Effective Isotropic Radiated Power (EIRP) is the single most important figure of merit in radio link engineering. It describes how much power a hypothetical isotropic antenna would need to radiate to match the signal strength produced by your actual directional antenna in its main lobe.
This calculator turns four field-measurable quantities — transmitter output, feeder losses, antenna gain and target distance — into a complete RF link budget. It instantly resolves EIRP in both logarithmic (dBW, dBm) and linear (Watts) scales, and derives the power density, electric field strength, free-space path loss, and ICNIRP compliance distances that regulators and site engineers require for every base station deployment.
Required Design Parameters
To produce a meaningful EIRP assessment, the following project specifications must be defined:
- Transmitter Power ($P_{tx}$) — the conducted RF power at the amplifier output, entered in Watts.
- System Loss ($L_c$) — the cumulative attenuation from coaxial cable, jumpers, connectors, duplexers and pointing error, expressed in dB.
- Antenna Gain ($G_{tx}$) — the directivity of the radiating element relative to an isotropic source, in dBi.
- Operating Frequency ($f$) — the carrier frequency in MHz, used to compute Free-Space Path Loss.
- Target Distance ($d$) — the line-of-sight range from the antenna aperture to the evaluation point, in meters.
Theoretical Foundation and Governing Equations
EIRP originates from the concept of the isotropic radiator — a mathematical point source that radiates equally in all directions. No real antenna behaves this way, but the isotropic reference provides a universal baseline against which every antenna on Earth can be compared.
The Core EIRP Equation
Working in the logarithmic domain, the EIRP of any transmitting system reduces to a simple algebraic sum:
$$EIRP_{dBW} = P_{tx,dBW} - L_{c,dB} + G_{tx,dBi}$$
The transmitter power is first converted from linear Watts to dBW using the decibel transform:
$$P_{tx,dBW} = 10 \cdot \log_{10}(P_{tx,W})$$
To obtain dBm — the standard reference used in cellular and Wi-Fi engineering — add 30 to the dBW value, since $1\text{ W} = 1000\text{ mW}$.
Power Density in the Far Field
Once the antenna radiates, the energy spreads over an expanding spherical surface. At distance $d$, the power density $S$ (also called Poynting vector magnitude) is given by:
$$S = \frac{EIRP_{W}}{4 \pi d^{2}}$$
This inverse-square relationship is the mathematical reason RF exposure drops dramatically with just a few extra meters of separation. Doubling the distance quarters the power density.
Electric Field Strength
For a plane wave in free space, the relationship between power density and the RMS electric field $E$ follows from the impedance of free space, $\eta_{0} \approx 120\pi \approx 377\,\Omega$:
$$E = \frac{\sqrt{30 \cdot EIRP_{W}}}{d}$$
The constant 30 comes from $\eta_{0} / (4\pi)$ and gives $E$ directly in volts per meter. This is the quantity measured by broadband field probes during compliance audits.
Free-Space Path Loss
Propagation through vacuum introduces no absorption, yet the received power still falls as a function of distance and frequency. The Friis transmission formula gives the FSPL in dB as:
$$FSPL_{dB} = 20 \log_{10}(d_{km}) + 20 \log_{10}(f_{MHz}) + 32.44$$
The constant 32.44 absorbs the unit conversions between kilometers, megahertz, and the $4\pi/\lambda$ term from Friis' original derivation.
ERP vs EIRP: A Frequent Confusion
European broadcast regulations often use ERP (Effective Radiated Power), which is referenced to a half-wave dipole instead of an isotropic source. The conversion is fixed:
$$ERP_{dBW} = EIRP_{dBW} - 2.15\text{ dB}$$
The 2.15 dB offset is the intrinsic gain of a lossless half-wave dipole over an isotropic radiator.
Reference Data for Antenna and System Parameters
The following table consolidates typical values drawn from commercial base station datasheets and ITU-R recommendations. Use it to sanity-check your design parameters before running a calculation.
| System Element | Typical Value | Band / Context | Notes |
|---|---|---|---|
| GSM 900 BTS | 40–60 W ($P_{tx}$) | 935–960 MHz | Per sector, before combining |
| LTE 1800 eNodeB | 20–80 W ($P_{tx}$) | 1805–1880 MHz | Per MIMO branch |
| 5G NR Macro | 120–320 W ($P_{tx}$) | 3.4–3.8 GHz | Aggregate across massive MIMO |
| Wi-Fi 6 AP | 0.1–1 W ($P_{tx}$) | 2.4 / 5 / 6 GHz | Conducted power |
| Omni antenna (collinear) | 6–11 dBi | Sub-6 GHz | Low-gain, 360° azimuth |
| Sector panel antenna | 15–18 dBi | 700 MHz – 3.5 GHz | 65° horizontal beamwidth |
| High-gain parabolic | 30–45 dBi | Microwave backhaul | Pencil beam |
| 7/8" coaxial feeder | 0.04 dB/m | at 2100 MHz | Derate with length |
| N-type connector pair | 0.1–0.2 dB | DC – 11 GHz | Per mated pair |
| ICNIRP general public | 10 W/m² | > 2 GHz | Occupational ≈ 50 W/m² |
Engineering Analysis and Field Application
Reading the Link Budget
The decibel summation in the EIRP equation creates a clear hierarchy of influence. Because antenna gain enters with a positive sign and losses with a negative sign, a 3 dB improvement anywhere in the chain is worth the same as doubling the transmitter output. This is why investing in a low-loss feeder or a higher-gain antenna is almost always more cost-effective than specifying a larger amplifier.
As an example, a 40 W cellular transmitter feeding a 15 dBi sector antenna through a 2.5 dB lossy run yields:
$$EIRP = 16.02 - 2.5 + 15 = 28.52\text{ dBW} \approx 711\text{ W}$$
That 711 W figure represents the power an isotropic source would need to emit to match the peak signal of the directional panel. It does not mean the transmitter has become more powerful — it means the energy has been concentrated into the main beam.
Interpreting Power Density and Safety Distances
The two distances produced by the calculator — public and occupational — are derived by inverting the power density equation against the respective ICNIRP reference levels:
$$d_{safe} = \sqrt{\frac{EIRP_{W}}{4 \pi S_{limit}}}$$
If the target distance you entered is greater than the public compliance distance, the point is in the unrestricted zone. If it falls between the public and occupational distances, access should be limited to trained RF workers. Any point closer than the occupational distance demands either physical barriers, transmitter shutdown procedures, or personal protective equipment.
Why Frequency Matters
Frequency does not enter the EIRP equation itself, but it governs the path loss and therefore the link margin at the receiver. A 10 GHz link suffers roughly 13 dB more loss than a 2 GHz link over the same distance. This is the practical reason millimeter-wave 5G cells are small — not because the power is lower, but because the geometric spreading loss is far higher.
Frequently Asked Questions
This is the single most common source of confusion for engineers new to RF. EIRP can exceed $P_{tx}$ by tens of decibels without violating any law of physics.
The antenna does not create energy; it redistributes it. A high-gain antenna steals power from directions you do not care about and funnels it into the main lobe. A parabolic dish with 40 dBi of gain fed by just 1 W produces an EIRP of 10 kW along its boresight — but the total radiated power integrated over the full sphere remains exactly 1 W minus losses.
Regulators set EIRP limits precisely because they care about peak field strength in any direction, not the conducted power at the amplifier port.
Field engineers typically bundle these unknowns into an implementation margin added to the explicit cable loss figure. A pragmatic approach is to start from the manufacturer's published cable attenuation per meter at the operating frequency, add 0.1–0.2 dB per mated connector pair, and then append a flat 0.5–1.5 dB for radome losses, weatherproofing tape, and small pointing errors.
For legacy sites with corroded connectors or aged feeders, a sweep test using a cable and antenna analyzer will reveal the true return loss and insertion loss. Any measured value worse than the datasheet should be entered into the system loss field.
Remember that mispointing has a nonlinear effect: a 3° error on a 2° beamwidth dish can cost 10 dB or more, whereas the same error on an 18 dBi sector panel is almost invisible.
The tool uses the conservative far-field approximation with reference levels of 10 W/m² (general public) and 50 W/m² (occupational), which correspond to ICNIRP guidance for frequencies above 2 GHz. This is a first-order screening method, suitable for preliminary site planning and classroom work.
A formal compliance assessment must additionally consider frequency-dependent reference levels below 2 GHz (which are more restrictive), near-field correction factors within the reactive and radiating near-field regions, time averaging over 6 or 30 minutes depending on population class, and cumulative exposure from co-located transmitters on the same mast.
For regulated deployments always corroborate the screening distance with a full analysis per IEC 62232, FCC OET-65, or your national equivalent, and follow up with on-site measurements using a calibrated isotropic probe.
Professional Conclusion
Manual EIRP arithmetic is error-prone because it mixes linear and logarithmic units, requires awareness of frequency-dependent safety thresholds, and must be repeated every time a cable is swapped or a sector is re-tilted. An automated calculation consolidates the Friis equation, the inverse-square law, and the ICNIRP reference levels into a single authoritative result — the same result that would otherwise take a spreadsheet and several minutes of attention to produce by hand.
For engineers commissioning a site, for students learning link budgets, and for safety officers validating exclusion zones, a deterministic numerical tool removes ambiguity and gives every stakeholder the same defensible number. Precision in EIRP estimation is not an academic nicety — it is the foundation of every compliant, efficient, and interference-free radio deployment.