Enter any 2 values (frequency, transmit power, or distance) into the calculator to estimate the missing variable under a simplified free-space (line-of-sight) model.

Broadcast Distance Calculator

Enter any 2 values to calculate the missing variable

Assumes free-space propagation, isotropic antennas (0 dBi), and a reference received power of 1 µW (−30 dBm). Real-world coverage can differ greatly due to antenna height, terrain, clutter, and receiver sensitivity.

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Broadcast Distance Formula

There is no single universal “broadcast distance” formula. This calculator uses a simplified free-space (Friis transmission) model with isotropic antennas and a fixed reference received power of 1 µW (−30 dBm) to produce an idealized range estimate.

D = \frac{c}{4\pi f}\sqrt{\frac{P}{P_{r,\text{ref}}}}

Variables:

  • D is the estimated free-space distance (meters, m)
  • P is the transmit power (watts, W)
  • f is the frequency (hertz, Hz)
  • c is the speed of light (≈ 299,792,458 m/s)
  • Pr,ref is the reference received power used by this calculator (1 µW = 1×10−6 W)

To estimate the distance, compute the square root term √(P / Pr,ref), multiply by c/(4πf), and convert the result to your preferred distance unit. This estimate assumes ideal free-space propagation and should not be used as a real-world coverage guarantee.

What is Broadcast Distance?

Broadcast distance (or coverage range) refers to how far a signal can be received with acceptable quality. In practice, range depends on transmitter power, frequency, antenna gains and heights, receiver sensitivity, required signal-to-noise ratio, losses (cables, connectors), and the propagation environment (terrain, buildings, foliage, atmospheric effects). All else equal, higher transmit power and lower frequency can increase range, but many broadcast services (e.g., VHF/UHF TV and FM) are often limited primarily by line-of-sight and antenna height rather than power alone.

How to Calculate Broadcast Distance?

The following steps outline how to calculate the distance estimate used by this calculator.

  1. Determine the signal frequency (f).
  2. Determine the transmitter power (P).
  3. Use the simplified free-space formula D = (c/(4πf)) √(P / Pr,ref) with Pr,ref = 1 µW.
  4. 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 (using the calculator’s assumptions).

Frequency (f) = 100 MHz

Power (P) = 400 Watts

Estimated Distance (D) ≈ 4.775 km (≈ 2.97 mi)