Free Space Path Loss Calculator
Calculate free-space path loss for a distance and frequency, and build a simple link budget from power, antenna gains, losses and receiver sensitivity.
The spreading of a signal
A radio wave spreads out as it travels, so the power reaching a receiving antenna of a given size falls with the square of the distance. Free-space path loss, FSPL, is that spreading between two isotropic antennas with nothing in the way. In decibels, FSPL = 20 log₁₀(distance in km) + 20 log₁₀(frequency in MHz) + 32.45. For a 2 m simplex contact at 146.52 MHz over 30 km, the loss is 105.3 dB. Doubling the distance adds 6.02 dB, and 100 km costs 115.8 dB. The frequency term looks as if higher frequencies are attenuated more, but it really reflects the smaller size of an isotropic antenna’s capture area at shorter wavelengths: an antenna of fixed physical size gains as frequency rises, which is why dishes work so well at microwave frequencies.
A link budget
A link budget adds up everything between the transmitter and the receiver. The 2 m example uses a 5 W handheld, 37.0 dBm; antennas with 2.15 dBi gain at each end, the gain of a half-wave dipole; and 2 dB of cable and connector loss. Received power is 37.0 + 2.15 + 2.15 − 2 − 105.3 = −66.0 dBm. A typical FM receiver needs about 0.2 µV, −121 dBm, for usable audio, so the link has about 54 dB of margin in free space, a very comfortable figure. The margin is the point: real paths add loss that free space does not include, and the budget tells you how much there is to spend.
Why real paths are worse
Free space assumes a clear line of sight with the first Fresnel zone, an ellipse around the direct path, unobstructed. On the ground, hills, buildings and trees block or diffract the signal, adding anything from a few to more than 30 dB, and at VHF and above the curvature of the Earth limits line of sight to roughly 4.12 × (√h₁ + √h₂) km for antenna heights in metres. A common misconception is that a link with positive margin in this calculator will work; it will work only if the path is clear, which is why VHF operators climb hills and raise antennas. On HF, signals travel by ground wave and by reflection from the ionosphere, and free-space loss is only one part of the story.
Using the margin
Engineers allow 10 to 20 dB of fade margin for a reliable fixed link and more for mobile paths. If the margin is too small, every 3 dB added by more power, more antenna gain or less cable loss helps equally, and gain at the receiving end helps both directions of a two-way contact. Height is often the cheapest improvement of all.
How to use it
- Enter the frequency and the distance between the stations.
- Enter the transmitter power and the antenna gains in dBi.
- Enter cable and connector losses and the receiver sensitivity in dBm.
- Read the path loss, received power and link margin, and allow for terrain and fading.
Questions from the shack
What is free-space path loss?
The loss in signal power between two isotropic antennas separated by a clear path in free space, caused by the signal spreading out. In decibels it is 20 log₁₀(km) + 20 log₁₀(MHz) + 32.45. At 146.52 MHz over 30 km it is 105.3 dB.
How much does doubling the distance reduce the signal?
In free space, doubling the distance adds about 6 dB of path loss, a quarter of the received power, roughly one S unit. Over real terrain the loss usually grows faster, especially once the path is no longer line of sight.
Why does path loss increase with frequency?
The formula assumes isotropic antennas, whose effective capture area shrinks with wavelength. With antennas of fixed physical size, such as dishes, higher frequencies have more gain and can overcome the extra loss, which is why microwave links use small dishes over long distances.
How much link margin do I need?
For a fixed point-to-point link, 10 to 20 dB above the receiver sensitivity is a common target to allow for fading and weather. Mobile and handheld use needs more, because the path and the antenna position change constantly.
Disclaimer: Radio results are calculations from handbook formulas and typical cable data for the values you enter. They are not a substitute for measuring your installation, an RF exposure evaluation or your licence conditions. Trim antennas with an analyser, transmit only within your licence privileges, and keep antennas well clear of power lines; installing antennas and towers can be dangerous.