Free Space Path Loss Calculator

Q: Does FSPL include antenna gains?

No. FSPL is the loss between two isotropic points in free space. Add transmitter and receiver antenna gains separately in your link budget.

Q: Can FSPL be negative?

No. FSPL is always a loss. In dB it is a positive number. Gains come from antennas or amplifiers, not from free space.

Q: When should I use the wavelength form instead of the frequency form?

Use the wavelength form when your design starts with antenna size or aperture. Use the frequency form when your system is specified by carrier frequency. Both are equivalent if units are consistent.

Q: Does FSPL apply in the near field?

No. FSPL assumes far‑field conditions. If d is smaller than the Fraunhofer distance for your antenna, coupling is not governed by the inverse‑square law alone.

Reviewed by Pero Mikić, Physics & Technical Education (Gimnazija Sisak) • Last updated 2026-10-14

The Free Space Path Loss Calculator computes the expected radio signal attenuation in decibels for given frequency and distance in free space.

Free Space Path Loss Calculator

Frequency

Enter frequency > 0.

Distance

Enter distance > 0.

Formula / Constant Set Pick a common engineering constant set, or use the wavelength form.

Output If you choose received power, enter Tx power and gains below.

Tx Power

Optional unless computing received power.

Antenna Gains & Other Losses

Tx gain (dBi)

Rx gain (dBi)

System loss (dB)

Received power: Pr(dBm) = Pt(dBm) + Gt(dBi) + Gr(dBi) − FSPL(dB) − Lsys(dB).

Example Presets

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About the Free Space Path Loss Calculator

Free Space Path Loss (FSPL) describes signal attenuation between two antennas with a clear line of sight and no obstacles. It is a core idea in wireless engineering and physics. The calculator applies the classic Friis transmission framework to return path loss as a decibel value and as a power ratio.

You provide distance and frequency. The tool converts units, computes wavelength from the speed of light, and outputs FSPL. Results help you compare technologies, plan Wi‑Fi or microwave links, and estimate satellite link budgets.

The calculator focuses on free space only. It does not include antenna gains, polarization mismatch, atmospheric absorption, or multipath. You can add those effects later in your link budget. Keeping FSPL separate helps you see the pure distance and frequency dependence.

Free Space Path Loss Formulas & Derivations

FSPL comes from energy spreading over the surface of a sphere as a wavefront expands. The Friis relation links power received to power transmitted. Rewriting it for loss yields a compact expression in terms of distance d, wavelength λ, and frequency f.

Power‑ratio form: FSPL = (4πd/λ)². This is dimensionless. It scales with the square of distance and inversely with the square of wavelength.
Decibel form using wavelength: L_fs(dB) = 20 log₁₀(4πd/λ).
Decibel form using frequency and the speed of light c: L_fs(dB) = 20 log₁₀(d) + 20 log₁₀(f) + 20 log₁₀(4π/c).
Common unit‑ready forms:
- d in meters, f in Hz: L_fs(dB) = 20 log₁₀(d_m) + 20 log₁₀(f_Hz) − 147.55.
- d in meters, f in GHz: L_fs(dB) = 32.45 + 20 log₁₀(d_m) + 20 log₁₀(f_GHz).

These expressions are the same equation written with different variables and units. The constants (−147.55, 32.45, 92.45) come from 20 log₁₀(4π/c) and unit conversions. The decibel version is convenient because link budgets add and subtract gains and losses in dB.

How the Free Space Path Loss Method Works

The method assumes an isotropic transmitter radiates power evenly in all directions. As the wavefront expands, power spreads over the surface area of a sphere, 4πd². The receiver captures only a small portion, set by its effective aperture. Converting the Friis equation into a loss term yields the FSPL you see in most link budgets.

Start with Friis: P_r = P_t G_t G_r (λ/(4πd))².
Rearrange to isolate loss: FSPL = (P_t G_t G_r)/P_r when antenna gains are removed.
Express FSPL as (4πd/λ)². This shows dependence on distance and wavelength.
Convert to decibels: L_fs(dB) = 20 log₁₀(4πd/λ).
Replace λ by c/f to get a frequency form that is easy to compute and check against units.

Because free space is idealized, FSPL is the lower bound on path loss for any real link with clear line of sight. Real paths often add extra loss from atmosphere, foliage, and hardware mismatch. Engineers add those effects after computing FSPL.

What You Need to Use the Free Space Path Loss Calculator

You only need a few variables. The calculator handles unit conversions and logarithms. It returns both the decibel loss and the linear power ratio.

Distance d between antennas (choose meters, kilometers, miles, or feet).
Frequency f of the signal (choose Hz, kHz, MHz, or GHz).
Propagation speed model (vacuum c, or custom value for another medium).
Output format (dB, linear ratio, or both).
Precision setting (number of decimal places).

Enter positive, nonzero values. Very short distances can fall in the near field where FSPL does not apply. Very high frequencies or very long paths can produce large numbers; the dB output is stable, but the raw ratio may overflow standard displays.

Step-by-Step: Use the Free Space Path Loss Calculator

Here’s a concise overview before we dive into the key points:

Select the distance unit and enter the separation between antennas.
Select the frequency unit and enter the carrier frequency.
Choose the propagation speed: vacuum (c) or a custom value if needed.
Pick the output format: decibels, ratio, or both.
Set your desired precision.
Click Calculate to compute FSPL from the chosen variables and units.

These points provide quick orientation—use them alongside the full explanations in this page.

Example Scenarios

Example 1: Outdoor Wi‑Fi at 2.4 GHz over 100 m. Using L_fs(dB) = 32.45 + 20 log₁₀(d_m) + 20 log₁₀(f_GHz), we get 32.45 + 20 log₁₀(100) + 20 log₁₀(2.4) ≈ 32.45 + 40 + 7.6 = 80.05 dB. If the access point transmits 20 dBm EIRP and the client has 0 dBi gain, the received level is about −60 dBm ignoring other losses. What this means: The signal should be strong enough for a stable link if the path is clear.

Example 2: 5G millimeter wave at 28 GHz over 200 m. Using the same form, L_fs(dB) = 32.45 + 20 log₁₀(200) + 20 log₁₀(28) ≈ 32.45 + 46.02 + 28.94 = 107.41 dB. With 30 dBm EIRP and 0 dBi at the receiver, the received level is about −77 dBm before other losses. What this means: The path requires line of sight and antenna gain or beamforming to maintain margin.

Accuracy & Limitations

FSPL is accurate for far‑field, line‑of‑sight paths in vacuum or dry air, with matched polarizations and ideal isotropic antennas. Real systems deviate from this ideal, so treat FSPL as a baseline loss.

Near‑field region: FSPL does not hold for distances shorter than the Fraunhofer distance, d < 2D²/λ, where D is antenna aperture.
Atmospheric effects: Oxygen and water vapor absorption add loss, especially above 10 GHz, and rain fading can be severe at mmWave.
Obstructions and multipath: Buildings, foliage, and terrain add shadowing and fading beyond FSPL.
Polarization and alignment: Cross‑polarization or mispointing reduces received power.
Medium changes: In media other than air or vacuum, use the correct phase velocity for λ = v/f.

Use FSPL to anchor your link budget. Then add antenna gains, feeder losses, atmospheric attenuation, polarization mismatch, fade margin, and implementation losses. Compare the final received level to receiver sensitivity and required SNR.

Units Reference

Correct units are essential because the constants in the decibel formulas depend on them. The calculator accepts several unit combinations and applies the right derivation each time. The table summarizes common variables and preferred units.

Common variables and units for Free Space Path Loss calculations
Symbol	Quantity	Typical Units	Notes
d	Distance	m, km, mi, ft	Use km with MHz or GHz constants; use m with Hz or GHz constants.
f	Frequency	Hz, kHz, MHz, GHz	Check that your constant matches your frequency unit.
λ	Wavelength	m	λ = v/f, where v is phase velocity (≈ c in air).
c	Speed of light	299,792,458 m/s	Use v = c/n in a medium with refractive index n.
L_fs	Free space path loss	dB or ratio	dB is additive in budgets; ratio is dimensionless.

To read the table: pick the unit column that matches your inputs. If you use d in km and f in MHz, the constant 32.45 applies. If you switch to f in GHz while keeping km, use 92.45 instead. The calculator picks the correct constant from your unit choices.

Tips If Results Look Off

Most surprises come from unit mix‑ups or log settings. A quick review usually fixes them.

Confirm that distance and frequency units match the formula constant you expect.
Use base‑10 logarithms. Do not use natural logs.
Make sure distance is not zero and frequency is not zero.
Check whether you entered EIRP or raw transmitter power elsewhere in your budget.
Verify you are in the far field for your antennas.

If your number is off by about 60 dB, you likely used MHz instead of GHz or m instead of km. If it is off by about 20 dB, you may be off by a factor of 10 in distance or frequency.

FAQ about Free Space Path Loss Calculator

Does FSPL include antenna gains?

No. FSPL is the loss between two isotropic points in free space. Add transmitter and receiver antenna gains separately in your link budget.

Can FSPL be negative?

No. FSPL is always a loss. In dB it is a positive number. Gains come from antennas or amplifiers, not from free space.

When should I use the wavelength form instead of the frequency form?

Use the wavelength form when your design starts with antenna size or aperture. Use the frequency form when your system is specified by carrier frequency. Both are equivalent if units are consistent.

Does FSPL apply in the near field?

No. FSPL assumes far‑field conditions. If d is smaller than the Fraunhofer distance for your antenna, coupling is not governed by the inverse‑square law alone.

Glossary for Free Space Path Loss

Free space

An ideal medium without obstacles, reflections, or absorption. It represents the lower bound on path loss for line‑of‑sight links.

Path loss

The reduction in signal power over distance, expressed as a ratio or in decibels. In free space it depends on distance and frequency.

Friis transmission equation

A relation between transmitted power and received power in the far field. It includes antenna gains and the wavelength‑dependent spreading factor.

Isotropic radiator

An ideal antenna that radiates equally in all directions. It is a reference model used to define gains and FSPL.

Wavelength

The spatial period of a wave, equal to the propagation speed divided by frequency. Shorter wavelengths imply higher path loss at the same distance.

EIRP

Equivalent isotropically radiated power. It is the transmitter power plus antenna gain minus feeder losses, referenced to an isotropic source.

dB (decibel)

A logarithmic unit that expresses ratios. For power, 10 log₁₀(ratio). For field quantities, 20 log₁₀(ratio).

Far field

The region far enough from an antenna where the wavefront is locally planar and field ratios are stable. FSPL and simple gain relationships apply there.

References