How this instrument works
Effective isotropic radiated power answers one question: how strong would this transmitter look if its antenna radiated equally in every direction instead of favoring one? An isotropic radiator is a theoretical antenna with no favored direction at all, a single point source with zero gain. Real antennas concentrate power into a lobe rather than spreading it as a sphere, so EIRP restates the whole transmit chain — power fed in, gain from the antenna's shape, loss along the feedline — as if that power had instead been handed to the idealized point source and aimed straight at the receiver.
The formula is addition and subtraction only because every term already lives in decibels. dBm is power referenced to one milliwatt, dBi is gain referenced to an isotropic source, and dB is a bare ratio — all three are logarithms, and multiplying linear ratios is identical to adding their logs. So EIRP = Pt + Gt − Lc replaces what would otherwise be a chain of multiplication and division — watts times a gain ratio divided by a loss ratio — with a sum a link budget can carry through in one line.
The number describes one direction only: the axis the antenna's main lobe points along. A dish or a sector panel can post an enormous EIRP dead ahead while radiating almost nothing to the side, which is exactly the point of trading raw power for gain, and exactly why licensing bodies cap this figure rather than the transmitter's own output. Off that axis, the real radiated power falls below the calculated EIRP by however many dB the antenna pattern rolls off.
- Enter the radio's output in the Transmitter power field, in dBm — 30 dBm is 1 watt if you only have a watts figure to start from.
- Enter the antenna's rating in the Antenna gain field, in dBi, taken straight from its datasheet relative to an isotropic radiator.
- Enter the total feedline loss in the Cable/connector loss field, in dB — sum the coax run and every connector between radio and antenna.
- Read the EIRP field in dBm: the figure a license or regulation actually limits, not the raw number the transmitter alone produces.
Worked example — a 1 W link through 2 dB of cable loss
Take a transmitter rated at 30 dBm, exactly 1 watt, since dBm is referenced to one milliwatt and 10·log10(1000) = 30, feeding a 15 dBi panel antenna through a coax run and connectors that together cost 2 dB. EIRP = 30 + 15 − 2 = 43 dBm, read straight off the sum of the three fields with no further conversion needed.
Converting 43 dBm back to watts gives 10^4.3 mW, about 19,953 mW or roughly 20 watts — the power an isotropic radiator would need to match this system's signal along its strongest direction, even though only 1 watt actually left the transmitter. That twenty-fold gap between transmitter power and EIRP is entirely the antenna's doing, and it is the number a regulator checks against a licensed limit, not the 30 dBm the radio itself produces.
Questions
Is EIRP the same thing as ERP?
No. ERP references a half-wave dipole rather than a theoretical isotropic radiator, and a dipole already carries 2.15 dBi of gain over isotropic. So ERP(dBm) = EIRP(dBm) − 2.15 — the same system reads about 2 dB lower quoted as ERP than as EIRP, and a limit written for one is not directly a limit for the other without that conversion.
Why does the formula add and subtract instead of multiply and divide?
Because dBm, dBi, and dB are all logarithmic units. Antenna gain and cable loss are really ratios that would multiply and divide the transmitter's power in watts, but a logarithm turns multiplication into addition and division into subtraction — so the whole chain collapses into EIRP = Pt + Gt − Lc, a sum a link-budget worksheet can carry through in a few lines instead of tracking ratios.
Can EIRP exceed the transmitter's own rated output power?
Yes, routinely. A transmitter putting out 30 dBm (1 W) into a 15 dBi antenna, even after 2 dB of cable loss, radiates a peak EIRP of 43 dBm, about 20 watts equivalent. Antenna gain does not add energy to the signal; it concentrates the same power into a narrower beam, so the figure aimed at the receiver rises even though nothing more powerful ever entered the cable.
Why do regulators limit EIRP instead of transmitter power?
Because EIRP, not raw transmitter output, determines how far a signal reaches and how much interference it can cause along its strongest direction. Two installers running identical 1 W radios get very different footprints once one of them bolts on a high-gain dish — which is why FCC rules such as 47 CFR 15.247 make directional-antenna users cut their conducted power by however many dB the antenna's gain exceeds a reference figure, holding EIRP to the same effective ceiling.
What should count toward cable and connector loss?
Everything the signal passes through between the transmitter and the antenna terminal: the coax run's loss per its datasheet at your operating frequency, every connector and adapter in the path (each commonly 0.1–0.5 dB), and any inline component such as a lightning arrestor or splitter. Leaving one of these out is the most common reason an installed system's real EIRP falls short of its calculated design figure.
How do I convert an EIRP result in dBm back to watts?
Compute P(W) = 10^(dBm ⁄ 10) ⁄ 1000. For the 43 dBm result in the worked example, that is 10^4.3 ⁄ 1000, about 19.95 W, call it 20 watts. The same relation converts any dBm figure, including the Transmitter power field's own reading of 30 dBm back to exactly 1 W before any gain or loss is applied.