Estimate a far-field model distance at a selected FCC MPE value, or compare predicted RF power density with that value, using average antenna input power, directional gain, and frequency. This is not a verified safe clearance or a compliance assessment.
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 modeled distance at the selected limit in meters. P is the time-averaged 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, and the directional gain scales the far-field density toward the evaluated location. The estimate excludes near-field behavior, reflections, other sources, and installation-specific effects.
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 MPE values in mW/cm2 for 0.3 to 100000 MHz. Below 30 MHz they are plane-wave-equivalent values, and electric and magnetic fields must be assessed separately. Occupational/controlled averaging is 6 minutes; general public/uncontrolled averaging is 30 minutes.
| Frequency (MHz) | Controlled | Uncontrolled |
|---|---|---|
| 0.3 to 1.34 | 100 | 100 |
| 1.34 to 3 | 100 | 180 / f^2 |
| 3 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 to occupational exposure where people are fully aware of their exposure and can control it; holding a license alone does not establish those conditions. 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 modeled distance at this limit 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 modeled density exceeds the 0.2 mW/cm2 uncontrolled value. Actual installation safety and compliance require an appropriate assessment; the far-field model may not apply at 3 m.
FAQ
What does this calculator tell you? It estimates the distance where a far-field, single-source model equals a selected MPE value. It can also compare modeled density at a distance with that value. Antenna geometry, near-field conditions, reflections, multiple sources and applicable assessment procedures must be considered before drawing safety or compliance conclusions.
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 modeled distance at a selected density limit.
