ERP & EIRP Calculator

Compute Effective Radiated Power (ERP) and Equivalent Isotropically Radiated Power (EIRP) from transmitter power, feed line loss, and antenna gain. Essential for RF link budgeting, broadcast compliance, and antenna system design.

Absolute transmitter output power (conducted).
dB
Positive value: cable & connector loss. Negative will be taken as absolute.
dBi = gain relative to isotropic; dBd → dBi = dBd + 2.15.
Quick examples:
? Wi-Fi AP (20 dBm + 5 dBi)
? FM Broadcast (5 kW, 6 dBd)
? Cellular Base (43 dBm, 18 dBi)
?️ Amateur Radio (100W, 9 dBd)
Local computation only – no data leaves your browser. All conversions are done client‑side with double precision.

Understanding ERP and EIRP in RF Systems

Effective Radiated Power (ERP) and Equivalent Isotropically Radiated Power (EIRP) are fundamental concepts in radio engineering, antenna theory, and regulatory compliance (FCC, ITU). They quantify the power that an antenna actually radiates in a given direction compared to reference antennas: a half‑wave dipole (for ERP) or an isotropic radiator (for EIRP).

Core formulas (logarithmic domain):
EIRP (dBm) = PTX(dBm) – Lfeeder(dB) + Gant(dBi)
ERP (dBm) = EIRP (dBm) – 2.15 dB
Where 2.15 dB is the theoretical gain of a half‑wave dipole relative to isotropic radiator.

Why ERP vs EIRP matter

Many broadcast regulations (FM, TV) specify maximum ERP because a dipole reference is historically common. For point‑to‑point links and satellite communications, EIRP is the standard because it references an ideal isotropic radiator. Converting between them is straightforward but critical: ERP = EIRP – 2.15 dB, and EIRP = ERP + 2.15 dB. Our calculator handles exact conversions, also taking into account feeder losses and the difference between dBd and dBi antenna gain figures.

In link budget analyses, EIRP determines the received signal strength via the Friis transmission equation. A higher EIRP extends coverage but must comply with local EIRP limits to avoid interference.

Step-by-Step Calculation Logic

  1. Normalize transmitter power – convert input (W, mW, dBW, dBm) to dBm reference.
  2. Subtract feeder loss (in dB) – representing cable, connector, and transmission line attenuation. Negative loss values are treated as absolute (loss is always positive).
  3. Add antenna gain – convert dBd to dBi if needed (dBd + 2.15 = dBi).
  4. Compute EIRP in dBm and then convert to dBW and Watts: Watts = 10((dBm-30)/10).
  5. ERP = EIRP(dBm) - 2.15 dB – then same unit conversions.
Case Study: FM Broadcast Station

A community radio station transmits with 2,000 W (33.01 dBm) at the transmitter output, feeder loss of 2.8 dB, and an antenna gain of 4 dBd. First, dBd→dBi = 4 + 2.15 = 6.15 dBi. EIRP (dBm) = 33.01 - 2.8 + 6.15 = 36.36 dBm → 4.32 kW EIRP. ERP = 36.36 - 2.15 = 34.21 dBm → 2.63 kW ERP. The station must ensure ERP does not exceed license limits (typically 3 kW ERP for this class), so this configuration is compliant. The calculator instantly validates such scenarios.

Reference Table: Common ERP/EIRP Values

Application Transmitter Power Antenna Gain ERP (approx.) EIRP (approx.)
Portable Walkie‑Talkie 5 W (37 dBm) 0 dBi -2.15 dBW / 0.61 W 5 W EIRP
4G LTE eNodeB 43 dBm (20 W) 18 dBi 58.85 dBm / 768 W 61 dBm / 1.26 kW
FM Broadcasting 10 kW (70 dBm) 6 dBd 73.85 dBm / 24.3 kW 76 dBm / 39.8 kW
Wi-Fi Access Point 20 dBm (100 mW) 5 dBi 22.85 dBm / 193 mW 25 dBm / 316 mW

Frequently Asked Questions (RF Engineering)

dBi refers to gain relative to an isotropic radiator (theoretical point source). dBd refers to gain relative to a half‑wave dipole. A dipole has 2.15 dBi gain, so dBd + 2.15 = dBi. Always ensure to convert before ERP/EIRP calculations.

ERP references a half‑wave dipole, which has a gain of 2.15 dBi over isotropic. Therefore, to refer to effective power compared to a dipole, the isotropic power (EIRP) must be reduced by 2.15 dB. For example, an EIRP of 30 dBm equals an ERP of 27.85 dBm.

Feeder loss should include transmission line loss, connector insertion loss, and any passive devices (diplexers, lightning arrestors) between the transmitter and antenna. Typically expressed in dB and always a positive value. Our calculator enforces absolute value internally.

Regulatory bodies like the FCC define maximum ERP to control coverage area and prevent co‑channel interference. Exceeding licensed ERP can result in fines and harmful interference. Use this calculator to verify compliance before system deployment.

Yes, antennas with intentional attenuation (e.g., dummy loads or poorly matched systems) can have negative gain, but for most radiators gains are positive dBi/dBd. The calculator accepts negative values for professional cases.

Engineering foundation – This calculator implements standard ITU‑R and IEEE definitions. Formulas are derived from “Antenna Theory” by Balanis and “RF Circuit Design” by Ludwig. Validated against industry EIRP/ERP conversion tables.

References: FCC OET Bulletin 65, ITU-R SM.328, and Wikipedia: Effective radiated power.

Real-World Applications

  • Satellite uplink design: EIRP determines power flux density at the satellite receiver.
  • 5G & mmWave: EIRP limits ensure human exposure safety (power density).
  • Amateur radio contesting: Legal ERP limits vary by license class – accurate calculation avoids violations.
  • Radio planning: Combining transmitter power, antenna gain, and line losses optimizes coverage radius.
Important: For accurate link budgets, also consider free‑space path loss, polarization mismatch, and atmospheric absorption. This calculator focuses solely on ERP/EIRP, the foundation of the transmit side.