Free-Space Path Loss

\[FSPL=\left(\frac{4\pi d}{\lambda}\right)^2\]

Variables

FSPLfree-space path loss

ddistance between antennas (m)

lambda[λ]signal wavelength (m)

Description

What is this formula?

Free-Space Path Loss (FSPL) quantifies the reduction in signal power as an electromagnetic wave propagates through free space without obstacles, reflections, or atmospheric effects.

When to use it

Use this formula when designing radio links, satellite communications, radar systems, microwave networks, and wireless communication systems operating under line-of-sight conditions.

Example

Two antennas are separated by 10 km and communicate at a wavelength of 0.125 m (2.4 GHz).

Formula:

FSPL = (4πd/λ)²

Substitution:

FSPL = (4π×10000/0.125)²

Result:

FSPL = 1.01×10^12

FSPL = 120.05 dB

Applications

Satellite communications, microwave links, Wi-Fi planning, radar systems, cellular network design, radio astronomy, and wireless link budgeting.

Note

This formula assumes ideal free-space propagation with no obstacles, multipath effects, atmospheric attenuation, diffraction, or polarization losses. Real-world propagation losses are often greater than the theoretical free-space value and may require additional correction factors depending on the environment.