Effective Radiated Power: ERP vs EIRP for Ham Radio Stations

When a license says that you may use 100 watts, what does that mean for the signal that actually leaves your antenna? A transmitter with 100 watts feeding a long cable and a big beam does not behave like a transmitter with 100 watts feeding a short dipole, and regulators, manufacturers and engineers use a measure that takes this into account. That measure is the effective radiated power, written ERP, and its close relative the effective isotropic radiated power, EIRP. This guide explains what each one means, how they differ by a fixed 2.15 decibels, how to calculate them from your own numbers and why the figures matter for rules, for RF exposure and for understanding the station you are building.

What the Two Terms Mean

Both quantities answer the same question: how strong is the signal in the direction in which the antenna radiates best, expressed as the power that a simple reference antenna would need to produce the same signal strength? The Wikipedia article on effective radiated power describes EIRP as the hypothetical power that would have to be radiated by an isotropic antenna to give the same signal strength as the actual antenna in the direction of its strongest beam. The article states that the difference between EIRP and ERP is that ERP compares the actual antenna with a half-wave dipole, while EIRP compares it with a theoretical isotropic antenna.

An isotropic antenna is an imaginary point source that radiates equally in all directions. It does not exist, but it makes a clean reference. A half-wave dipole is a real antenna, and it already has some gain compared with the isotropic one, because it concentrates energy toward its sides. That gain is 2.15 dBi, which is the reason for the fixed difference between the two measures: the EIRP is always larger than the ERP of the same system by 2.15 dB, which is a factor of about 1.64 in power. If you meet a power limit written in one and your calculation is in the other, add or subtract that number.

The Calculation

You need three things: the power delivered by the transmitter, the loss between the transmitter and the antenna, and the gain of the antenna. In decibels the calculation is a simple sum. Convert the transmitter power to decibels relative to one watt, subtract the feed line loss, including connectors and any switches, and add the gain of the antenna in dBi to get the EIRP in dBW. For the ERP, use the antenna gain in dBd, which is relative to a dipole, or subtract 2.15 dB from the EIRP. Our guide to dBi versus dBd explains the two gain scales.

A worked example shows how it goes. A transmitter produces 100 watts, which is 20 dBW. The coaxial cable and connectors lose 3 dB, so the power at the antenna is 17 dBW, or 50 watts. The antenna has a gain of 8 dBi. The EIRP is 20 minus 3 plus 8, which is 25 dBW, or about 316 watts. The ERP is 25 minus 2.15, which is 22.85 dBW, or about 193 watts. The same transmitter with a short run of low-loss cable and a simple dipole produces very different results, as the table shows.

The first row shows the useful check: a 100 watt transmitter feeding a lossless, perfectly matched half-wave dipole has an ERP of exactly 100 watts, since the reference antenna is the dipole itself. The fifth row shows how a handheld with a small beam turns a few watts into the equivalent of a much stronger station in one direction.

Why Cable Loss Matters So Much

The table also shows why feed line loss is one of the biggest items in the calculation. Each 3 dB of loss halves the power that reaches the antenna, and the same applies to the signal you receive. On the lower HF bands the loss in a short run of good cable is small, but at VHF and UHF it grows quickly, and a long run of thin cable can waste more than the antenna gains. Our comparison of ladder line and coax shows what the choice of line can do for the numbers, and the same effects apply to the SWR on the cable.

Notice also that the calculation takes into account the antenna gain only in the direction of the main lobe. In other directions the effective power is smaller, down to a deep null where it may be many decibels below the peak. The figure that is quoted is therefore the best case, and your signal at a given distant station depends on where that station lies in your pattern, as our article on the antenna radiation pattern explains.

A Second Worked Example: Is the Amplifier Worth It?

Suppose that you are deciding between two upgrades for a station with a 100 watt transmitter, 20 meters of coaxial cable with a loss of 2 dB and a dipole. The first option is an amplifier that raises the power to 400 watts. That is a factor of four, or 6 dB, so the EIRP rises by 6 dB. The second option is to replace the dipole with a beam that has a gain of 6 dB over the dipole. The EIRP rises by 6 dB in the direction of the beam, but not in the others. A third option, replacing the cable with a low-loss type that has only 0.5 dB of loss, adds 1.5 dB at no cost in the power bill. The comparison shows that the options are not equivalent, even if some of the numbers are: the amplifier raises the signal in all directions, and it also raises the noise and the exposure, while the beam concentrates the energy and improves the reception in the same direction.

That is why experienced operators say that an antenna is the best amplifier. On receive, the amplifier does nothing at all, whereas the beam improves the signal-to-noise ratio. The calculation of the EIRP therefore gives only half the story: the other half is the receiving performance, which depends on the gain of the antenna and the noise level around it. Use the number for the transmit side and keep the receive side in mind when you decide where to put your money.

Common Mistakes

• Mixing dBi and dBd. A gain of 8 dBd is 10.15 dBi. Using the wrong scale makes the result wrong by 2.15 dB.
• Forgetting the connectors. Adapters, lightning arrestors and switches each add a small loss, and together they may account for half a decibel or more.
• Using the gain of a stacked or phased array without checking. The published gain applies to the main lobe and often to ideal conditions, not to a particular installation over real ground.
• Applying the peak figure to an average limit. Limits and exposure estimates may be given in terms of peak or average power, so check which one applies.

Where ERP and EIRP Appear in Rules

Amateur power limits are often specified at the transmitter output, usually as peak envelope power, a quantity that we discussed in our article on PEP and wattmeters. Not every limit is like that. Some countries specify power on certain bands, in particular narrow allocations such as 5 MHz, in terms of ERP or EIRP, so that a high-gain antenna reduces the permitted transmitter power. The right approach is to read the licence conditions and the national band plan, which will say which measure applies, and then use the calculation above to check your station. If a limit is stated in ERP and you use a beam with several decibels of gain, the transmitter power that you may use is the limit divided by the gain factor, after the loss in the cable.

The same measures appear in the specification of commercial equipment, in the rules for unlicensed devices and in the descriptions of broadcast and mobile services, where a transmitter’s coverage is given as an ERP. If you read a document about interference to or from other services, you will find the same quantities, which is why an amateur who understands them can follow the discussion.

ERP, EIRP and RF Exposure

The calculation has a safety side. Estimates of RF exposure depend on the power that is radiated in the direction of a person, and a high-gain antenna concentrates that power. The EIRP is the most useful quantity for exposure calculations, since the field strength at a distance in the main beam depends on it. Our guide to RF exposure safety explains how to use these numbers, and the calculators of national bodies use the transmitter power, the duty cycle and the antenna gain in the same way. A station with a high EIRP, such as a big beam and an amplifier, needs a larger safe distance than a station with a modest dipole, and the distance must be checked for the places where people are actually present, such as a neighbouring garden or a balcony.

Remember also that the duty cycle matters. A CW or SSB signal that is on for only a part of the time produces a lower average than the peak, and a digital mode such as FT8 that transmits continuously for half of the time produces a higher average. The ERP and the EIRP are normally stated for the peak, so apply the correction for the mode when you make an exposure estimate.

Practical Uses of the Numbers

• Compare antennas fairly. A beam with 10 dBi of gain and a long cable can be matched with a dipole and a short cable in terms of EIRP, which helps you to see what an upgrade really adds.
• Decide whether an amplifier is worth it. An amplifier that raises your power from 100 W to 400 W adds 6 dB, the same as an antenna gain of 6 dB. The cheapest option may be a better antenna or a shorter feed line.
• Check a power limit. If a band limit is given in ERP, calculate your station before you transmit, and keep a note of the figures in your log of the equipment.
• Plan a link. For a VHF or satellite link, the EIRP at your end and the sensitivity of the receiver at the other end decide whether the path closes.

The Bottom Line

Effective radiated power is the transmitter power adjusted for the gain of the antenna and the loss of the feed line, referenced to a half-wave dipole; EIRP is the same quantity referenced to an isotropic antenna and is always 2.15 dB, a factor of about 1.64, higher. To calculate it, convert the transmitter power to decibels, subtract the cable and connector loss, add the antenna gain in dBi for EIRP or in dBd for ERP and convert back to watts. Use the result to compare antennas, to decide whether an amplifier or a better cable is the better investment, to check any limit that is written in ERP or EIRP and to estimate RF exposure in the main beam.

Frequently Asked Questions

What is the difference between ERP and EIRP?

ERP compares the radiated signal with a half-wave dipole, while EIRP compares it with a theoretical isotropic antenna. EIRP is 2.15 dB higher than ERP for the same system.

How do I convert ERP to EIRP?

Add 2.15 dB, or multiply the power by about 1.64. To go from EIRP to ERP, subtract 2.15 dB or divide by 1.64.

Does cable loss reduce ERP?

Yes. The loss in the feed line and connectors reduces the power that reaches the antenna, and it is subtracted in the calculation.

What is the ERP of 100 W into a dipole?

With no feed line loss and a perfect match, exactly 100 W, because the half-wave dipole is the reference. In practice it is a little lower because of the loss.

Is my legal power limit in ERP?

It depends on the band and the country. Many limits are given as transmitter output power, but some bands use ERP or EIRP, so read your licence conditions.

Why does EIRP matter for RF exposure?

Because it describes the power density in the main beam. A higher EIRP needs a larger safe distance from the antenna.