Free Space Path Loss Calculator

Overview

The Free Space Path Loss (FSPL) calculator computes signal attenuation in free space based on frequency, distance, and antenna gains.

Formula

The FSPL is calculated using:

FSPL (dB) = 20×log₁₀(4π/c) + 20×log₁₀(f) + 20×log₁₀(d) - G_TX - G_RX

Where:

  • f = frequency in Hz

  • d = distance in meters

  • c = speed of light (299,792,458 m/s)

  • G_TX = transmitter antenna gain in dBi

  • G_RX = receiver antenna gain in dBi

  • 20×log₁₀(4π/c) ≈ -147.55 dB (constant term)

Input Parameters

Parameter

Range

Units Available

Frequency

0 to 10¹⁵

Hz, kHz, MHz, GHz, THz

Distance

0 to 10¹⁵

m, km, cm, mm, ft, mi, nmi

G_TX

-50 to 100 dB

dBi

G_RX

-50 to 100 dB

dBi

Output

The calculator displays path loss for five distance points:

  • d/4 (quarter distance)

  • d/2 (half distance)

  • d (specified distance, highlighted)

  • 2×d (double distance)

  • 4×d (quadruple distance)

Example

Input:

  • Frequency: 1000 MHz (1 GHz)

  • Distance: 1 km

  • G_TX: 0 dBi

  • G_RX: 0 dBi

Calculation:

f = 1×10⁹ Hz
d = 1000 m
FSPL = -147.55 + 20×log₁₀(10⁹) + 20×log₁₀(1000) - 0 - 0
     = -147.55 + 180 + 60
     = 92.45 dB

Output Table:

Distance

Path Loss

250 m (d/4)

80.43 dB

500 m (d/2)

86.44 dB

1 km (d)

92.45 dB

2 km (2×d)

98.47 dB

4 km (4×d)

104.48 dB

Notes

  • Distance doubling increases path loss by approximately 6 dB

  • Higher frequencies result in greater path loss

  • Antenna gains reduce overall path loss

  • Invalid inputs (frequency or distance ≤ 0) display “Error”