Compute far‑field power density (W/m², mW/cm²) and electric field strength from transmit power, antenna gain, and distance. Essential for EMF exposure assessment, RF safety compliance (ICNIRP/FCC), and wireless system planning.
Power density (S) describes the amount of radio frequency power per unit area passing through a point in space. In the far‑field of an antenna, it is given by the classical formula for an isotropic radiator modified by antenna gain:
S = P · G / (4π R²)
where P = transmit power (W), G = antenna gain (linear), R = distance (m). Gain from dBi: G_lin = 10(G_dBi/10).
For example, a 0.1 Wi‑Fi access point with 3 dBi antenna at 2 m: G_lin = 100.3 ≈ 2.0, S = (0.1·2) / (4π·4) ≈ 0.004 W/m² = 0.0004 mW/cm².
RF exposure limits are set by international bodies like ICNIRP (International Commission on Non‑Ionizing Radiation Protection) and national authorities such as the FCC (USA). For frequencies above 400 MHz, the ICNIRP public reference level for power density is 2 W/m² (0.2 mW/cm²) averaged over 30 min; occupational limit is 10 W/m². The FCC uses similar values in OET Bulletin 65. These limits prevent excessive heating of tissue (thermal effects). Our calculator helps compare computed power density against these benchmarks.
The power density formula derives from the Poynting vector magnitude for a plane wave: S = E×H. In free space, E/H = 377 Ω, and S = E²/377 = 377 H². Therefore, if you have computed S, the rms electric field strength (far‑field) is:
E = √(377 · S) (V/m)
For example, S = 1 W/m² yields E ≈ 19.4 V/m. This relation holds for a single carrier in the far‑field (Fraunhofer region).
Antenna gain conversion: Gain in dBi is often provided by manufacturers. Use G_linear = 10^(G_dBi/10). Isotropic gain (0 dBi) means G_linear = 1. A directional antenna focuses power, increasing power density in the main lobe.
All results are shown in the panel above. A reference exposure limit (ICNIRP public) is displayed for quick comparison, but always consult local regulations.
| Authority | Exposure type | Frequency range | Power density limit |
|---|---|---|---|
| ICNIRP (2020) | General public | 400–2000 MHz | 2 W/m² (0.2 mW/cm²) |
| ICNIRP (2020) | Occupational | 400–2000 MHz | 10 W/m² (1 mW/cm²) |
| FCC OET‑65 | General population / uncontrolled | 1500–100,000 MHz | 1 mW/cm² (10 W/m²) |
| FCC OET‑65 | Occupational / controlled | 1500–100,000 MHz | 5 mW/cm² (50 W/m²) |
| EU Council Rec. | General public | 2 GHz – 300 GHz | 10 W/m² |
A mobile operator installs a 5G massive‑MIMO antenna with total radiated power of 200 W (average) and maximum array gain 24 dBi. To ensure public exposure below ICNIRP’s 2 W/m² limit, what is the minimum safe distance? Using the calculator with P=200, G=24 dBi (linear ≈251), we adjust R until S ≤ 2 W/m². For R=20 m, S = (200·251)/(4π·400) ≈ 200·251/(5026) ≈ 10 W/m² → too high. At R=40 m, S ≈ 2.5 W/m² (slightly above). At R=45 m, S ≈ 1.98 W/m². Thus a 45 m clearance is recommended in the main beam direction. This quick estimate helps site planners and regulators.
The formula used assumes far‑field (Fraunhofer) conditions, typically valid for distances R > 2D²/λ (where D is antenna diameter, λ wavelength). Inside the near‑field, power density varies unpredictably and may be higher or lower; our calculator gives an approximate value. Always use professional assessment for compliance near large antennas.
function linearGain(dBi) { return Math.pow(10, dBi/10); }
function powerDensity(P, gainLin, R) { return (P * gainLin) / (4 * Math.PI * R * R); }
// P in W, R in m → S in W/m²
function mWpercm2(S) { return S * 0.1; } // 1 W/m² = 0.1 mW/cm²
function eField(S) { return Math.sqrt(377 * S); }