Calculate antenna range, transmitter power, or total gain using the Friis free-space equation from frequency, receiver sensitivity, and losses.
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Antenna dBi Range Formula
The antenna dBi range calculator uses the Friis free-space transmission equation. It assumes a clear line-of-sight path with no terrain, building, foliage, multipath, or Fresnel-zone blockage losses unless you enter them in the other losses field.
lambda = c/f
Pr = Pt*G*(lambda/(4*pi*R))^2/L
To solve for transmitter power:
Pt = Pr*L*(4*pi*R/lambda)^2/G
To solve for total antenna gain:
G = Pr*L*(4*pi*R/lambda)^2/Pt
To solve for range:
R = lambda/(4*pi)*sqrt(Pt*G/(Pr*L))
The calculator also converts logarithmic inputs before applying the Friis equation:
Pr_W = 10^((Pr_dBm - 30)/10)
Pr_W = 10^(Pr_dBW/10)
G_linear = 10^(G_dBi/10)
L_linear = 10^(Loss_dB/10)
- lambda = wavelength in meters
- c = speed of light, 299,792,458 m/s
- f = frequency in Hz
- Pr = minimum received power, also called receiver sensitivity, in watts
- Pt = transmitter power in watts
- G = total antenna gain as a linear ratio, based on the combined transmit and receive antenna gain
- G_dBi = total antenna gain in dBi
- R = free-space range in meters
- L = other losses as a linear ratio
- Loss_dB = cable, mismatch, connector, polarization, or other added losses in dB
If you leave transmitter power blank, the calculator solves for the power needed to reach the entered range. If you leave total antenna gain blank, it solves for the combined gain needed from both antennas. If you leave range blank, it estimates the ideal free-space range for the entered power, gain, frequency, sensitivity, and losses.
For gain units, dBd is converted to dBi before the calculation. The conversion used is:
dBi = dBd + 2.15
Common Antenna Gain and Unit Reference
| Item | Typical value | Use in the calculator |
|---|---|---|
| Isotropic reference | 0 dBi | Baseline gain reference |
| Half-wave dipole | 2.15 dBi, or 0 dBd | Use dBi directly, or select dBd if entering dipole-referenced gain |
| Small whip or PCB antenna | -3 to 3 dBi | Common for compact devices |
| Omnidirectional vertical antenna | 3 to 9 dBi | Common for base stations and access points |
| Panel or Yagi antenna | 8 to 18 dBi | Directional links with moderate gain |
| Dish antenna | 20 dBi and higher | Longer directional links |
| Quantity | Conversion | Note |
|---|---|---|
| dBm to watts | W = 10^((dBm – 30)/10) | 0 dBm = 1 mW |
| dBW to watts | W = 10^(dBW/10) | 0 dBW = 1 W |
| dBd to dBi | dBi = dBd + 2.15 | dBd is referenced to a half-wave dipole |
| Loss dB to linear loss | L = 10^(Loss_dB/10) | Higher loss reduces received power and range |
Example Calculations
Example 1: Calculate range
Suppose you enter these values:
- Frequency = 2.4 GHz
- Receiver sensitivity = -90 dBm
- Other losses = 2 dB
- Transmitter power = 1 W
- Total antenna gain = 6 dBi
- Range is left blank
The calculator converts -90 dBm to 1.0e-12 W, converts 6 dBi to a linear gain of about 3.981, and applies the Friis range formula. The result is about 15.8 km in ideal free space.
Example 2: Calculate required total antenna gain
Suppose you enter these values:
- Frequency = 915 MHz
- Receiver sensitivity = -100 dBm
- Other losses = 2 dB
- Transmitter power = 0.1 W
- Range = 30 km
- Total antenna gain is left blank
The required total antenna gain is about 3.2 dBi. This is the combined transmit and receive antenna gain, so it could be split between the two antennas in different ways.
FAQs
What does total antenna gain mean?
Total antenna gain is the combined gain of the transmit antenna and receive antenna in dB terms. For example, if the transmit antenna is 4 dBi and the receive antenna is 6 dBi, the total antenna gain entered is 10 dBi. The calculator converts that combined dBi value to a linear gain ratio for the Friis equation.
Why is the calculated range different from real-world range?
The result is a free-space estimate. Real links can be shorter because of obstacles, ground reflections, Fresnel-zone blockage, polarization mismatch, antenna misalignment, cable loss, interference, noise, and regulatory power limits. Add known cable and mismatch losses in the other losses field, but treat the final number as an ideal line-of-sight estimate unless you have a full link budget.
Does higher frequency reduce range?
Yes, for the same transmitter power, antenna gain, receiver sensitivity, and losses, higher frequency gives a shorter wavelength. In the Friis equation, a shorter wavelength increases free-space path loss, which reduces the calculated range.