Use this free-space path loss calculator to get the loss between two antennas from the distance and frequency, or to solve for the distance or frequency that gives a certain loss. Results use the ITU-R P.525 formula and are compared across the common radio bands.
Accepts 433M, 2.4G.
Free-space path loss
100.05 dB
Free space between isotropic antennas: no ground, obstacles or atmosphere. Antenna gains and every real-world loss are added separately in a link budget.
Path loss over 1 km, by band
| Band | Wavelength | Path loss |
|---|---|---|
| 433 MHz | 692 mm | 85.18 dB |
| 868 MHz | 345 mm | 91.22 dB |
| 915 MHz | 328 mm | 91.68 dB |
| 2.4 GHz | 125 mm | 100.05 dB |
| 5.8 GHz | 51.7 mm | 107.72 dB |
Use FSPL = 20 log₁₀(4πd ÷ λ), or with frequency in MHz and distance in km, FSPL = 32.45 + 20 log₁₀(f) + 20 log₁₀(d) dB. A 2.4 GHz signal over 1 km has a free-space path loss of 100.05 dB. Each doubling of the distance or the frequency adds 6.02 dB.
The free-space path loss equation here follows ITU-R P.525, which defines the loss between two isotropic antennas in free space. Power spreads over a sphere of area 4πd², and the receiving antenna collects from an effective aperture of λ² ÷ 4π.
The FSPL equation with frequency in place of wavelength, in the unit pairs people use most:
This FSPL calculator evaluates the first form with the exact speed of light. ITU-R P.525 rounds the MHz and km constant to 32.4, which is 0.048 dB lower. Solving for distance gives d = (λ ÷ 4π) × 10^(FSPL ÷ 20).
λ = 299,792,458 ÷ (2.4 × 10⁹) = 124.9 mm. FSPL = 20 log₁₀(4π × 100 ÷ 0.1249) = 80.05 dB.
At 868 MHz the loss is 105.20 dB; at 2.4 GHz it is 114.03 dB. The higher band loses 8.83 dB more, which is 20 log₁₀(2400 ÷ 868). Antennas of the same physical size have more gain at the higher frequency, which is why this penalty applies to antennas of fixed gain and not to antennas of fixed size.
d = (λ ÷ 4π) × 10^(120 ÷ 20) = (327.6 mm ÷ 4π) × 10⁶ = 26.07 km. The calculator's Distance tab gives the same figure.
Loss in dB between isotropic antennas, from FSPL = 20 log₁₀(4πd ÷ λ).
| Frequency | 10 m | 100 m | 1 km | 10 km | 100 km |
|---|---|---|---|---|---|
| 433 MHz | 45.2 dB | 65.2 dB | 85.2 dB | 105.2 dB | 125.2 dB |
| 868 MHz | 51.2 dB | 71.2 dB | 91.2 dB | 111.2 dB | 131.2 dB |
| 915 MHz | 51.7 dB | 71.7 dB | 91.7 dB | 111.7 dB | 131.7 dB |
| 2.4 GHz | 60.1 dB | 80.1 dB | 100.1 dB | 120.1 dB | 140.1 dB |
| 5.8 GHz | 67.7 dB | 87.7 dB | 107.7 dB | 127.7 dB | 147.7 dB |
The free-space distance at which the path loss reaches each value. If a link budget allows a given path loss, this is the range it can reach under ideal conditions.
| Frequency | 80 dB | 100 dB | 120 dB | 140 dB |
|---|---|---|---|---|
| 433 MHz | 551 m | 5.51 km | 55.1 km | 551 km |
| 868 MHz | 275 m | 2.75 km | 27.5 km | 275 km |
| 915 MHz | 261 m | 2.61 km | 26.1 km | 261 km |
| 2.4 GHz | 99.4 m | 994 m | 9.94 km | 99.4 km |
| 5.8 GHz | 41.1 m | 411 m | 4.11 km | 41.1 km |
Real paths lose more than this formula predicts. Near the ground, the reflected wave interferes with the direct one, and an obstructed first Fresnel zone adds diffraction loss. Walls, foliage and buildings add attenuation that depends on the material and the frequency, and above about 10 GHz atmospheric gases and rain start to matter. The formula also assumes the far field: the distance should be much larger than the wavelength and than 2D² ÷ λ for an antenna of largest dimension D, so the calculator warns when a path is under ten wavelengths long. Treat the result as a best-case estimate, then add margin for everything your path has that free space does not.
FSPL stands for free-space path loss: the loss between two isotropic antennas in empty space, also called free-space basic transmission loss (Lbf in ITU-R P.525). It leaves out antenna gain, walls, ground reflections and everything else a real path adds.
FSPL = 20 log₁₀(4πd ÷ λ), with d and λ in the same unit. With frequency in MHz and distance in km it becomes FSPL = 32.45 + 20 log₁₀(f) + 20 log₁₀(d) dB.
100.05 dB. At 100 m it is exactly 20 dB less, 80.05 dB, because the loss changes by 20 dB per decade of distance.
6.02 dB, because 20 log₁₀(2) = 6.02. Doubling the frequency adds the same amount.
The power density at the receiver does not depend on frequency. What shrinks is the effective aperture of the receiving antenna: an isotropic antenna collects from an area of λ² ÷ 4π, so a shorter wavelength captures less power. The loss is a geometry term, not dissipation.
All three appear, and the difference is rounding. With the exact speed of light the constant is 32.4478, or 32.45. ITU-R P.525 rounds it to 32.4, and references that take c as 3 × 10⁸ m/s get 32.44.
No. FSPL is defined between isotropic antennas. To get received power, add the antenna gains and subtract cable and other losses in a link budget.
The formula goes negative inside d = λ ÷ 4π (9.94 mm at 2.4 GHz), but that result has no physical meaning: the antennas are in each other's near field, where the formula does not apply. The calculator returns an error there.
Only as a rough best case. Walls, ground reflections and multipath are not in the formula. Measured loss is usually well above it, apart from a few dB of constructive interference at some spots.
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