ERP and EIRP Calculator for Amateur Stations

Effective radiated power is what leaves the antenna in the direction that matters, rather than what leaves the transmitter. It is the number that decides how strong you sound, the number the RF exposure evaluation needs, and on one amateur band the number the rules actually regulate. The arithmetic is three terms and one common mistake.

The two references, and why both exist

Antenna gain is always relative to something, and radio uses two references that differ by a fixed 2.15 decibels.

Isotropic means a theoretical point source radiating equally in every direction, including straight up and straight down. It does not exist and cannot be built, which is exactly why it makes a clean mathematical reference: it has no pattern of its own to complicate the comparison. Gain against it is written dBi, and power against it is EIRP.

Dipole means a half-wave dipole in free space, which is a real antenna with a real doughnut-shaped pattern. It concentrates energy broadside and has nulls off the ends, which gives it 2.15 dBi of gain over isotropic. Gain against it is written dBd, and power against it is ERP.

So EIRP is always ERP plus 2.15 dB for the same station, and dBi is always dBd plus 2.15 for the same antenna. The single most common error in this whole subject is comparing a dBi figure with a dBd figure and concluding one antenna is better when the difference is entirely the reference.

Typical antenna gains

The rubber duck row deserves attention. A stock handheld antenna commonly measures around minus 3 dBi, meaning it radiates less than an isotropic radiator would, because it is an electrically short element with substantial loss. That is a 5 dB deficit against the dipole reference before you have even considered the transmitter, and it is why replacing it with a Nagoya NA-771C 15-inch whip$15.98 for sixteen dollars is measurably the best value change available to a handheld operator.

Where the ERP sum actually bites

Sixty metres, the one band regulated by ERP

United States amateurs on the five 60 metre channels are limited to 100 watts PEP effective radiated power relative to a half-wave dipole, rather than 100 watts of transmitter output. For an operator using an actual dipole the two are the same and there is nothing to do. For an operator using a gain antenna, transmitter power must be reduced so that the ERP stays at or below 100 watts.

In practice the case that catches people is the opposite one: a shortened or loaded antenna with negative gain against a dipole means you may run more than 100 watts of transmitter output and remain legal, which the rules permit and which most operators never bother to exploit. The band plan detail is on the United States amateur band plan.

RF exposure evaluation, required of every station

Power density at a distance is proportional to power at the antenna multiplied by antenna gain in the direction concerned, which is precisely what EIRP expresses. That makes EIRP, not transmitter output, the input the exposure calculation needs.

The practical consequence is that a beam changes your exposure situation dramatically in one direction and improves it in every other. A 5 element 2 metre Yagi at 11 dBi produces roughly twelve times the power density on axis that an isotropic source would, so the compliance distance in front of it is about three and a half times further than behind it. If that axis crosses a neighbour's garden, that is the case to evaluate. Run it on the RF exposure calculator.

Comparing an upgrade honestly

ERP is the right way to compare two possible spends, because it puts power, feedline and antenna on the same scale. Consider a 100 watt VHF station with 100 feet of RG-58, which is 5 dB of loss at 146 MHz, feeding a rooftop vertical at 2.35 dBd.

The coax row is the one people skip and it is the best value on the table: a Bolton400 low-loss coax, 100 ft with PL-259$119.95 beats doubling transmitter power, costs a fraction of an amplifier, and works on receive as well. The beam row buys more but only where it points, which is the honest limitation of gain. A Diamond A144S5 5-element 2 m Yagi$87.99 on a Yaesu G-450ADC antenna rotator$479.95 is the practical version of that upgrade.

Gain is redistribution, not creation

An antenna does not amplify. It takes the power delivered to it and directs more of it one way and less another way, and the total remains what the feedline delivered. That is worth stating because gain figures read like free power and they are not.

Three consequences follow. First, a high-gain omnidirectional vertical achieves its numbers by flattening its pattern, which works beautifully across level terrain and can send the main lobe over the head of a station in a valley below you. On hilly ground a lower-gain antenna often works better. Second, a beam is weaker off the back by design, typically 15 to 25 dB down, so a station running 1500 watts into a beam pointed elsewhere sounds weaker than a station running 100 watts into a dipole. Third, gain applies on receive too, in both the helpful sense of hearing weak signals and the useful sense of rejecting noise arriving from the wrong direction.

Be sceptical of large gain claims from small antennas. Physics sets a rough relationship between aperture and achievable gain, so an antenna claiming 12 dBi in the length of a quarter-wave whip is measuring optimistically or comparing against something unstated. Believable figures for real antennas are in the table above, and the roundups at VHF and UHF base antennas quote manufacturer specifications with that caveat attached.

Do not forget the losses between the radio and the antenna

The subtraction term in the sum is not only the coax. Everything in the path contributes.

• Feedline. The dominant term, and the one the coax loss calculator handles.
• Connector pairs. Roughly 0.05 to 0.1 dB each at HF and up to 0.2 dB at UHF, when properly made. A corroded or badly soldered one can be several decibels on its own.
• An antenna switch. A Daiwa CS-201A two-position coax switch$42.99 adds a fraction of a decibel, plus the connector pairs at each end.
• A tuner. Typically 0.2 to 1 dB when matching a modest mismatch, and considerably more when working hard against a very reactive load.
• A lightning arrester. A Proxicast ProGrade coaxial lightning arrester, SO-239$19.95 is close to lossless at HF and adds a little at UHF. Not a reason to omit it.
• An SWR meter left permanently in line. Negligible, but it is another two connector pairs.

Add them all before running the sum. A station that thinks it has 1.5 dB of coax loss and actually has 1.5 dB of coax, 0.4 dB of connectors, 0.3 dB of switch and 0.6 dB of tuner is giving away nearly a decibel it has not accounted for.