Free Space Path Loss Calculator Formula

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

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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

    Ready to run the numbers?

    Open Free Space Path Loss Calculator