Friis Transmission Calculator

Enter the Tx Power, Tx Gain, Rx Gain, Wavelength and the Distance to calculate the power received at the antenna.

Calculate the Power Received by the Receiver

  • dBi
  • dBi
  • meter


  • Power Received (dBm):
  • Power Received (W):
Formula for Friis Transmission Calculator

The Friis transmission equation gives the power received by an antenna from another antenna that is transmitting a known amount of power at a distance under ideal conditions. The formula was derived by Herald T. Friis at Bell Labs in 1945.


The Derivation of the Formula can be seen below:


Assumption: Assume that the Transmitting antenna sends out a power (Pt). We assume that the transmit antenna is omni-directional, lossless and that the receive antenna is in the far field.


Step 1: The Power Density of the plane wave incident on the receive antenna which is at a distance ® from the transmitting antenna, can be calculated by:

power density

Step 2: We assume that the transmit antenna has a gain (Gt), then the power density becomes:

Power Density with Gain

Step 3: We assume that the receive antenna has an effective aperture of Ae. Then the power received by the receive antenna is (Pr):

Power Received

Step 4: The Effective Antenna Aperture Ae, can also be defined as:

Antenna Aperture

Step 5: The Final formula for the power received at the antenna can be denoted by the Friis Transmission Equation:

Friis Equation Wavelength

OR – If you prefer to use frequency over wavelength

Friis Equation Frequency



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