Free Space Path Loss Calculator

What the free space path loss calculator does

A radio signal weakens as it travels through empty space, and free space path loss measures how much. This calculator finds that loss in decibels from the distance and frequency, and can fold in transmitter and receiver antenna gains for a rough link budget.

Below is what free space path loss is, the equation behind it, why distance and frequency both raise it, and a worked example.

How to use it

1. Enter the distance between transmitter and receiver, and the frequency.
2. Optionally enter the antenna gains for the transmitter and receiver.
3. Press Calculate for the path loss in decibels, or Reset to clear it.

What free space path loss is

Free space path loss is the amount by which a radio signal weakens as it spreads out travelling through empty space from a transmitter to a receiver. Even with nothing in the way, no walls, no obstacles, no absorption, a signal still gets weaker with distance, simply because its energy spreads over an ever-larger area as it radiates outward. Free space path loss measures this unavoidable spreading loss, the baseline weakening that any wireless link must overcome, expressed in decibels.

It is called free space path loss because it describes the loss in ideal, obstacle-free conditions, the best case for a wireless signal. Real signals face additional losses from obstacles, absorption, and reflections, but the free space loss is the fundamental floor beneath all of that, set purely by distance and frequency. It is the starting point for planning any radio link, from a Wi-Fi connection across a room to a satellite link across space. This calculator computes the free space path loss for a given distance and frequency, the core figure in working out whether a wireless link will succeed.

The equation it uses

The free space path loss in decibels is given by:

FSPL (dB) = 20 log₁₀(d) + 20 log₁₀(f) + constant

where d is the distance, f is the frequency, and the constant depends on the units used for distance and frequency. Both the distance and the frequency enter through a twenty-times logarithm, which means each contributes to the loss in the same logarithmic way. The calculator uses the appropriate constant for its units and computes the loss directly. It can also subtract the transmitter and receiver antenna gains, which offset the loss in a complete link calculation, giving a net figure.

Why distance and frequency both raise the loss

Two things increase the free space path loss: greater distance and higher frequency. The distance dependence is the more intuitive one. As a signal radiates outward, its energy spreads over the surface of an expanding sphere, whose area grows with the square of the distance, so the power reaching any given point falls with the square of the distance. In decibels, this means the loss rises steadily with distance, adding the same amount each time the distance is multiplied by ten.

The frequency dependence is less obvious but just as real. Higher-frequency signals have shorter wavelengths, and a receiving antenna of a given size captures less of a short-wavelength signal, so for a fixed antenna the loss rises with frequency. This is why higher-frequency links, like those at microwave and millimetre-wave frequencies, face greater path loss than lower-frequency ones over the same distance, all else being equal. Both effects add together, so a long-distance, high-frequency link must overcome a large path loss. The calculator shows how the loss grows with each factor, which is essential for understanding the reach of a wireless system.

Antenna gain and the link budget

Free space path loss is only part of the story of whether a radio link will work. The full picture is called the link budget, an accounting of all the gains and losses between the transmitter and the receiver. The transmitter sends out a certain power, the antennas at each end provide gain that concentrates the signal in the useful direction, and the path loss weakens it along the way. Adding up the gains and subtracting the losses tells you how strong the signal arrives, and whether it is strong enough to be received.

This is why the calculator lets you enter the transmitter and receiver antenna gains, which it subtracts from the path loss to give a net figure. Antenna gain helps because a directional antenna focuses the signal rather than radiating it equally in all directions, effectively recovering some of the loss. A link succeeds when the received signal, after accounting for the path loss minus the antenna gains, stays above the level the receiver needs. The free space path loss is the central term in this budget, and combining it with the antenna gains gives a practical estimate of link performance, which is exactly what the calculator provides.

Units and precision

The calculator takes the distance in a range of units from millimetres to nautical miles, the frequency in units from hertz up to terahertz, and the antenna gains in decibels, returning the free space path loss in decibels. It applies the standard path loss relationship with the correct constant for its units, and subtracts the antenna gains for a net link figure. The result describes the ideal free-space case; real links carry additional losses from obstacles and absorption that are not included in this baseline.

A worked example

Suppose a signal at 1 gigahertz travels 1 kilometre through free space, with no antenna gain entered.

The free space path loss works out to about 92.5 decibels, the standard figure for this distance and frequency. Increase the distance to 10 kilometres and the loss rises by 20 decibels to about 112.5 decibels, since multiplying the distance by ten adds a fixed amount to the loss. Entering antenna gains would subtract from these figures, improving the link.

Questions people ask

How do you calculate free space path loss?

Use FSPL in decibels = 20 log₁₀(d) + 20 log₁₀(f) + a constant that depends on the units, from the distance and frequency.

Why does path loss increase with distance?

Because the signal's energy spreads over an expanding sphere, whose area grows with the square of distance, so the power at any point falls with distance squared.

Why does path loss increase with frequency?

Because a fixed-size antenna captures less of a shorter-wavelength signal. Higher frequencies mean shorter wavelengths, so the loss rises with frequency for a given antenna.

What does antenna gain do in the calculation?

It offsets the loss. Directional antennas focus the signal, so their gain is subtracted from the path loss to give the net figure in a link budget.

References

A quick note on where this comes from. Free space path loss and the link budget are standard radio engineering, based on the Friis transmission equation and documented by the ITU and in radio references. The links are worth a quick click to confirm they land where you expect.

1. International Telecommunication Union (ITU-R), Recommendation P.525, Calculation of free-space attenuation. https://www.itu.int/rec/R-REC-P.525/en
2. Wikipedia, Free-space path loss. https://en.wikipedia.org/wiki/Free-space_path_loss
3. Wikipedia, Friis transmission equation. https://en.wikipedia.org/wiki/Friis_transmission_equation