireless link budget calculation:
FSPL(dB) = 20·log₁₀(d) + 20·log₁₀(f) + 20·log₁₀(4π/c), with d in meters, f in hertz, and c = 299,792,458 m/s.
3-Way Solver
Mini Link Budget Context
FSPL is the largest loss component in a link budget: Prx = EIRP − FSPL + Gr (all in dB/dBm).
FSPL vs Distance Table (dB)
Values computed with the formula above (c = 299,792,458 m/s).
| Band | 100 m | 1 km | 10 km | 100 km |
|---|---|---|---|---|
| LoRa 868 MHz | 71.22 | 91.22 | 111.22 | 131.22 |
| FM 100 MHz | 52.45 | 72.45 | 92.45 | 112.45 |
| LTE 900 MHz | 71.53 | 91.53 | 111.53 | 131.53 |
| LTE 1800 MHz | 77.55 | 97.55 | 117.55 | 137.55 |
| WiFi 2.4 GHz | 80.05 | 100.05 | 120.05 | 140.05 |
| WiFi 5 GHz | 86.43 | 106.43 | 126.43 | 146.43 |
| 5G mmWave 28 GHz | 101.39 | 121.39 | 141.39 | 161.39 |
Scope limits vs the EIRP calculator
This tool computes free space path loss (FSPL) as the primary quantity — a 3-way solver (FSPL from d & f, d from FSPL & f, f from FSPL & d) plus link budget context. This tool does not compute transmit power (EIRP), ERP↔EIRP conversion, or regulation tables — that is the EIRP calculator’s scope. Its “Friis Distance” tab is a distance estimator from the power side (EIRP, receiver gain, minimum power), while the “Distance” mode here solves distance purely from the FSPL figure and frequency.
Frequently Asked Questions
- What is the free space path loss formula?
- FSPL(dB) = 20·log₁₀(d) + 20·log₁₀(f) + 20·log₁₀(4π/c), with d in meters, f in hertz, and c = 299,792,458 m/s. This formula is derived from the Friis transmission equation for isotropic antennas in free space.
- What is the FSPL for a 1 km distance at 2.4 GHz?
- FSPL = 100.05 dB. Calculation: 20·log₁₀(1000) + 20·log₁₀(2,400,000,000) + 20·log₁₀(4π/299,792,458) = 60 + 187.60 − 147.55 = 100.05 dB.
- Why do higher frequencies suffer greater loss?
- Because an isotropic antenna captures power proportional to the square of the wavelength (λ²). Each time frequency doubles, FSPL rises 20·log₁₀(2) = 6.02 dB at the same distance — for example: 1 km at 4.8 GHz (twice 2.4 GHz) = 106.07 dB, exactly 6.02 dB above 100.05 dB. For comparison, 1 km at 5 GHz = 106.43 dB.
- How do you use FSPL in a link budget?
- Received power Prx = EIRP − FSPL + Gr. Example: EIRP 36 dBm, FSPL 100.05 dB (1 km @ 2.4 GHz), receiver gain 5 dBi → Prx = −59.05 dBm, still far above typical WiFi sensitivity (−85 dBm).
- How does this tool differ from the EIRP calculator?
- This tool makes FSPL the primary output with a 3-way solver, while the EIRP calculator computes effective radiated power and ERP↔EIRP conversion. The two complement each other in one link budget: EIRP provides the transmit power, FSPL provides the loss.
Free tool by NRTechStudio