Free Space Path Loss Calculator Formula

Understand the math behind the free space path loss calculator. Each variable explained with a worked example.

Use the Free Space Path Loss Calculator

Formulas Used

Free Space Path Loss

fspl_db = 20 * log10(distance_km) + 20 * log10(frequency_mhz) + 32.44

FSPL at 10x Distance

fspl_10km = 20 * log10(distance_km * 10) + 20 * log10(frequency_mhz) + 32.44

Variables

VariableDescriptionDefault
distance_kmDistance(km)10
frequency_mhzFrequency(MHz)2400

How It Works

How Free Space Path Loss Works

FSPL is the loss in signal strength as a radio wave spreads out over distance, assuming no obstacles.

Formula

FSPL (dB) = 20 x log10(d_km) + 20 x log10(f_MHz) + 32.44

This comes from the Friis equation: FSPL = (4 x pi x d / lambda)^2, converted to decibels.

Key Points

  • Doubling the distance adds 6 dB of loss
  • Doubling the frequency adds 6 dB of loss
  • This is the absolute minimum loss; real-world losses are higher due to obstacles, rain, and atmospheric absorption

    • Worked Example

    2.4 GHz Wi-Fi signal over 10 km in free space.

    distance_km = 10frequency_mhz = 2400
    1. 01FSPL = 20 x log10(10) + 20 x log10(2400) + 32.44
    2. 02= 20 + 67.60 + 32.44
    3. 03= 120.0 dB

    Frequently Asked Questions

    Why is FSPL so high even in free space?

    FSPL accounts for the spreading of energy over the surface of an expanding sphere. It is geometric, not absorption loss.

    Does free space path loss depend on power?

    No. FSPL is independent of transmit power. It describes attenuation, not the received signal level.

    When is the free space model appropriate?

    For satellite links, point-to-point microwave, and as a baseline for more complex propagation models.

    Ready to run the numbers?

    Open Free Space Path Loss Calculator