Antenna Radiation & Link Transmission Utility
EIRP Calculator
Compute Effective Isotropic Radiated Power (EIRP) in dBm, dBW, and linear Watts from transmitter power, feed line attenuation, and antenna gain.
dB
dBi
Effective Isotropic Radiated Power Ref: Isotropic (0 dBi)
70.79 Watts EIRP
Logarithmic Level: +48.50 dBm EIRP (+18.50 dBW)
Dipole Equivalent (ERP) Ref: Dipole (0 dBd)
43.15 Watts ERP
Logarithmic Level: +46.35 dBm ERP (EIRP − 2.15 dB)
Net System Gain
+21.50 dB Radiation Multiplier
141.25 × PTX Power at Feedpoint
354.8 mW Estimated HPBW
14.4° Cone Step-by-Step Mathematical Derivation
Step 1: P_TX = +27.00 dBm (0.501 Watts)
Step 2: Feeder Loss = −1.50 dB → Antenna Terminal = +25.50 dBm (0.355 W)
Step 3: EIRP = 25.50 + 23.00 dBi = +48.50 dBm EIRP (70.79 Watts)
Step 4: ERP = 48.50 − 2.15 = +46.35 dBm ERP (43.15 Watts)
Step 2: Feeder Loss = −1.50 dB → Antenna Terminal = +25.50 dBm (0.355 W)
Step 3: EIRP = 25.50 + 23.00 dBi = +48.50 dBm EIRP (70.79 Watts)
Step 4: ERP = 48.50 − 2.15 = +46.35 dBm ERP (43.15 Watts)
Worked Examples
Step-by-Step EIRP Calculations
Review step-by-step mathematical examples computing Effective Isotropic Radiated Power across terrestrial wireless links and satellite earth stations:
Example A: 5.8 GHz P2P Wireless Bridge Carrier Backhaul
A wireless Internet service provider configures a 5.8 GHz bridge with a +27.0 dBm (500 mW) transmitter, 1.5 dB coaxial loss, and a +23.0 dBi parabolic dish.
System Inputs:
• Transmitter Power (P_TX): +27.0 dBm (0.501 W)• Cable & Jumper Loss (L_c): 1.5 dB
• Antenna Gain (G_TX): +23.0 dBi
Step-by-Step Solution:
1. Feedpoint Power = 27.0 − 1.5 = +25.50 dBm (354.8 mW)2. EIRP (dBm) = 25.50 + 23.0 = +48.50 dBm EIRP
3. Linear Radiated Power = 10^(48.50 / 10) / 1000 = 70.79 Watts EIRP
4. Equivalent ERP = 48.50 − 2.15 = +46.35 dBm ERP (43.15 W)
Engineering Verdict: Antenna gain multiplies radiated power by 141.25×. Verify link margins on our RF Link Budget Calculator.
Example B: Ka-Band Satellite Earth Station Satellite Uplink
A satellite earth station operates a +50.0 dBm (100 W = +20 dBW) high-power amplifier with 0.8 dB waveguide loss into a 2.4m dish with +52.5 dBi gain.
System Inputs:
• Transmitter Power (P_TX): +50.0 dBm (+20.0 dBW)• Waveguide Feeder Loss (L_c): 0.8 dB
• Earth Station Gain (G_TX): +52.5 dBi
Step-by-Step Solution:
1. Feedpoint Power = 50.0 − 0.8 = +49.20 dBm (+19.20 dBW)2. EIRP in dBW = 19.20 + 52.5 = +71.70 dBW EIRP (+101.70 dBm)
3. Linear Radiated Power = 10^(71.70 / 10) = 14.79 Megawatts (MW)
4. Power Density at 1 km: S = 14.79 MW / (4π × 1000²) = 1.177 W/m²
Engineering Verdict: Multi-megawatt EIRP overcomes 210 dB space path loss. Check field exposure with our dBm to Power Density Calculator.
Antenna Gain Physics
dBi vs. dBd: Understanding Antenna Reference Standards
Antenna gain specifications depend on the chosen reference standard:
1. dBi (Isotropic Sphere Reference)
dBi measures antenna gain relative to a theoretical isotropic radiator—a zero-loss point source radiating equally in all directions (0 dBi). Used for Wi-Fi, microwave dishes, satellite terminals, and FCC Part 15 EIRP calculations.
EIRP(dBm) = P_TX(dBm) − Losses(dB) + Gain(dBi)
2. dBd (Half-Wave Dipole Reference)
dBd measures gain relative to a physical half-wave dipole antenna, which inherently possesses +2.15 dBi gain. Used primarily in land mobile radio (LMR), PMR, and broadcast ERP ratings.
Formula: Gain(dBi) = Gain(dBd) + 2.15 dB • See our ERP Calculator.
Antenna Aperture Radiation
Antenna Directivity & Half-Power Beamwidth (HPBW) Visualizer
Antenna gain does not create new RF energy—it focuses radiation from an omnidirectional sphere into a tight directional beamwidth cone:
Higher dBi gain narrows the 3 dB beamwidth angle (θ3dB), concentrating energy toward the horizon while attenuating unwanted interference from the side and rear:
Approximate Half-Power Beamwidth (HPBW)
14.4° Azimuth & Elevation Formula: HPBW ≈ √(41253 / 10^(G_dBi/10))
Main Lobe Radiation Concentration Cone
FCC Part 15 Regulatory Compliance
FCC Part 15.247 PtP 3:1 Rule Compliance Checker
Under FCC Part 15.247 rules for 2.4 GHz and 5.8 GHz fixed point-to-point wireless bridges, high-gain antennas require conducted transmitter power derating:
FCC PtMP Legal Max EIRP
+36.0 dBm (4.0 W) Max Conducted TX Allowed (PtP)
+24.33 dBm (271 mW) Your Calculated Status
DERATE TX BY 2.7 dB
Because your antenna gain (23 dBi) exceeds the 6 dBi baseline by 17 dB, the FCC 3:1 derating rule requires reducing transmitter power by 5.67 dB below +30 dBm (maximum legal PTX = +24.33 dBm).
Global Regulatory Rulebook
Global Regulatory EIRP Limits Comparison
Compare maximum legal EIRP transmission limits across international jurisdictions:
| Jurisdiction / Standard | 2.4 GHz Wi-Fi / ISM | 5.15–5.35 GHz (UNII-1/2A) | 5.725–5.850 GHz (UNII-3) | Regulatory Agency |
|---|---|---|---|---|
| United States & Canada | +36 dBm (4.0 W EIRP) | +30 dBm (1.0 W EIRP) | +36 dBm (PtMP) / +53 dBm (PtP) | FCC Part 15 / ISED RSS-247 |
| European Union (CE RED) | +20 dBm (100 mW EIRP) | +23 dBm (200 mW EIRP) | +30 dBm (1.0 W EIRP with TPC) | ETSI EN 300 328 / EN 301 893 |
| Japan (MIC / TELEC) | +22 dBm (160 mW EIRP) | +23 dBm (200 mW EIRP) | +30 dBm (1.0 W EIRP) | Ministry of Internal Affairs (MIC) |
| Australia & New Zealand | +36 dBm (4.0 W EIRP) | +23 dBm (200 mW EIRP) | +36 dBm (4.0 W EIRP) | ACMA AS/NZS 4268 |
| United Kingdom (Ofcom) | +20 dBm (100 mW EIRP) | +23 dBm (200 mW EIRP) | +36 dBm (4.0 W EIRP) | Ofcom Wireless Telegraphy Act |
Knowledge Base
Frequently Asked Questions: Effective Isotropic Radiated Power (EIRP)
Common questions about RF power conversions, negative dBm, and voltage calculations.
Effective Isotropic Radiated Power (EIRP) is the total apparent RF power that a theoretical isotropic antenna (which radiates uniformly in all directions with 0 dBi gain) would need to emit to produce the same peak signal intensity as your actual directional antenna.
The fundamental formula is: EIRP (dBm) = P_TX (dBm) − L_cable (dB) + G_antenna (dBi). In linear Watts: EIRP (Watts) = P_TX (Watts) × 10^((G_dBi − L_cable)/10).
EIRP is referenced to an isotropic radiator (0 dBi), while ERP is referenced to a half-wave dipole (0 dBd). Because a dipole has +2.15 dBi of inherent directivity gain: EIRP = ERP + 2.15 dB (or in linear Watts: EIRP = ERP × 1.641).
Under FCC Title 47 CFR Part 15.247 for Point-to-Multipoint (PtMP): Maximum conducted TX power is 30 dBm (1.0 Watt) with a 6 dBi antenna, yielding a legal maximum EIRP of +36 dBm (4.0 Watts).
For fixed 2.4 GHz PtP bridges, if antenna gain exceeds 6 dBi, conducted transmitter power must be reduced by 1 dB for every 3 dB of antenna gain above 6 dBi (PTX, max = 30 − (G − 6)/3 dBm).
Transmitter power alone does not reflect biological RF exposure, spectrum interference potential, or effective coverage reach. A low-power 100 mW transmitter on a high-gain 30 dBi dish produces the same directional EIRP (+50 dBm = 100 Watts) as a 100-Watt omni transmitter.
For parabolic dish and high-gain directional antennas, the approximate half-power beamwidth is: HPBW ≈ √(41,253 / 10^(G_dBi / 10)) degrees. For example, a 24 dBi dish has an extremely narrow beamwidth of ≈ 12.8 degrees.
Under ETSI / CE RED regulations in the European Union, the maximum allowed EIRP for 2.4 GHz is strictly +20 dBm (100 mW EIRP), which is 16 dB lower than the US FCC limit (+36 dBm).