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Friis Transmission Calculator

Enter transmit power, gains, frequency and distance to get the received power.

How it is calculated

The tool works in decibels, which turns the Friis equation into an addition: Pr = Pt + Gt + Gr − FSPL. Here Pt is the transmit power in dBm, Gt and Gr are the antenna gains in dBi, and the free-space path loss is FSPL = 20·log10(d) + 20·log10(f) + 32.44 with d in kilometres and f in megahertz. The result is the received power in dBm, and the path loss in dB is shown beside it. Frequency and distance must be above zero. Cable and connector losses, fading, obstacles and polarisation mismatch are not included, so enter them by lowering the gains or the transmit power.

Worked example

A 5.8 GHz link of 2 km uses a 20 dBm transmitter and a 12 dBi antenna at each end. The path loss is 20·log10(2) + 20·log10(5800) + 32.44 ≈ 6.02 + 75.27 + 32.44 = 113.73 dB. The sum of power and gains is 20 + 12 + 12 = 44 dBm. Received power is 44 − 113.73, which the tool shows as -69.73 dBm. Compare that value with your receiver's sensitivity to see the margin.

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Common mistakes

  • Entering the frequency in GHz or the distance in metres. The fields are MHz and kilometres, so 5.8 GHz is 5800 and 500 m is 0.5.
  • Entering power in watts or milliwatts. Transmit power must be in dBm; 100 mW is 20 dBm.
  • Entering gain as a plain ratio. Gains are in dBi, so a power gain of 100 times is entered as 20, not 100.
  • Forgetting cable and connector losses. They reduce the real received power, so subtract them from the gains or from the transmit power.
  • Reading the result as a guarantee. It is an ideal free-space figure; real links also need a fade margin above the receiver's sensitivity.

About this calculator

The Friis transmission equation, Pr = Pt·Gt·Gr·(λ/4πd)², relates the power received by an antenna to the transmit power, the transmit and receive antenna gains, the signal's wavelength, and the distance between them in free space, capturing how radiated power spreads out and weakens with the square of distance (and, equivalently, drops as frequency rises for a fixed distance).

RF and wireless communication engineers use it as a first-pass link budget calculation when designing Wi-Fi, satellite, radar and point-to-point microwave links, to check whether a receiver will get enough signal above its noise floor before ever building or testing the hardware.

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