Effective isotropically radiated power

Effective radiated power (ERP), synonymous with equivalent radiated power, is an IEEE standardized definition of directional radio frequency (RF) power, such as that emitted by a radio transmitter. It is the total power in watts that would have to be radiated by a half-wave dipole antenna to give the same radiation intensity (signal strength in watts per square meter) as the actual source at a distant receiver located in the direction of the antenna's strongest beam (main lobe). ERP measures the combination of the power emitted by the transmitter and the ability of the antenna to direct that power in a given direction. It is equal to the input power to the antenna multiplied by the gain of the antenna. It is used in electronics and telecommunications, particularly in broadcasting to quantify the apparent power of a broadcasting station experienced by listeners in its reception area.

An alternate parameter that measures the same thing is effective (or equivalent) isotropic radiated power (EIRP). Effective isotropic radiated power is the total power that would have to be radiated by a hypothetical isotropic antenna to give the same signal strength as the actual source in the direction of the antenna's strongest beam. The difference between EIRP and ERP is that ERP compares the actual antenna to a half-wave dipole antenna, while EIRP compares it to an isotropic antenna. Since a half-wave dipole antenna has a gain of 1.64, or 2.15 decibels compared to an isotropic radiator, if ERP and EIRP are expressed in watts their relation is

If they are expressed in decibels

In terms of decibels referred to one milliwatt or one watt respectively.

Effective radiated power and effective isotropic radiated power both measure the amount of power a radio transmitter and antenna (or other source of electromagnetic waves) radiates in a specific direction: in the direction of maximum signal strength (the "main lobe") of its radiation pattern. This maximum radiated power is dependent on two factors: the total power output and the radiation pattern of the antenna – how much of that power is radiated in the desired direction. The latter factor is quantified by the antenna gain, which is the ratio of the signal strength radiated by an antenna to that radiated by a standard antenna. For example, a 1,000-watt transmitter feeding an antenna with a gain of 4 (6 dBi) will have the same signal strength in the direction of its main lobe, and thus the same ERP and EIRP, as a 4,000-watt transmitter feeding an antenna with a gain of 1 (0 dBi). So ERP and EIRP are measures of radiated power that can compare transmitters with different antennas on an equal basis.

...
Wikipedia