Broadcast & Land Mobile Radiated Power Utility
ERP Calculator (Effective Radiated Power)
Compute dipole-referenced Effective Radiated Power (ERP) and equivalent isotropic EIRP for FM broadcast, land mobile radio (LMR), and amateur repeaters.
dB
Effective Radiated Power (ERP) Ref: Half-Wave Dipole (0 dBd)
121.34 Watts ERP
Logarithmic Level: +50.84 dBm ERP
Isotropic Equivalent (EIRP) Ref: Isotropic Sphere (0 dBi)
199.07 Watts EIRP
Logarithmic Level: +52.99 dBm EIRP
Net System Gain
+3.85 dB Dipole Multiplier
2.43 × PTX Power at Feedpoint
31.55 Watts Dissipated Cable Heat
18.45 Watts Step-by-Step Mathematical Derivation
Step 1: Convert P_TX to dBm = 10×log₁₀(50 W × 1000) = +46.99 dBm
Step 2: Antenna at Terminals = 46.99 − 2.0 dB loss = 44.99 dBm
Step 3: ERP (dBm) = 44.99 + 5.85 dBd = +50.84 dBm ERP (121.34 Watts)
Step 4: Isotropic EIRP = 50.84 + 2.15 = +52.99 dBm EIRP (199.07 Watts)
Step 2: Antenna at Terminals = 46.99 − 2.0 dB loss = 44.99 dBm
Step 3: ERP (dBm) = 44.99 + 5.85 dBd = +50.84 dBm ERP (121.34 Watts)
Step 4: Isotropic EIRP = 50.84 + 2.15 = +52.99 dBm EIRP (199.07 Watts)
Worked Examples
Step-by-Step ERP Calculations
Review step-by-step mathematical examples computing Effective Radiated Power for commercial broadcast transmitters and public safety repeaters:
Example A: Commercial FM Broadcast Station (Class A) FM Broadcast
An FM broadcast station operates a 1,500 Watt (+61.76 dBm) transmitter connected through 1-5/8 inch rigid line with 0.8 dB attenuation to a 4-bay circularly polarized array with +6.8 dBd gain.
System Inputs:
• Transmitter Power (P_TX): 1,500 W (+61.76 dBm)• Transmission Line Loss (L_c): 0.8 dB
• Antenna Gain (G_dBd): +6.8 dBd (+8.95 dBi)
Step-by-Step Solution:
1. Feedpoint Power = 61.76 − 0.8 = +60.96 dBm (1,247.38 W)2. ERP (dBm) = 60.96 + 6.8 = +67.76 dBm ERP
3. Linear ERP (Watts) = 10^(67.76 / 10) / 1000 = 5,970.35 Watts ERP (≈ 6.0 kW)
4. Equivalent EIRP = 67.76 + 2.15 = +69.91 dBm EIRP (9,794.9 W)
Regulatory Verdict: 5,970 W ERP complies perfectly with the FCC Class A 6,000 W maximum ERP ceiling. Check power conversions with our Watts to dBm Calculator.
Example B: Public Safety VHF Dispatch Repeater LMR Part 90
An emergency services 155 MHz repeater outputs 45 Watts (+46.53 dBm) through a cavity duplexer and 1/2" Heliax (2.5 dB total loss) into a collinear dipole with +5.0 dBd gain.
System Inputs:
• Transmitter Power (P_TX): 45 W (+46.53 dBm)• Duplexer & Feed Loss (L_c): 2.5 dB
• Dipole Gain (G_dBd): +5.0 dBd (+7.15 dBi)
Step-by-Step Solution:
1. Feedpoint Power = 46.53 − 2.5 = +44.03 dBm (25.29 W)2. ERP (dBm) = 44.03 + 5.0 = +49.03 dBm ERP
3. Linear ERP (Watts) = 10^(49.03 / 10) / 1000 = 79.98 Watts ERP (≈ 80 W)
4. Equivalent EIRP = 49.03 + 2.15 = +51.18 dBm EIRP (131.2 W)
Engineering Verdict: 80 W ERP delivers robust suburban coverage. Calculate propagation path loss with our Free Space Path Loss Calculator.
Regulatory Standards
ERP vs. EIRP: Why Regulators Use Different Radiated Standards
Understanding the historical and physical differences between dipole-referenced and isotropic-referenced radiation:
1. Effective Radiated Power (ERP)
ERP is referenced to a physical half-wave dipole (0 dBd). It is the legally mandated metric for FCC Part 73 commercial FM and TV broadcasting, Land Mobile Radio (Part 90), and VHF marine radio.
ERP(dBm) = EIRP(dBm) − 2.15 dB • ERP(W) = EIRP(W) / 1.64
2. Effective Isotropic Radiated Power (EIRP)
EIRP is referenced to an ideal theoretical point source (0 dBi). It is standard for Wi-Fi, satellite dishes, radar, cellular LTE/5G base stations, and microwave links. Calculate EIRP with our dedicated EIRP Calculator.
EIRP(dBm) = ERP(dBm) + 2.15 dB • EIRP(W) = 1.64 × ERP(W)
Propagation Coverage Sandbox
Tower Height & Radio Horizon Coverage Estimator
Adjust the transmitter tower height to estimate the radio horizon distance incorporating standard 4/3 atmospheric refraction.
150 meters (492 ft)
10m (Poles) 150m (Standard FM) 300m (Regional Tower) 600m (Mountain Mast)
Optical Line-of-Sight Horizon
50.46 km (31.3 miles) 4/3 Refraction Radio Horizon
58.27 km (36.2 miles) Service Coverage Area
10,667 km² Regulatory Rulebook
FCC Part 73 / Part 90 Station Class Checker
Select a commercial broadcast or land mobile radio tier to evaluate your calculated ERP against legal transmission limits.
Transmission Line Engineering
Coaxial Transmission Line Loss & Hardline Comparison
In high-power transmitter installations, cable loss can waste thousands of Watts of expensive RF energy before it ever reaches the antenna. Choose the right transmission line:
| Coaxial Cable Type | Loss @ 100 MHz (FM) | Loss @ 450 MHz (UHF) | Max Power Rating | Typical Installation |
|---|---|---|---|---|
| RG-58 (Thin Coax) | 4.5 dB / 100ft | 10.8 dB / 100ft | 150 Watts | Short lab test jumpers only |
| LMR-400 Low Loss | 1.1 dB / 100ft | 2.7 dB / 100ft | 1.5 kW | Amateur radio & small LMR towers |
| 1/2" Heliax Foam Hardline | 0.68 dB / 100ft | 1.51 dB / 100ft | 3.2 kW | Commercial cell tower jumpers |
| 7/8" Heliax Foam Hardline | 0.38 dB / 100ft | 0.86 dB / 100ft | 7.8 kW | Medium FM broadcast stations |
| 1-5/8" Air-Dielectric Hardline | 0.19 dB / 100ft | 0.46 dB / 100ft | 25 kW | High-power regional broadcast towers |
Antenna Physics Proof
Mathematical Derivation of Dipole vs. Isotropic Offset (+2.15 dB)
A theoretical isotropic radiator sends energy equally in all 4π steradians of a sphere (gain = 1.0 = 0 dBi). In contrast, a standard half-wave resonant dipole focuses radiation into a donut-shaped toroidal pattern with an on-axis directivity of 1.641 linear gain:
Dipole to Isotropic Derivation:
G_dipole = 10 × log₁₀(1.641) = +2.15 dBi
EIRP (dBm) = ERP (dBm) + 2.15 dB ERP (Watts) = EIRP (Watts) / 1.641
| ERP in Watts | ERP in dBm | Equivalent EIRP (Watts) | Equivalent EIRP (dBm) | Application Benchmark |
|---|---|---|---|---|
| 5 Watts ERP | +36.99 dBm | 8.21 Watts | +39.14 dBm | Handheld Land Mobile Radio (LMR) |
| 50 Watts ERP | +46.99 dBm | 82.05 Watts | +49.14 dBm | Vehicular Public Safety Mobile Unit |
| 500 Watts ERP | +56.99 dBm | 820.5 Watts | +59.14 dBm | FCC Part 90 Commercial LMR Repeater |
| 6,000 Watts (6 kW) | +67.78 dBm | 9,846 Watts | +69.93 dBm | FCC Class A FM Broadcast Station |
| 50,000 Watts (50 kW) | +76.99 dBm | 82,050 Watts | +79.14 dBm | FCC Class B Regional FM Broadcast |
| 100,000 Watts (100 kW) | +80.00 dBm | 164,100 Watts | +82.15 dBm | FCC Class C Maximum Super-Station |
Knowledge Base
Frequently Asked Questions: Effective Radiated Power (ERP)
Common questions about RF power conversions, negative dBm, and voltage calculations.
Effective Radiated Power (ERP) is the standardized measure of total apparent RF power radiated by an antenna system in its direction of maximum directivity, referenced specifically to a half-wave resonant dipole antenna (0 dBd).
The sole difference is the reference antenna standard. ERP is referenced to a half-wave dipole (0 dBd), whereas EIRP is referenced to a theoretical isotropic point source (0 dBi). Because a resonant dipole has an inherent directivity gain of +2.15 dBi, the mathematical conversion is: EIRP = ERP + 2.15 dB (or in linear Watts: EIRP = ERP × 1.641).
The step-by-step formula is: 1) Convert transmitter Watts to dBm: P(dBm) = 10 × log₁₀(P_Watts × 1000). 2) Subtract cable attenuation (L). 3) Add antenna gain in dBd (G_dBd). 4) Resulting ERP (dBm) = P(dBm) − L + G_dBd. 5) Convert back to Watts: ERP(Watts) = 10^((ERP_dBm − 30)/10).
The exact conversion formula is: dBd = dBi − 2.15 and dBi = dBd + 2.15. For example, a 6.0 dBi omnidirectional collinear antenna provides 3.85 dBd of gain referenced to a dipole.
Transmitter power alone does not account for antenna gain or tower line losses. A 100-Watt transmitter connected to a high-gain directional array can create the same localized electromagnetic field strength as a 2,000-Watt transmitter on an omni antenna. Regulating ERP standardizes physical coverage boundaries and interference zones.
Under FCC Title 47 CFR Part 73: Class A FM stations are permitted up to 6,000 Watts (6 kW) ERP at 100m HAAT; Class B FM stations up to 50,000 Watts (50 kW) ERP at 150m HAAT; and Class C FM stations up to 100,000 Watts (100 kW) ERP at 600m HAAT.
Height Above Average Terrain (HAAT) measures antenna phase center elevation relative to surrounding terrain between 3 and 16 km from the mast. Higher HAAT extends the optical and radio horizon ($d approx 4.12 imes sqrt{h_{ ext{HAAT}}}$ km), allowing lower ERP to achieve equal geographic coverage.
On a 500-foot tower run using thin RG-8 coax at 450 MHz, cable attenuation can exceed 6 dB (meaning 75% of your RF power turns into thermal heat inside the cable). Switching to 1-5/8" Heliax hardline drops attenuation to under 0.5 dB, preserving over 89% of power for radiation.