Friis Transmission Equation Calculator
Accurately calculate received power based on distance, frequency, and antenna gain.
Calculation Results:
Received Power (Pr) in dBm: -
Received Power (Pr) in Watts: -
Path Loss: - dB
What is the Friis Transmission Equation?
The Friis Transmission Equation is a fundamental formula used in telecommunications and radio frequency (RF) engineering. Developed by Danish-American engineer Harald T. Friis in 1946, it relates the power received by an antenna to the power transmitted, accounting for the distance between antennas, the operating frequency, and the gains of both antennas.
In simple terms, this equation helps engineers predict how much signal strength will be available at a receiver under ideal (free space) conditions. It is the cornerstone for link budget calculations in satellite communications, Wi-Fi network planning, and cellular network design.
The Formula Explained
The core mathematical representation for the power received ($P_r$) is:
Pr(dBm) = Pt(dBm) + Gt(dBi) + Gr(dBi) + 20 log10(λ / (4πd))
- Pt: Transmitted power.
- Gt & Gr: Antenna gains of the transmitter and receiver.
- λ: Wavelength (Speed of light / Frequency).
- d: Distance between the antennas.
How to Use This Calculator
Follow these simple steps to get accurate results:
- Input Transmitted Power: Enter the power level of your source in dBm or Watts.
- Specify Gains: Enter the gain of both the transmitting and receiving antennas in dBi.
- Set Frequency: Input the operational frequency (e.g., 2.4 GHz for standard Wi-Fi).
- Define Distance: Enter the physical gap between the antennas.
- Click Calculate: Instantly view the received power in both logarithmic (dBm) and linear (Watts) scales.
Frequently Asked Questions (FAQs)
Q: Does this account for obstacles?
A: No. The Friis equation assumes "Free Space Path Loss," meaning a clear line of sight with no obstructions, reflections, or atmospheric interference.
Q: Why does higher frequency reduce received power?
A: According to the formula, received power is inversely proportional to the square of the frequency. Higher frequencies have shorter wavelengths, resulting in higher path loss over the same distance.