Effective Radiated Power (ERP) Calculator

Results

ERP (dBW)

0

EIRP (dBW)

0

ERP (W)

0

EIRP (W)

0

dBm

0

Table of Contents

1

What is Effective Radiated Power?

This radio-frequency calculator estimates both effective isotropic radiated power (EIRP) and effective radiated power (ERP) from transmitter power, antenna gain and transmission-line loss. EIRP uses an ideal isotropic radiator as its reference. ERP uses a half-wave dipole reference, so the same system is about 2.15 dB lower when expressed as ERP.

The antenna-gain entry is treated as dBi because it is first used to form EIRP. The calculator then subtracts 2.15 dB to obtain ERP. This distinction is essential: entering dBd as though it were dBi shifts both reported results.

2

How to Use This Calculator

  1. Enter transmitter output power and choose milliwatts, watts, kilowatts or megawatts. The value must be greater than zero because logarithmic power is undefined at zero.
  2. Enter antenna gain in dBi. Gain may be negative for an antenna system with less gain than the isotropic reference.
  3. Enter total transmission-line and connector loss in decibels as a nonnegative value.
  4. Calculate. Power is converted to watts and then dBW. Net antenna-system gain is added to produce EIRP in dBW.
  5. The page subtracts 2.15 dB for ERP, converts both logarithmic results back to watts, and reports EIRP in dBm as well.

Use power measured at the point before the entered line loss. If the supplied transmitter figure already reflects power delivered at the antenna, entering the same feed-line loss again would count it twice.

3

Formula Used

Transmitter power (dBW) = 10 log₁₀(power in watts)

EIRP (dBW) = transmitter dBW + antenna gain (dBi) − line loss (dB)

ERP (dBW) = EIRP (dBW) − 2.15 dB

Power (W) = 10dBW/10, and dBm = dBW + 30. Decibels are added and subtracted in the link budget; ordinary watts are not. The 2.15 dB relationship is the nominal gain difference between an ideal half-wave dipole and an isotropic radiator.

4

Variables Explained

Entry or outputMeaning
Transmitter powerRF output at the reference point before the entered feed-line loss, converted internally to watts.
Antenna gainDirectional gain entered in dBi, relative to an isotropic radiator.
Line lossTotal attenuation in cable, connectors and applicable feed components, in dB.
EIRPEquivalent radiated power referenced to an isotropic antenna, reported in dBW, watts and dBm.
ERPEquivalent radiated power referenced to a half-wave dipole, reported in dBW and watts.
5

Worked Example

Take a 10 W transmitter, an antenna rated at 3 dBi and 1 dB of line loss. Transmitter power is 10 log₁₀(10) = 10 dBW. EIRP is 10 + 3 − 1 = 12.00 dBW, which is 101.2 = 15.85 W. In dBm, that is 42.00 dBm.

ERP is 12 − 2.15 = 9.85 dBW. Converting back gives about 9.66 W ERP. The ERP watts are lower than EIRP watts because the reference antennas differ; the transmitter did not lose power during this reporting conversion.

If the antenna specification were 3 dBd instead, convert it to about 5.15 dBi before using this form. With the same transmitter and loss, that would produce 14.15 dBW EIRP and 12.00 dBW ERP.

6

Why Use This Calculator?

EIRP and ERP describe radiation relative to reference antennas and are useful in link budgets, coverage planning and regulatory checks. They are not the same as transmitter nameplate power. Antenna gain concentrates radiation by direction, so the result generally refers to the direction of stated maximum gain.

Regulatory limits may specify ERP or EIRP, averaging method, bandwidth, antenna height, location and service-specific conditions. Match the exact reference and definitions in the applicable rule. A calculator result does not establish compliance by itself, particularly when cable loss, antenna pattern or measured transmitter power is uncertain.

Reported hundredths of a decibel or watt do not imply that field measurements are that precise. Cable attenuation varies with frequency, length, temperature and installation. Connector and duplexer losses may also matter. Use documented values at the operating frequency and retain an uncertainty margin where appropriate.

7

Common Mistakes

    • Confusing dBi and dBd: this gain field is used as dBi; add about 2.15 dB to convert dBd to dBi.
    • Calling EIRP ERP: the references differ even when both are expressed in watts.
    • Entering milliwatts as watts: choose the actual unit before calculating.
    • Adding line loss: attenuation must be subtracted from the link budget.
    • Counting loss twice: know whether the power figure is measured at the transmitter or antenna input.
    • Treating maximum radiated power as uniform: real antenna patterns vary with direction and polarization.
8

Frequently Asked Questions

What is the difference between ERP and EIRP?

ERP is referenced to a half-wave dipole, while EIRP is referenced to an isotropic radiator. For the same system, EIRP in dB is about 2.15 dB higher.

Should antenna gain be entered as dBi or dBd?

Enter dBi. If a specification gives dBd, add about 2.15 dB before entering it.

Why must transmitter power be above zero?

The calculation takes 10 log₁₀ of power. Zero and negative watt values do not have a finite real logarithmic power level.

Is the dBm output ERP or EIRP?

The displayed dBm value corresponds to EIRP. It is the EIRP dBW result plus 30.

Does the result include cable and connector losses?

Only the loss value you enter is included. Add the relevant documented losses together without double-counting any already reflected in the power measurement.

Can this result prove regulatory compliance?

No. The governing service rules may add measurement, averaging, location, exposure and antenna requirements. Use the specified reference and a complete compliance assessment.

9

Sources & References

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