Friis Transmission Equation Calculator

Use this Friis Transmission Equation Calculator to calculate received power using transmitter power,transmitter gain,receiver gain,distance and frequency.

Friis Transmission Equation Calculator
Transmitter Power (Pt)
Transmitter Gain (Gt)
Receiver Gain (Gr)
Distance (d)
Frequency (f)
Wavelength (λ)
Recieved Power (Pr): {{friisTransmissionResult()}}

How to use Friis Transmission Equation Calculator?

Step 1 - Enter the Transmitter Power (Pt)

Step 2 - Enter the Receiver Gain (Gr)

Step 3 - Enter the Distance (d)

Step 4 - Enter the Frequency (f)

Step 5 - Enter the Wavelength (λ)

Step 6 - Calculate Recieved Power (Pr)

Friis Transmission Equation Calculator Formula:

Pr=Pt × Gt × Gr × $(c/(4 × π × d× f))^2$

P(dB)r=Pt + Gt + Gr + (20 × log(c/(4 × π × d × f)))

Where,

Pr = Received Power

Pt = Transmitter Power

Gt = Transmitter Gain

Gr = Receiver Gain

d = Distance

f = Frequency

P(dB)r = Received Power in dB

c = Speed of light (equal to 3 * $10^8$ m/s)

Frequently Asked Questions

What is the Friis Transmission Equation and why is it important?

The Friis Transmission Equation is a fundamental formula in RF and wireless communication that determines how much signal power is received at the antenna when transmitted over free space. It accounts for transmitter power, antenna gains, operating frequency, and propagation distance. This equation is essential for designing wireless systems, predicting link budgets, and troubleshooting communication failures in satellite, radar, and mobile networks.

How do I use this calculator?

Enter your transmitter power (in Watts or dBm), transmitter and receiver antenna gains (in dBi or linear ratio), the distance between antennas (in meters), and the operating frequency (in Hz or GHz). The calculator will compute the received power level. You can specify either frequency or wavelength - the calculator uses the relationship c = f × λ to convert between them.

When should I use the Friis Transmission Equation?

Use this calculation when analyzing free-space RF propagation in clear line-of-sight conditions. Typical applications include satellite communication link analysis, antenna radiation pattern measurements, radar performance estimation, and wireless network planning. It assumes ideal propagation with no obstructions, absorption, or multipath effects.

What are the assumptions for this calculation?

The equation assumes free-space propagation with no obstacles between antennas, no atmospheric absorption, perfect antenna efficiency, and ideal receiver impedance matching. Real-world systems experience additional path loss from terrain, buildings, weather, and interference. The equation is valid for the far-field region of the antenna where the propagating wave is approximately planar.

The Friis equation uses antenna gain, which is directly related to antenna directivity and effective aperture. Arrays of antennas increase overall gain by coherent combination of signals, improving received power. The effective aperture determines how efficiently an antenna captures incident electromagnetic waves, making it essential for optimizing receiver sensitivity.

Physical Basis & References

This calculator applies the Friis Transmission Equation (Friis, 1946):

$$P_r = P_t \cdot G_t \cdot G_r \cdot \left(\frac{\lambda}{4\pi d}\right)^2$$

Key Physics Principles:

  • Friis Transmission Equation - Fundamental law relating received and transmitted power in free space
  • Inverse Square Law - Power density decreases as distance squared from the transmitter
  • Antenna Gain - Directivity multiplied by radiation efficiency determines power concentration
  • Free-Space Path Loss - Signal attenuation independent of medium in vacuum or air

Key Assumptions:

  • Line-of-sight propagation with no obstructions
  • Far-field region of antenna (distance » wavelength)
  • Ideal antenna impedance matching
  • No atmospheric absorption or multipath effects
  • Antenna gains are in the same reference plane

Typical Range of Values:

  • Transmitter power: 0.1W to 100W (20 to 50 dBm)
  • Antenna gains: -3 dBi to +20 dBi (omnidirectional to directional)
  • Frequency: 300 MHz to 100 GHz (UHF to mm-wave)
  • Distance: 100m to 1000 km (short range to satellite)

Further Reading:

  • Friis, H.T. (1946). “A Note on a Simple Transmission Formula”, Proceedings of the I.R.E.
  • Balanis, C.A. (2016). Antenna Theory: Analysis and Design, 4th Edition. Wiley.
  • IEEE Antennas and Propagation Society standards and technical papers

Conclusion

You can read more about Friis Path Loss Calculator using below link

Read more about other Physics Calculator on below links