EIRP Calculator (Effective Isotropic Radiated Power)

Calculate the Effective Isotropic Radiated Power (EIRP) of any radio transmitter system. Account for transmitter amplifier output, feeder cable and connector insertion losses, and directional antenna gain (dBi or dBd).

Load Engineering Presets:
Raw RF output power at the transmitter power amplifier (PA) port
dB
Total attenuation from jumper cables, lightning arresters, and connectors
Directional peak forward antenna gain (0 dBd = 2.15 dBi)
Effective Isotropic Radiated Power (EIRP) +59.00 dBm 794.33 kW
EIRP in Decibel-Watts
+29.00 dBW
Conducted Antenna Port
+41.00 dBm
Equivalent ERP (dBm)
+56.85 dBm
Equivalent ERP (Watts)
484.17 kW
Step-by-Step Mathematical Substitution
EIRP (dBm) = 43.00 dBm (Tx) - 2.00 dB (Loss) + 18.00 dBi (Gain) = +59.00 dBm (794.33 kW peak equivalent isotropic radiated power)

Engineering Principles: Effective Isotropic Radiated Power (EIRP)

An authoritative technical reference on the physics of directional radio emission, mathematical derivations, distinction between EIRP and ERP, regulatory compliance thresholds (FCC and ETSI), and Maximum Permissible Exposure (MPE).

1. Understanding Effective Isotropic Radiated Power (EIRP)

In electromagnetic theory and telecommunications engineering, Effective Isotropic Radiated Power (EIRP) quantifies the directional energy radiated by an antenna system. Rather than measuring the total physical RF energy discharged into space, EIRP defines the hypothetical linear power that a theoretical isotropic antenna (a lossless, omnidirectional point source radiating with equal intensity in all three dimensions, \( 0\text{ dBi} \)) would need to emit to produce the identical power flux density (\( S \)) observed along the peak bore-sight of a directional transmitting antenna.

Directional antennas—such as parabolic reflectors, horn feeds, patch arrays, or cellular Massive MIMO panels—do not amplify physical electromagnetic energy. Instead, they act as spatial focusing lenses, focusing power into a narrow, concentrated beamwidth while suppressing radiation in unwanted directions. EIRP represents the virtual equivalent power concentrated within that main lobe.

2. Mathematical Derivations

Calculating EIRP involves cascading the transmitter's raw conducted power, the passive transmission line attenuation, and the forward antenna gain:

\text{EIRP}_{\text{(dBm)}} = P_{\text{tx (dBm)}} - L_{\text{c (dB)}} + G_{\text{tx (dBi)}}

Where:
• \( P_{\text{tx (dBm)}} \) is the transmitter output power measured at the amplifier output flange.
• \( L_{\text{c (dB)}} \) is the aggregate insertion loss of coaxial cable jumpers, waveguides, connectors, surge arresters, and preselectors.
• \( G_{\text{tx (dBi)}} \) is the forward antenna directivity gain referenced to a theoretical isotropic sphere.

To convert logarithmic EIRP into absolute linear Watts:

\text{EIRP}_{\text{(Watts)}} = 10^{\frac{\text{EIRP}_{\text{(dBm)}} - 30}{10}} = P_{\text{tx (Watts)}} \cdot 10^{\frac{G_{\text{tx (dBi)}} - L_{\text{c (dB)}}}{10}}
Worked Field Example: Cellular 5G NR Macro Base Station (3.5 GHz n78)

Scenario: A wireless network operator deploys a 5G New Radio macrocell sector operating in the 3.5 GHz band. The remote radio head (RRH) generates 40 Watts (+46.0 dBm) per polarization. A 1/2-inch superflexible jumper introduces 0.8 dB of coaxial attenuation. The 64T64R beamforming Massive MIMO antenna delivers a peak forward boresight gain of +24.0 dBi.

1. Antenna Port Net Power:
\( P_{\text{ant}} = +46.0\text{ dBm} - 0.8\text{ dB} = +45.2\text{ dBm} \) (33.11 Watts conducted)

2. Peak Sector EIRP:
\( \text{EIRP} = +45.2\text{ dBm} + 24.0\text{ dBi} = +69.2\text{ dBm} \)

3. Conversion to Linear Kilowatts:
\( \text{EIRP}_{\text{Watts}} = 10^{(69.2 - 30)/10} = 10^{3.92} \approx 8,317.6\text{ Watts} \approx 8.32\text{ kW} \)

Engineering Consequence: Although the transmitter consumes only 40 Watts of raw RF power, a receiving terminal aligned directly in the antenna's bore-sight main lobe experiences the same electromagnetic field intensity as if it were illuminated by an 8.32-Kilowatt isotropic lightbulb.

3. EIRP vs. ERP: The Isotropic vs. Dipole Reference

In RF regulatory filings and broadcast engineering, two primary metrics quantify radiated emission:

  • EIRP (Effective Isotropic Radiated Power): References a theoretical isotropic radiator (\( 0\text{ dBi} \)). Used almost universally by 3GPP, ETSI, ITU, and IEEE for microwave, cellular, satellite, and Wi-Fi networks.
  • ERP (Effective Radiated Power): References an ideal center-fed half-wave dipole antenna in free space (\( 0\text{ dBd} \)). Extensively mandated by the US Federal Communications Commission (FCC) for FM broadcast, VHF/UHF television, and Land Mobile Radio (LMR).

Because a physical half-wave dipole naturally exhibits directivity in its doughnut-shaped radiation pattern, it delivers a forward gain of 2.15 dBi over a theoretical isotropic point source:

G_{\text{(dBi)}} = G_{\text{(dBd)}} + 2.15\text{ dB}
\text{EIRP}_{\text{(dBm)}} = \text{ERP}_{\text{(dBm)}} + 2.15\text{ dB} \iff \text{ERP}_{\text{(dBm)}} = \text{EIRP}_{\text{(dBm)}} - 2.15\text{ dB}
\text{ERP}_{\text{(Watts)}} = \frac{\text{EIRP}_{\text{(Watts)}}}{10^{2.15/10}} = \frac{\text{EIRP}_{\text{(Watts)}}}{1.641}

4. Regulatory Compliance & Maximum Permissible Exposure (MPE)

Telecommunications authorities worldwide cap EIRP to protect adjacent spectrum users from interference and prevent excessive electromagnetic human exposure:

  • Unlicensed Bands (Wi-Fi 2.4 GHz / 5 GHz): Under FCC Title 47 Part 15.247, Point-to-Multipoint (PtMP) Wi-Fi networks are capped at a maximum of +30 dBm (1 Watt) conducted transmitter power and +36 dBm (4 Watts) EIRP with a 6 dBi antenna. If an antenna exceeds 6 dBi, conducted power must be reduced by 1 dB for every 1 dBi above 6 dBi.
  • Fixed Point-to-Point (PtP) Exceptions: Under FCC Part 15.407 (5 GHz UNII-3 band), fixed backhaul links enjoy relaxed rules: for every 3 dBi of antenna gain above 6 dBi, conducted power only needs to be reduced by 1 dB, enabling parabolic dishes to produce legal EIRPs exceeding +53 dBm (200 Watts).
  • Human Radiation Safety (MPE Limits): FCC OET Bulletin 65 and ICNIRP international standards mandate exclusion safety zones around transmitter towers based on power density \( S = \frac{\text{EIRP}}{4 \pi R^2} \). Higher EIRP expands the required physical safety perimeter for tower maintenance personnel and the public.

5. Standard Reference Lookup Table

The table below cross-references legal EIRP limits, typical transmitter power levels, and antenna gains across common telecommunications systems:

Wireless Standard / Frequency Maximum Legal EIRP Max Conducted Tx Power Typical Antenna Gain Regulatory Reference
Wi-Fi 2.4 GHz (PtMP) +36 dBm (4 W) +30 dBm (1 W) 6.0 dBi (Omni / Patch) FCC Part 15.247 / ETSI EN 300 328
Wi-Fi 5 GHz UNII-1 (Client) +30 dBm (1 W) +24 dBm (250 mW) 6.0 dBi (Internal) FCC Part 15.407
Wi-Fi 5 GHz UNII-3 (Fixed PtP) +53 dBm+ (200 W+) +30 dBm (1 W) 23+ dBi (Parabolic Dish) FCC PtP Fixed Rule
5G NR FR1 Macro Cell (3.5 GHz n78) +78 dBm (63 kW equiv.) +46 dBm (40 W / port) 24 dBi (64T64R Massive MIMO) 3GPP TS 38.104 Base Station Spec
LTE Microcell / Small Cell +38 dBm (6.3 W) +30 dBm (1 W) 8.0 dBi (Directional Panel) 3GPP Local Area BS
Point-to-Point Microwave (11 GHz) +55 to +70 dBm +27 dBm (500 mW) 38 to 44 dBi (Parabolic Dish) ITU-R F.758 / ETSI Class 3
Bluetooth Low Energy (Class 1) +20 dBm (100 mW) +20 dBm (100 mW) 0.0 dBi (Ceramic Chip) Bluetooth SIG Core Spec