Received Power Calculator - Calculator Academy

Reviewed By: Patrick Myers (BSME)

Enter the transmitted power, the carrier frequency, the antenna gain (linear ratio or dBi), and the propagation distance into the calculator to determine the received power using the free-space Friis transmission equation.

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Received Power Formula

The following formula (the free-space Friis transmission equation) is used to calculate the received power.

P_r = P_t \cdot G \left(\frac{c}{4\pi f d}\right)^2

Where P_r is the received power (W)
P_t is the transmitted power at the antenna input (W)
G is the combined antenna gain (dimensionless, linear), where G = G_t · G_r. (If you have gains in dBi, convert to linear with G = 10^(G_dBi/10).)
f is the carrier frequency (Hz)
d is the propagation distance (m)
c is the speed of light (≈ 299,792,458 m/s)

To calculate received power, multiply transmitted power by the combined antenna gain, then multiply by (c/(4π f d))².

How to Calculate Received Power?

The following example problems outline how to calculate received power.

Example Problem #1

First, determine the transmitted power. In this example, the transmitted power is 12 W.
Next, determine the carrier frequency. For this problem, the carrier frequency is 50 MHz.
Next, determine the propagation distance. In this case, the propagation distance is 86 m.
Next, determine the combined antenna gain. In this case, the gain is 2 (linear).
Finally, calculate the received power using the formula above.

P_r = P_t · G · (c/(4π f d))²

Inserting the values from above and solving yields:

P_r = 12 · 2 · (299792458/(4π · 50000000 · 86))² ≈ 0.000739 (W)

Example Problem #2

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

combined antenna gain (linear) = 5

transmitted power = 105 W

carrier frequency = 3 GHz

propagation distance = 14 m

Enter these given values into the calculator above to get:

P_r = 105 · 5 · (299792458/(4π · 3000000000 · 14))² ≈ 0.000169 (W)