# ERP to EIRP Calculator

Use this tool to find the EIRP (Effective Isotropic Radiated Power) from ERP (Effective Radiated Power).

EIRP to ERP

## Formula

EIRP = 1.64 * ERP

EIRPdBm = ERPdBm + 2.15

## Background

ERP is the power that would have to be radiated by a half-wave dipole antenna to provide the same signal level as the actual source antenna in the direction of the antenna’s strongest beam.

EIRP is the power that would have to be radiated by an isotropic antenna to provide the same signal level as the actual source antenna in the direction of the antenna’s strongest beam.

A half-wave dipole can be realized practically. The rabbit ears antenna on older television sets is an example. Use this calculator to determine the dimensions of a half wave dipole.

An isotropic antenna cannot be built practically. It is a hypothetical or an ideal antenna type and radiates energy equally in all directions.

## Equations

In linear terms, the ratio of the gain of a half-wave dipole antenna to that of an isotropic antenna is given by the following relationship:

GD/GI = 0.6098

Therefore on the Log scale 10*Log10(GD/GI) = 10*Log10(0.6098) = -2.15

or

EIRP (dBm) = ERP (dBm) + 2.15 dB

???? The way to understand this intuitively: An isotropic antenna would have to radiate 2.15 dB more energy to provide the same signal level as a half-wave dipole.

## Notes

[1] In this publication the FCC has provided guidelines on how to determine the EIRP and ERP practically.

[2] ERP can be specified in Watt. Use this tool to convert Watt to dBm for the above calculations.