EIRP & ERP Calculator: Radiated Power in dBm and Watts with a Regulatory Check

How it works

P (dBm) = 10 × log₁₀(P in mW) · EIRP (dBm) = P_tx − feedline loss + G (dBi) · ERP = EIRP − 2.15 dB · dBi = dBd + 2.15 · P (W) = 10^(dBm ÷ 10) ÷ 1,000 · power density S = EIRP (W) ÷ (4π r²) · field strength E = √(30 × EIRP) ÷ r

Regulators limit the power a station radiates in its strongest direction, because that is what causes interference. EIRP is the power an ideal isotropic antenna would need to produce the same peak field: the transmitter power in dBm, minus the loss in cables and connectors, plus the antenna gain in dBi. ERP is the same figure referenced to a half-wave dipole, which itself has 2.15 dBi of gain, so ERP is always 2.15 dB below EIRP for the same station. Broadcast, land-mobile and EU sub-GHz SRD rules are usually written in ERP; Wi-Fi and most other unlicensed bands use EIRP. In the US, FCC Part 15.247 allows 1 W of conducted output in the 902–928 MHz, 2.4 GHz and 5.8 GHz bands with antennas up to 6 dBi (36 dBm EIRP). With more gain, point-to-multipoint systems must cut power dB for dB; fixed point-to-point links at 2.4 GHz cut 1 dB for every 3 dB of extra gain, and at 5.725–5.85 GHz need no cut at all. In the EU, 2.4 GHz wideband data is capped at 100 mW (20 dBm) EIRP, 5.15–5.35 GHz Wi-Fi at 200 mW and 5.47–5.725 GHz at 1 W with transmit power control, and the 868 MHz SRD sub-bands at 25 mW or 500 mW ERP. The arithmetic also shows the cost of feedline: 3 dB of loss throws away half of the transmitter’s power before it reaches the antenna. Rules change and vary by country and equipment certification, so treat the check as a first look, not a compliance test.

Worked example

5 W is 10 × log₁₀(5,000 mW) = 36.99 dBm. After 1.5 dB of coax it is 35.5 dBm (3.54 W) at the antenna, and a 9 dBi antenna gives 36.99 − 1.5 + 9 = 44.49 dBm EIRP, about 28.1 W, or 42.3 dBm (17.0 W) ERP. Under the FCC point-to-multipoint rule a 9 dBi antenna is 3 dB over 6 dBi, so the power reaching it may be at most 27 dBm and EIRP at most 36 dBm. The station is 8.5 dB over, so the transmitter would need to drop to 28.5 dBm, about 0.71 W.

Sources: eCFR 47 CFR 15.247: power limits for 902–928 MHz, 2.4 GHz and 5.8 GHz, antenna gain and point-to-point rules · ETSI EN 300 328 V2.2.2: 2.4 GHz wideband data, 20 dBm e.i.r.p. · Wikipedia: List of WLAN channels (EU 5 GHz e.i.r.p. limits) · Wikipedia: Short Range Devices (EU 863–870 MHz sub-bands, ERP and duty cycle) · Omni Calculator: EIRP calculator (example 21 dBm, 4 dB loss, 11 dBi → 28 dBm)

Frequently asked questions