EIRP, ERP and Field Strength Calculator (Antenna Power and Exposure Distance)
Effective radiated power from the transmitter power, cable loss and antenna gain, the field strength and power density at a distance, and how far away a power-density limit is met.
Results
The dashed line marks the value you entered.
What this tool does
What a regulator or a link budget cares about is not the transmitter's power but the power an ideal isotropic antenna would need to give the same signal in the strongest direction: EIRP = power − cable loss + antenna gain, in dB. ERP uses a half-wave dipole as reference instead, which is 2.15 dBi, so it is 1.64 times smaller than the EIRP. In the far field the power density is EIRP ÷ 4πd² and the electric field is √(30 × EIRP) ÷ d; very close to the antenna these formulas overestimate or fail, and exposure limits depend on frequency, so use the limit your own regulator gives.
Formula
EIRP = P × 10^((G − L) ÷ 10) · ERP = EIRP ÷ 1.64 (2.15 dB) · S = EIRP ÷ (4π d²) · E = √(30 × EIRP) ÷ d (far field, free space)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
p | Transmitter power | W |
ll | Cable and connector loss | dB |
gi | Antenna gain | dBi |
d | Distance from the antenna | m |
lim | Power density limit you want to respect | W/m² |
EI | EIRP | W |
ED | EIRP in dBm | dBm |
ER | ERP (relative to a half-wave dipole) | W |
EF | Electric field strength at that distance | V/m |
SD | Power density at that distance | W/m² |
DS | Distance at which the density falls to your limit | m |
Worked example
- Transmitter power10 W
- Cable and connector loss2 dB
- Antenna gain8 dBi
- Distance from the antenna10 m
- Power density limit you want to respect10 W/m²
- EIRP39.81 W
- EIRP in dBm46.0 dBm
- ERP (relative to a half-wave dipole)24.27 W
- Electric field strength at that distance3.456 V/m
- Power density at that distance0.0317 W/m²
- Distance at which the density falls to your limit0.56 m
Limitations
- The formula assumes ideal geometry — an infinitely long wire or coil, a perfectly uniform sphere — in empty space or a uniform material. Real parts come close, but ends, nearby metal and magnetic materials change the field.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.