ERP to EIRP Converter

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.

ERP → EIRP

Enter ERP value and select unit. EIRP = ERP + 2.15 dB (dipole reference).

Reference: dipole antenna gain (2.15 dBi).
? EIRP (dBm): --
? EIRP (Watts): --

⚡ ERP (dBm equivalent): --
? 100 mW ERP (0.1W) ? 1 Watt ERP ? 25W ERP (ISM band) ? 500 dBm (example only)

EIRP → ERP

Convert EIRP back to ERP (reverse formula: ERP = EIRP - 2.15 dB).

? ERP (dBm): --
? ERP (Watts): --
? 37 dBm EIRP ? 2W EIRP ? 46 dBm (40W ERP)
Power comparison (dBm scale) – ERP vs EIRP
ERP (dBm)
0 dBm
EIRP (dBm)
0 dBm
ERP (relative to dipole) EIRP (isotropic reference) Difference = 2.15 dB always
Local processing only: All conversions occur in your browser. No data transmitted or stored.

What is ERP and EIRP? Technical Fundamentals

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:

EIRP (dBm) = ERP (dBm) + 2.15 dB
Because a dipole has 2.15 dBi gain over isotropic.

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.

Mathematical Derivation & Unit Handling

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).

Real-World Applications & Engineering Use Cases

  • Broadcast Radio/TV: FCC specifies ERP limits for FM stations (e.g., 100 kW ERP). Engineers convert to EIRP for interference analysis with international coordination.
  • Satellite Communications: EIRP is the standard for uplink and downlink budgets; our tool helps ground station designers convert legacy ERP specs.
  • Wi-Fi / Cellular Planning: Access points and base stations often have ERP ratings. Convert to EIRP for path loss calculations (Free Space Path Loss formula uses EIRP).
  • Amateur Radio (Ham): Many transceivers output power rated in ERP when using specific antennas; use the converter to compare with isotropic requirements.
  • EMC/RF Exposure: Safety compliance sometimes requires EIRP for maximum permissible exposure (MPE) calculations.
  • Regulatory Compliance: FCC Title 47, Part 74, and ETSI EN 300 422 often reference ERP for licensed transmitters; EIRP is mandated for earth stations (ITU-R S.580). This converter ensures seamless switching between the two regimes.
Case Study: FM Broadcast Station ERP to EIRP

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.

Reference Table: Common ERP ↔ EIRP Values

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

Frequently Asked Questions

The half-wave dipole has a gain of 2.15 dBi relative to an isotropic radiator. ERP references dipole gain (0 dBd), while EIRP references isotropic gain. Since 0 dBd = 2.15 dBi, the conversion offset is fixed.

No. ERP and EIRP are both referenced to the same transmitted power after antenna gain. The relationship only involves the dipole/isotropic gain difference, not the absolute efficiency. However, actual radiated power depends on feedline losses and antenna efficiency, but the conversion constant remains unchanged.

Absolutely. The ERP/EIRP relationship is frequency-independent — the 2.15 dB offset applies to all frequencies as it's derived from antenna directivity pattern of a half-wave dipole versus isotropic, valid across RF spectrum.

Our JavaScript uses 64-bit floating point arithmetic, with typical relative error < 1e-12. The conversion is exact per definition; no rounding approximation is applied except for display.

Yes, the bar chart displays ERP and EIRP in dBm scaled linearly within the range of current values, plus a dynamic scaling factor, so the difference (2.15 dB) is visually clear for both low and high power values.

No, the 2.15 dB offset is purely based on antenna directivity. However, the actual radiated ERP/EIRP values must account for transmission line and connector losses before the antenna. This tool assumes the input power is already the power delivered to the antenna terminals.

Engineering & Standards References — This tool follows ITU-R SM.328 and IEEE Std 145 definitions. Conversion constants are derived from dipole gain (2.15 dBi) as per classical antenna theory. Data validated against industry calculators and NIST guidelines. Maintained by GetZenQuery tech team, updated May 2026.

Recommended resources: FCC EngineeringITU-R StandardsARRL Antenna Book