EIRP Calculator

EIRP Calculator finds effective isotropic radiated power from transmitter power, cable loss and antenna gain in dBm, dBW or watts, plus ERP, field strength and an EIRP limit check.

How the EIRP Calculator Adds Up a Radio Link

The EIRP Calculator takes the power leaving a transmitter, subtracts what the cable loses and adds the gain of the antenna. The answer is the effective isotropic radiated power, the signal level in the direction where the antenna is strongest.

EIRP is also written as equivalent isotropically radiated power. US rules define it in 47 CFR 2.1 as the power supplied to the antenna multiplied by the antenna gain, in a given direction, relative to an isotropic antenna. An isotropic antenna is an ideal point that radiates equally in every direction.

Put simply, EIRP is the power an isotropic antenna would need to match your signal in the main beam. A real antenna reaches that level with less power, because it squeezes the same energy into a narrower pattern.

Three fields are enough for a result. Transmitter power can be typed in dBm, watts, milliwatts or dBW. Cable loss goes in as a positive number of dB. Antenna gain can be in dBi, or in dBd if the data sheet rates the antenna against a dipole.

The options panel adds connector losses, a distance for field strength and an EIRP limit to test against. With the default entries of 24 dBm, 2 dB and 9 dBi, the EIRP Calculator shows 31 dBm, which is 1.259 W.

EIRP Formula in dBm, dBW and Watts

The EIRP formula is a simple sum when every term is in decibels. Power is in dBm or dBW, loss is in dB and gain is in dBi. Losses are subtracted and gains are added, with no multiplying needed.

$$EIRP = P_T – L_C + G_A$$

P_T is the transmitter output power, L_C is the total cable and connector loss, and G_A is the antenna gain. The result comes out in the same unit as the power, so dBm in gives dBm out. For the default setup the working is 24 − 2 + 9 = 31 dBm.

If your radio is rated in watts, the EIRP Calculator converts it to dBm first. The reference for dBm is one milliwatt, so the power is put in milliwatts before the logarithm is taken.

$$P_{dBm} = 10 \log_{10}(P_{mW})$$

A 250 mW radio is 23.98 dBm, and a 1 W radio is exactly 30 dBm. A level in dBW uses one watt as the reference, so it always reads 30 lower than the same level in dBm. The 31 dBm result above is 1 dBW.

Connectors are added to the cable loss before the sum. Two connectors at 0.5 dB each raise the 2 dB cable loss to 3 dB, and the EIRP drops from 31 dBm to 30 dBm. The step list under the results shows that line whenever the connector count is above zero.

How do I convert EIRP to watts?

Subtract 30 from the dBm figure, divide by 10 and raise 10 to that power. The result is in watts. For an EIRP in dBW, skip the subtraction, because dBW is already referenced to one watt.

$$P_W = 10^{(P_{dBm} – 30) / 10}$$

For 31 dBm this gives 10 to the power 0.1, which is 1.259 W. For 36 dBm it gives 3.98 W, usually rounded to 4 W. The first result card always shows the EIRP on the scales you did not choose as the main unit, so dBm, dBW and watts appear together.

EIRP Chart: dBm, dBW and Watts

This EIRP chart lists common levels on all three scales. Adding 3 dB doubles the power and adding 10 dB multiplies it by ten, which is why the watt column grows so quickly.

The same chart explains why EIRP can be larger than the transmitter power. A 1 W radio feeding a 10 dBi antenna has an EIRP of 10 W. The antenna has not made any power. It has pointed the one watt it was given into a tighter beam.

EIRP vs ERP

ERP stands for effective radiated power. It is the same idea as EIRP with a different yardstick. EIRP compares the signal with an isotropic antenna, and ERP compares it with a half-wave dipole.

A half-wave dipole has a gain of 2.15 dBi, so the two figures for one station are always 2.15 dB apart. The EIRP number is the larger one, since a dipole is a slightly better radiator than the isotropic point.

$$ERP = EIRP – 2.15$$

To convert ERP to EIRP, add 2.15 dB instead. In watts, 2.15 dB is a factor of 1.64, so 100 W ERP equals 164 W EIRP. The second result card of the EIRP Calculator does this for you. For the default setup it reads 28.85 dBm ERP, which is 767.4 mW.

To calculate ERP directly, use the EIRP formula with the antenna gain in dBd. Gain in dBd is the gain in dBi minus 2.15. A 9 dBi antenna is 6.85 dBd, and 24 − 2 + 6.85 gives the same 28.85 dBm.

The gain field accepts either unit. If a data sheet lists dBd and you type it in as dBi, the EIRP comes out 2.15 dB too low, which understates the watts by 39 percent. Pick dBd in the unit menu and the conversion is handled before the sum.

Which figure matters depends on the rule you work under. Wi-Fi and most microwave limits are written in EIRP. Some amateur limits are written in ERP. On the 60 meter band, 47 CFR 97.313 caps most channels at 100 W PEP ERP and treats a half-wave dipole as 0 dBd.

EIRP Limits and the 36 dBm Rule

An EIRP limit is a cap on the signal in the main beam, set by a regulator to control interference. It limits the combination of radio, cable and antenna. A low-power radio with a high-gain dish can break a limit that a stronger radio with a small antenna stays under.

The limit field in the EIRP Calculator starts at 36 dBm because that figure follows from the main US rule for unlicensed digital radios. Under 47 CFR 15.247, transmitters in the 902–928 MHz, 2400–2483.5 MHz and 5725–5850 MHz bands may deliver up to 1 W with antennas of up to 6 dBi. That is 30 dBm plus 6 dBi, or 36 dBm EIRP.

Above 6 dBi the rule makes you turn the transmitter down. The standard case takes off 1 dB of power for every 1 dB of extra gain, which holds the EIRP at 36 dBm. Fixed point-to-point links get more room, as the table shows.

Each cell gives the highest transmitter power and the EIRP that results, before cable loss. At 2.4 GHz a fixed point-to-point link loses only 1 dB of power for every 3 dB of gain above 6 dBi. At 5.8 GHz it loses none. A 24 dBi dish on a 2.4 GHz link can run 24 dBm, for an EIRP of 48 dBm or 63 W.

Europe uses a much lower figure. ETSI EN 300 328 sets the RF output power of 2.4 GHz wideband equipment at 20 dBm EIRP, which is 100 mW. Type 20 into the limit field and the default setup shows as 11 dB over.

The fourth result card in the EIRP Calculator reports the margin in dB. It also gives the highest transmitter power and the highest antenna gain that would still fit, which answers the common question of how much antenna gain a given radio can take. The table under the results repeats the check for gains from 0 to 24 dBi.

Field Strength to EIRP

Many emission limits are written as a field strength at a set distance, not as a power. In free space the two are tied together by one formula from Recommendation ITU-R P.525.

$$E = \frac{\sqrt{30 \times EIRP}}{d}$$

E is the field strength in volts per meter, EIRP is in watts and d is the distance in meters. For 1.259 W at 100 m the field is 61.46 mV/m, or 95.77 dBµV/m. The third result card in the EIRP Calculator shows both forms for whatever distance you set.

To go from field strength to EIRP, turn the formula around. Multiply the measured field by the distance it was measured at, square the product and divide by 30.

$$EIRP = \frac{(E \times d)^2}{30}$$

The FCC uses this same relation in its guidance on determining ERP and EIRP, KDB 412172. As an example, 47 CFR 15.249 allows a fundamental field strength of 50 mV/m at 3 m in several unlicensed bands. That works out to (0.05 × 3)² ÷ 30 = 0.00075 W, which is 0.75 mW or −1.25 dBm EIRP.

In decibels the conversion is one line, which suits test reports that list readings in dBµV/m. With E in dBµV/m and d in meters, the constant is 104.77.

$$EIRP_{dBm} = E_{dB\mu V/m} + 20 \log_{10}(d) – 104.77$$

At the usual 3 m test distance this reduces to EIRP in dBm equals E in dBµV/m minus 95.23. To use the EIRP Calculator as a field strength to EIRP calculator, set the distance and adjust the power until the third card matches your reading.

The same card lists power density, which is the EIRP spread over a sphere of radius d. At 100 m the 1.259 W example gives 10.02 µW/m². Power density falls with the square of distance, the same inverse-square pattern that the Gravitational Force Calculator shows for gravity. These figures hold in the far field with a clear path and no reflections.

EIRP in Satellite Communication

Satellite engineers quote EIRP in dBW, because the powers are large and the link equations are built around watts. The EIRP formula in satellite communication is the same sum, with the feed loss between amplifier and dish taking the place of cable loss.

$$EIRP_{dBW} = P_{dBW} + G_{dBi} – L_{dB}$$

A small ground station with 10 W and an 18 dBi antenna has 10 dBW + 18 dB = 28 dBW. A large uplink with 100 W, 2 dB of circuit loss and a 51.6 dBi dish has 20 − 2 + 51.6 = 69.6 dBW. Set the result unit to dBW and the EIRP Calculator returns both figures directly.

EIRP is the first line of every link budget. It tells you how strong the signal is as it leaves the antenna, before the long path to the receiver takes its share. The ratio of carrier power to noise density then follows from four terms.

$$\frac{C}{N_0} = EIRP – L_s + \frac{G}{T} + 228.6$$

L_s is the free-space loss in dB, G/T is the receiver figure of merit in dB/K and 228.6 comes from Boltzmann’s constant. In a link budget presented at an ITU small-satellite workshop, a 28 dBW uplink at 438 MHz over 1,000 km gives 28 − 145.3 − 26.8 + 228.6 = 84.5 dBHz.

Every extra dB of EIRP adds one dB to that result. This is why satellite operators publish EIRP contour maps for each beam, and why the University of Toronto link budget notes start their worked uplink example from the 69.6 dBW figure above.

EIRP in Practice

What is EIRP used for?

EIRP has three main jobs. Regulators use it to write limits that apply to any mix of radio and antenna. Engineers use it as the starting figure in a link budget. Buyers use it to compare transmitters fairly, since two systems with the same EIRP put the same signal on the target.

It is also the input for field strength and power density estimates, which matter for interference studies and for RF exposure checks. The energy, work and power calculators hub has more on how decibel units describe power as a ratio.

Can EIRP be lower than the transmitter power?

Yes. EIRP is lower than the transmitter power whenever the cable loss is larger than the antenna gain. A 20 dBm radio with 3 dB of cable and a 2 dBi antenna has an EIRP of 19 dBm.

Antenna gain can also be negative. Small embedded antennas in phones and sensors often radiate less than an isotropic source in every direction. The gain field takes negative numbers, and the power level diagram under the results then slopes down at the antenna as well as at the cable.

How do I find the cable loss to enter?

Cable makers publish attenuation in dB per 100 feet or per 100 meters at set frequencies. Multiply that figure by your cable length, then add the loss of each connector, adapter or lightning arrestor in the line. Loss rises with frequency, so use the row for your band.

Enter the total as a positive number. The EIRP Calculator subtracts it and shows the power that actually reaches the antenna in the first result card. If that figure looks low, a shorter run or a thicker cable will recover more signal than a small step up in antenna gain.

Can I save the EIRP calculation as a PDF?

Yes. The Print Results button opens your browser’s print dialog, and choosing Save as PDF there stores the inputs, the EIRP and the step-by-step working in one file. Copy Results puts the same figures on the clipboard as plain text.

A saved copy is useful for an installation record. Fixed point-to-point links under the US rules above depend on the installer keeping the system inside its limit, and a dated sheet with the power, loss, gain and EIRP is a simple way to show that.