Calculate antenna range, transmitter power, or total gain using the Friis free-space equation from frequency, receiver sensitivity, and losses.

Antenna dBi Range Calculator (Free-Space / Friis)

Enter Frequency and Receiver Sensitivity. Then enter any 2 of Transmitter Power, Total Antenna Gain, or Range to calculate the missing value.

dB

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Antenna dBi Range Formula

This calculator uses the Friis free-space transmission equation (ideal line-of-sight with no obstructions or fading). Real-world ranges are often lower due to terrain, buildings, multipath fading, polarization mismatch, and other losses.

R = \frac{\lambda}{4\pi}\sqrt{\frac{P_t\,G_t\,G_r}{P_{r,\min}\,L}}

Variables:

  • R is the range (meters)
  • λ is the wavelength (meters), where λ = c / f
  • Pt is the transmitter power (watts)
  • Gt is the transmit antenna gain (linear, unitless)
  • Gr is the receive antenna gain (linear, unitless)
  • Pr,min is the minimum received power required (watts) (often called receiver sensitivity)
  • L is the total loss factor (linear, unitless). If you enter losses in dB, then L = 10(LdB/10).

If you enter antenna gain in dBi, convert to linear gain using G = 10(G(dBi)/10). In the calculator, the “Total Antenna Gain” field represents Gt + Gr in dB (so the linear product GtGr is 10((Gt+Gr)/10)).

What is Antenna Gain?

Antenna gain, measured in dBi (decibels relative to an isotropic radiator), is a measure of how well an antenna converts input power into radio waves in a specific direction. Higher gain indicates a more focused beam, which can extend the range and improve the quality of the signal. Antenna gain is a critical parameter in designing communication systems, as it affects the overall performance and efficiency of the antenna.

How to Calculate Antenna dBi Range?

The following steps outline how to calculate the antenna range using the free-space (Friis) equation.

  1. Determine the transmitter power (Pt) in watts.
  2. Determine the transmit and receive antenna gains. If you only have one gain value per antenna in dBi, convert each to linear (G = 10(dBi/10)) and use the product GtGr. If using a combined value in dB, use (Gt + Gr) in dBi.
  3. Determine the frequency f (to get wavelength λ = c / f) and the receiver sensitivity Pr,min.
  4. Include any additional losses L (cable/mismatch/etc.). If losses are in dB, convert with L = 10(LdB/10).
  5. Calculate the range using R = (λ/(4π))·√(PtGtGr/(Pr,minL)).
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge (free-space line-of-sight).

Transmitter Power (Pt) = 50 W

Total Antenna Gain (Gt + Gr) = 15 dBi

Frequency (f) = 2.4 GHz

Receiver Sensitivity (Pr,min) = -50 dBm

Other Losses (LdB) = 0 dB

Result (Range): R ≈ 3.95 km