Calculate the minimum safe distance from a transmitting antenna so RF power density stays within FCC exposure limits, using transmitter power, antenna gain, and frequency.
RF Exposure Distance Formula
R = sqrt( P * G / (4 * pi * S) )
The same relationship solved for power density at a known distance is:
S = P * G / (4 * pi * R^2)
Where:
R is the minimum safe distance from the antenna in meters. P is the transmitter power reaching the antenna in watts. G is the antenna gain as a linear ratio, found from the gain in dBi using G = 10^(dBi/10). S is the maximum permissible exposure (MPE) power density limit in watts per square meter. The term 4 * pi * R^2 is the surface area of a sphere at radius R, so the power spreads evenly over that area in the far field.
Power density falls off with the square of distance, so doubling the distance reduces the power density to one quarter. To compare against published limits in mW/cm2, note that 1 mW/cm2 equals 10 W/m2.
FCC MPE Power Density Limits
The limit S depends on frequency and on whether the location is a controlled (occupational) or uncontrolled (general public) environment. The values below are the FCC limits in mW/cm2.
| Frequency (MHz) | Controlled | Uncontrolled |
|---|---|---|
| 1.34 to 30 | 900 / f^2 | 180 / f^2 |
| 30 to 300 | 1.0 | 0.2 |
| 300 to 1500 | f / 300 | f / 1500 |
| 1500 to 100000 | 5.0 | 1.0 |
Here f is the frequency in MHz. Controlled limits apply where people are aware of and can control their exposure, such as licensed operators. Uncontrolled limits apply to the general public.
Example
Suppose a transmitter delivers 100 W to an antenna with a gain of 6 dBi, operating at 146 MHz in an uncontrolled environment. First convert the gain to a linear ratio: G = 10^(6/10) = 3.98. At 146 MHz the uncontrolled limit is 0.2 mW/cm2, which is 2 W/m2. The minimum safe distance is R = sqrt( (100 * 3.98) / (4 * pi * 2) ) = sqrt( 398 / 25.13 ) = sqrt( 15.84 ) = 3.98 m.
If you instead want the power density at 3 m for the same setup, S = (100 * 3.98) / (4 * pi * 3^2) = 398 / 113.1 = 3.52 W/m2, which is 0.352 mW/cm2. This exceeds the 0.2 mW/cm2 uncontrolled limit, so 3 m is too close.
FAQ
What does this calculator tell you? It estimates the minimum distance you should keep from a transmitting antenna so the RF power density stays at or below the maximum permissible exposure limit. It can also report the power density at a specific distance and flag whether that distance is safe.
Should you use the controlled or uncontrolled limit? Use the uncontrolled (general public) limit for areas where people are not aware of their exposure or cannot avoid it. Use the controlled (occupational) limit only where people are trained, aware of the source, and able to limit their own exposure.
Why does antenna gain matter so much? Gain concentrates power in a direction, so a higher gain antenna produces a higher power density in the main beam for the same input power. The calculation uses the linear gain, so even a few dBi of gain noticeably increases the required safe distance.