Free Space Path Loss Calculator
Enter a frequency and distance to find the free space path loss (FSPL) in decibels. Add transmit and receive antenna gains plus feeder cable losses to get the full link budget. Switch between metric and imperial distance units and between Hz, MHz or GHz for frequency. Results update as you type, with a step-by-step derivation and a chart of how loss changes with distance.
What is free space path loss?
Free space path loss (FSPL) is the attenuation a radio signal experiences as it travels through a vacuum (or clear air) between two isotropic antennas. It is not caused by absorption or scattering but by the geometric spreading of the wavefront over an ever-larger sphere. The further the wave travels, the thinner the energy is spread, so the receiving antenna captures a smaller fraction of it. FSPL is expressed in decibels and increases with both distance and frequency.
The FSPL formula and how to use it
The standard formula is FSPL(dB) = 20 log10(d) + 20 log10(f) + 20 log10(4 pi / c), where d is the distance in metres and f is the frequency in Hz. A practical shortcut that avoids large exponents is FSPL = 20 log10(d_km) + 20 log10(f_MHz) + 32.44. Both give the same result. The 32.44 constant is derived from 20 log10(4 pi / c), where c = 299,792,458 m/s. Because both terms use a 20x multiplier, doubling the distance adds 6 dB, and doubling the frequency also adds 6 dB.
Link budget: antenna gains and feeder losses
In a real system, antenna gains reduce the effective loss and feeder losses increase it. The link budget equation is: Effective loss = FSPL - TX antenna gain (dBi) - RX antenna gain (dBi) + TX feeder loss (dB) + RX feeder loss (dB). Isotropic antennas (0 dBi) give exactly FSPL. A 10 dBi directional antenna on each end reduces effective loss by 20 dB, which is equivalent to shortening the link by a factor of 10. Feeder cable losses of 1-3 dB per end are common and eat into that margin.
FSPL vs real-world path loss
Free space path loss is the best-case scenario: a clear, unobstructed line of sight with no atmosphere, no reflections, and no interference. Real links add a system margin (also called fade margin) of 10-20 dB to account for multipath fading, rain attenuation at frequencies above 10 GHz, diffraction around obstacles, vegetation loss, and antenna misalignment. The Friis transmission equation and FSPL are the starting point; models such as ITU-R P.452 and the Okumura-Hata model extend the calculation to include terrain and atmospheric effects.
Typical FSPL values by frequency and distance
| Frequency | 100 m | 1 km | 10 km | 100 km | Use case |
|---|---|---|---|---|---|
| 100 MHz | 52 dB | 72 dB | 92 dB | 112 dB | FM radio, public safety |
| 433 MHz | 65 dB | 85 dB | 105 dB | 125 dB | IoT, ISM, LPWAN |
| 900 MHz | 71 dB | 91 dB | 111 dB | 131 dB | GSM, LoRa, sub-GHz IoT |
| 2.4 GHz | 80 dB | 100 dB | 120 dB | 140 dB | Wi-Fi, Bluetooth, LTE |
| 5 GHz | 86 dB | 106 dB | 126 dB | 146 dB | Wi-Fi 5/6, point-to-point |
| 28 GHz | 101 dB | 121 dB | 141 dB | 161 dB | mmWave 5G |
| 60 GHz | 108 dB | 128 dB | 148 dB | 168 dB | WiGig, in-building 60 GHz |
Calculated for isotropic antennas (0 dBi gain, 0 dB feeder loss). Values in dB.
Frequently asked questions
What is the difference between FSPL and total path loss?
FSPL is the loss between two isotropic antennas in a vacuum, caused purely by geometric spreading of the wavefront. Total path loss in a real link adds multipath fading, atmospheric absorption, diffraction losses, vegetation, building penetration, antenna misalignment, and feeder cable losses on top of FSPL. Engineers add a fade margin of 10-20 dB on top of the calculated FSPL when designing links to ensure reliable operation.
Why does path loss increase with frequency?
A higher-frequency signal has a shorter wavelength. For a fixed physical antenna aperture, a higher-frequency antenna captures a smaller fraction of the incoming wavefront, which appears as increased loss. The FSPL formula assumes isotropic antennas, which by definition scale their effective aperture with wavelength squared - so a higher frequency appears more lossy even though the wave itself does not attenuate faster.
How does doubling the distance affect path loss?
Doubling the distance increases FSPL by 20 log10(2) which is approximately 6 dB. This is the inverse-square law: power spreads over a sphere whose surface area grows as the square of the radius, so received power drops by a factor of 4 (6 dB) each time the distance doubles.
What does dBi mean for antenna gain?
dBi stands for decibels relative to an isotropic antenna. An isotropic antenna radiates equally in all directions and has a gain of 0 dBi. A directional antenna with 10 dBi concentrates 10 times more power in its main beam compared to an isotropic antenna with the same input power. In the link budget, higher dBi directly reduces the effective path loss.
What is a good FSPL for a Wi-Fi link?
A typical indoor Wi-Fi link at 2.4 GHz over 10 metres has an FSPL of about 60 dB. Over 50 metres it rises to about 74 dB. Wi-Fi access points have receiver sensitivities around -70 to -90 dBm, so a transmit power of 20 dBm (100 mW) with standard antennas can close a 90-100 dB link in free space. In practice, walls and furniture add 10-30 dB of additional loss.