Seamlessly convert between Effective Radiated Power (ERP) and Effective Isotropic Radiated Power (EIRP). Perfect for RF engineers, ham radio operators, and wireless system designers. Includes real‑time bar chart comparison.
Enter ERP value and select unit. EIRP = ERP + 2.15 dB (dipole reference).
Convert EIRP back to ERP (reverse formula: ERP = EIRP - 2.15 dB).
Effective Radiated Power (ERP) and Effective Isotropic Radiated Power (EIRP) are two critical metrics in antenna theory and radio communication. ERP represents the total power radiated by a transmitting antenna relative to a half-wave dipole reference (gain ≈ 2.15 dBi). EIRP, in contrast, refers to the power radiated relative to an ideal isotropic radiator (a theoretical point source radiating equally in all directions). The key relationship is:
This fixed offset (2.15 dB) arises from the fundamental gain difference: a half-wave dipole has a gain of 2.15 dBi. Therefore, any antenna specification expressed in ERP can be converted to EIRP by simply adding 2.15 dB. Conversely, subtract 2.15 dB to go from EIRP to ERP. The conversion holds regardless of actual antenna design; it’s a mathematical reference shift.
Regulatory bodies like the FCC often specify maximum ERP for broadcast stations (FM, TV) while EIRP is more common in satellite and point-to-point links (ITU-R recommendations). Understanding both ensures compliance and accurate link budget calculations.
Given ERP in linear watts (W), first convert to dBm: PERP,dBm = 10·log₁₀(PERP,W × 1000). Then PEIRP,dBm = PERP,dBm + 2.15. To obtain EIRP in watts: PEIRP,W = 10(PEIRP,dBm - 30)/10. Our converter automatically applies these formulas with double precision. The bar graph dynamically scales both values (dBm) using a linear mapping relative to maximum reference (max of ERP_dBm and EIRP_dBm, with floor at -30 dBm for visibility).
A local FM station operates with 50 kW ERP (effective radiated power) using a dipole array. The station wants to coordinate with a neighboring country that uses EIRP limits. Using our converter: 50 kW ERP = 77 dBm (since 10*log10(50,000*1000) = 77 dBm). Adding 2.15 dB yields 79.15 dBm EIRP, which corresponds to about 82.2 kW EIRP. This precise conversion ensures regulatory cross-border agreements and prevents interference.
| ERP (W) | ERP (dBm) | EIRP (dBm) | EIRP (W) | Typical Use |
|---|---|---|---|---|
| 0.1 W (100 mW) | 20 dBm | 22.15 dBm | 0.164 W | Bluetooth / IoT sensor |
| 1 W | 30 dBm | 32.15 dBm | 1.64 W | Wi-Fi router / Small cell |
| 10 W | 40 dBm | 42.15 dBm | 16.4 W | Amateur radio mobile |
| 100 W | 50 dBm | 52.15 dBm | 164 W | VHF base station |
| 1000 W (1 kW) | 60 dBm | 62.15 dBm | 1.64 kW | FM broadcast (low power) |
| 50,000 W (50 kW) | 77 dBm | 79.15 dBm | 82.2 kW | High-power FM station |