Free-Space Path Loss Calculator
Calculate the free-space path loss in dB between two antennas from distance and frequency, plus the wavelength.
Free-space path loss
As a radio wave spreads out from an antenna, its power is diluted over an ever-larger sphere. Free-space path loss (FSPL) is that geometric spreading loss between two antennas with a clear line of sight and no obstacles.
FSPL(dB) = 20·log₁₀(d) + 20·log₁₀(f) − 147.55
with distance d in metres and frequency f in hertz. Loss rises by 6 dB each time the distance doubles, and by 6 dB each time the frequency doubles — so higher bands need more link budget for the same range.
How it works
Path loss isn't the wave being absorbed — in free space nothing is lost to the medium. It's pure geometry: a transmitter radiates power over an expanding sphere, and a receiving antenna of fixed size catches a smaller and smaller slice of that sphere as it grows. Because a sphere's area goes as the square of its radius, received power falls as the square of distance, which is the 20·log₁₀(d) term. The frequency term appears because a higher-frequency wave has a smaller wavelength, and a fixed-size antenna captures less of a shorter wave — which is why, all else equal, higher bands reach less far.
Worked example
At 868 MHz over 1 km: FSPL = 20·log₁₀(1000) + 20·log₁₀(868 000 000) − 147.55 ≈ 60 + 178.8 − 147.55 ≈ 91.2 dB. Move to 2.4 GHz over the same kilometre and the loss climbs by about 8.8 dB — roughly the penalty for choosing the higher band, which you'd have to recover with more transmit power, antenna gain, or receiver sensitivity.
The real-world caveat
FSPL is a best case: a clear line of sight with the Fresnel zone unobstructed. Real links lose more to buildings, terrain, foliage, ground reflections, and rain, so treat it as the floor, not the expected value. Feed this figure into the RF link budget calculator to find the received power and link margin, or size an antenna with thewavelength calculator.
Common questions
- Why does a higher frequency lose more signal over the same distance?
- Strictly, the loss is not in the air — free space does not attenuate more at higher frequencies. What changes is the receiving antenna: for a given gain, a higher-frequency antenna has a smaller effective aperture, so it intercepts less of the passing wave. The FSPL formula folds that into a frequency term, which is why 2.4 GHz reaches less far than 868 MHz with otherwise identical hardware.
- Is free-space path loss what I will actually see outdoors?
- No — treat it as a best case that reality never quite reaches. The formula assumes a clear line of sight with nothing nearby. Real deployments add losses from walls, foliage, rain and ground reflection, and multipath can cause deep fades even with perfect line of sight. Practitioners commonly design 10–20 dB of margin beyond the FSPL figure precisely because of this.
- What is the 32.44 constant in the formula?
- It is a unit-conversion term, not physics. FSPL is fundamentally 20·log(4πd/λ); writing distance in kilometres and frequency in megahertz instead of metres bundles all the constants into 32.44. Use miles and megahertz and it becomes 36.6; use metres and hertz and it disappears entirely. If your answer is off by tens of dB, check which variant you used.
- How much does doubling the distance cost me?
- Exactly 6 dB, at any frequency — the loss goes with the square of distance, and 20·log(2) is 6.02. That is a useful figure to carry around: every doubling of range costs 6 dB of budget, so going four times further costs 12 dB. Pair it with the link budget calculator to see whether you have that margin to spend.