Effective Radiated Power
ERP = Ptx × Gt
Quick answer
This calculator solves ERP = Ptx × Gt for Effective Radiated Power. With Transmitter Power 22 W, Antenna Gain (linear) 0.5, the result is 11 W. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Effective Radiated Power is the total power that would need to be radiated by an isotropic antenna to produce the same signal strength in the direction of maximum antenna gain. It combines the transmitter output power with the antenna gain to give a single figure of merit for the transmitting system. Regulatory agencies (FCC, ETSI) specify maximum ERP or EIRP limits for various frequency bands and applications. ERP uses a dipole reference while EIRP uses an isotropic reference (EIRP = ERP + 2.15 dB).
Variables
- ERP — Effective radiated power (W)
- Ptx — Transmitter output power (W)
- Gt — Antenna gain (linear, not dB)
Practical Notes
Convert dBi gain to linear: Gt = 10^(GdBi/10). FCC Part 15 limits for 2.4 GHz ISM band: 1W conducted power with up to 6 dBi antenna gain (4W EIRP). Higher gain antennas require proportionally lower transmitter power to stay within limits. Cable losses between transmitter and antenna reduce ERP and must be accounted for.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| ERP | Effective Radiated Power | W | µW, mW, W, kW |
| Ptx | Transmitter Power | W | µW, mW, W, kW |
| Gt | Antenna Gain (linear) | — | — |
Step by step
- 1. What you know: Transmitter Power 22 W, Antenna Gain (linear) 0.5
- 2. The relation: ERP = Ptx × Gt
- 3. Substitute: Ptx = 22 W, Gt = 0.5
- 4. Result: Effective Radiated Power = 11 W
Worked examples
Minimum range
Given: Transmitter Power 22 mW, Antenna Gain (linear) 0.025
Result: Effective Radiated Power = 0.55 mW
Low range
Given: Transmitter Power 0.22 W, Antenna Gain (linear) 0.25
Result: Effective Radiated Power = 55 mW
Typical
Given: Transmitter Power 22 W, Antenna Gain (linear) 0.5
Result: Effective Radiated Power = 11 W
High range
Given: Transmitter Power 2.2 kW, Antenna Gain (linear) 0.8
Result: Effective Radiated Power = 1.76 kW
Maximum range
Given: Transmitter Power 22 kW, Antenna Gain (linear) 8
Result: Effective Radiated Power = 176 kW
Solving for each variable
Solve for Effective Radiated Power
Transmitter Power 22 mW, Antenna Gain (linear) 0.025 → 0.55 mW
Solve for Transmitter Power
Effective Radiated Power 10 mW, Antenna Gain (linear) 0.025 → 0.4 W
Solve for Antenna Gain (linear)
Effective Radiated Power 10 mW, Transmitter Power 22 mW → 0.4545
How Effective Radiated Power changes with Transmitter Power
| Transmitter Power (input) | Effective Radiated Power (result) |
|---|---|
| 4.84 W | 5.324 W |
| 12.1 W | 13.31 W |
| 24.2 W | 26.62 W |
| 36.3 W | 39.93 W |
| 48.4 W | 53.24 W |
| 72.6 W | 79.86 W |
| 96.8 W | 106.5 W |
| 0.1936 kW | 0.213 kW |
| 0.3388 kW | 0.3727 kW |
| 0.484 kW | 0.5324 kW |
The same result in other units
| Unit | Value |
|---|---|
| mW | 11000 |
| W | 11 |
| kW | 0.011 |
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<p><a href="https://vbatpower.com/formulas/erp/">Effective Radiated Power</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Effective Radiated Power?
Use ERP = Ptx × Gt. With Transmitter Power 22 W, Antenna Gain (linear) 0.5, Effective Radiated Power works out to 11 W.
How do you calculate effective radiated power chart?
Rearrange for Effective Radiated Power: with Transmitter Power 0.22 W, Antenna Gain (linear) 0.25, Effective Radiated Power is 55 mW.
What is the formula for Effective Radiated Power?
The formula is ERP = Ptx × Gt. Effective Radiated Power is the total power that would need to be radiated by an isotropic antenna to produce the same signal strength in the direction of maximum antenna gain.
How do you find Transmitter Power when you know the other values?
Rearrange for Transmitter Power: with Effective Radiated Power 10 mW, Antenna Gain (linear) 0.025, Transmitter Power is 0.4 W.
How do you find Antenna Gain (linear) when you know the other values?
Rearrange for Antenna Gain (linear): with Effective Radiated Power 10 mW, Transmitter Power 22 mW, Antenna Gain (linear) is 0.4545.
What units does Effective Radiated Power use?
Effective Radiated Power is shown in mW, W, kW. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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