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# EIRP Calculator — Effective Isotropic Radiated Power

Definition: What is the EIRP?EIRP calculation example: How to use the antenna EIRP calculatorIsotropic antennas vs. practical antennasDecibels: dB vs. dBmWERP vs. EIRPFAQs

Welcome to the EIRP calculator! This tool calculates the effective isotropic radiated power (EIRP) for a system consisting of a transmitter, a cable, and an antenna.

• What the EIRP is;
• How to calculate the EIRP; and
• The difference between the effective radiated power and the effective isotropic radiated power — ERP vs. EIRP.

Continue to read if you want to know how to calculate the EIRP of an antenna using the EIRP calculation formula.

## Definition: What is the EIRP?

EIRP stands for effective isotropic radiated power or equivalent isotropic radiated power. This term is often used in telecommunications (mainly in link budgets). EIRP is defined as the amount of power that a theoretical isotropic antenna (which distributes power uniformly in all directions) would radiate to produce the peak power density observed in the direction of maximum antenna gain.

Radio communication systems must comply with specific rules established by regulatory bodies, such as the Federal Communications Commission (FCC) in the US or the European Telecommunications Standards Institute (ETSI) in Europe. One rule is that radio equipment must not exceed certain EIRP values.

The effective isotropic radiated power is calculated according to the following EIRP calculation formula:

$\footnotesize \mathrm{EIRP = T_{x} - L_{c} + G_{a}}$

where:

• Tx — Output power of the transmitter (dBmW);
• Lc — Sum of cable and connectors losses (if present) (dB); and
• Ga — Antenna gain (dBi).

As you can see from the formula above, the EIRP considers losses in transmission cables and connectors and includes antenna gain. It is often expressed in decibels relative to a reference power emitted by an isotropic antenna with equivalent signal power. To know more about decibels, check out the section below.

## EIRP calculation example: How to use the antenna EIRP calculator

Let's see a concrete example of how to use our EIRP calculator. Here is the data that you have:

• The transmitter output power: 21 dBmW;
• The total cable loss: 3 dB;
• The connectors loss: 0.5 dB per connector (you have 2); and
• The antenna gain: 11 dBi.

1. First, based on what you know, select: total cable loss. Then, in the field for Total cable loss, input 3 dB.

2. Enter the data for the transmitter output power (21 dBmW). Your input is in decibel-milliwatts (written as dbmW or dBm), but you can also convert it to watts. Click on the unit next to your input or use our dBm to watts converter.

3. Enter the antenna gain in the corresponding field: 11 dBi.

4. Check the box for I have connectors. As you can see, the default value for No. of connectors is already 2. You don't need to input anything new. Next to it, you have the field for the Connectors loss — enter 0.5 dB.

5. Here is your result: the EIRP equals 28 dBmW or 0.631 W.

If you want to solve this EIRP calculation example by hand, here's what the equation looks like:

\scriptsize \begin{align*} \mathrm{EIRP} &= \mathrm{21\, dBmW} - (\mathrm{3\, dB} + 2 \times 0.5\, \mathrm{dB})\\ &\quad + \mathrm{11\, dBi}\\ & = \mathrm{21\, dBmW} - \mathrm{4\, dB} + \mathrm{11\, dBi}\\ & = \mathrm{28\, dBmW} \end{align*}

But that's not it!

• If you know the type of cable you want to use at a specific frequency, select cable type and frequency. Choose your cable from a list of the most common cables and the frequency. Finally, enter the cable length.

• If your cable type is not included in the calculator, select the third option — cable loss per unit of length. Then, all you have to do is enter the known cable loss per unit of length and its length.

Next, you can follow the same step as in the example and input the transmitter output power, the antenna gain, and the connectors loss (if any). Our EIRP calculator will compute the effective or equivalent isotropic radiated power in decibel-milliwatts or watts. Please continue to read to learn more about decibels, or go directly to our dB calculator.

## Isotropic antennas vs. practical antennas

An isotropic antenna is a hypothetical point source antenna that radiates its powers uniformly in all directions. It is considered a lossless antenna, which means it has an antenna efficiency of 0 dB (or 100%).

In practice, antennas are not isotropic, i.e., they do not have homogeneous scattering and will favor radiation in certain directions, as you can see in the following diagram:

The gain of an antenna is, therefore, not really a gain in power but simply a concentration of radio waves — more power at one point and none or less at another. When we express the gain of an antenna, we compare the actual power measured in the optimum direction to a point at the same distance from an isotropic source.

An antenna can have a negative gain. A negative gain means that the antenna radiates less than the reference (isotropic) antenna, and a positive number means that the antenna radiates more than the reference antenna.

## Decibels: dB vs. dBmW

#### Decibel (dB)

The decibel (dB) is the unit expressing a power ratio in logarithmic form. In the EIRP formula, the decibel is used to express the ratio of electrical powers, i.e., watts (W), and can be written as follows:

$\footnotesize \mathrm{dB = 10 \times log_{10}\left(\frac{P_o }{ P_i}\right)}$

where:
dB — Decibel gain or loss;
Po — Output power (W); and
Pi — Input power (W).

Remember that the decibel is a ratio. It does not represent an absolute value, unlike the decibel-milliwatt.

#### Decibel-milliwatt (dBmW)

If we use a reference input power of 1 mW (Pi = 1 mW), the unit is expressed as dBmW (also written as dBm).

$\footnotesize \mathrm{dBmW = 10 \times log_{10}\left(\frac{P_o }{ 1}\right)}$

dBmW represents an absolute value, using a fixed reference value of 1 mW. To better understand the relationship between these two units, take a look at our dBmW to watts conversion table.

dBmW to watts conversion table.

Decibel-milliwatts (dBmW)

Watts (W)

-30 dBmW

0.000001 W

-20 dBmW

0.00001 W

-10 dBmW

0.0001 W

0 dBmW

0.001 W

1 dBmW

0.001259 W

2 dBmW

0.001585 W

3 dBmW

0.0019953 W

4 dBmW

0.002512 W

5 dBmW

0.003162 W

6 dBmW

0.003981 W

7 dBmW

0.005012 W

8 dBmW

0.00631 W

9 dBmW

0.007943 W

10 dBmW

0.01 W

20 dBmW

0.1 W

30 dBmW

1 W

40 dBmW

10 W

50 dBmW

100 W

## ERP vs. EIRP

When looking for how to calculate the EIRP of an antenna, you may have stumbled upon another term: ERP. This section will explain what the ERP is and how it is linked to the EIRP.

After reading the article, you now know that the EIRP (effective isotropic radiated power) is the total power radiated by a hypothetical isotropic antenna in a single direction. You know that its equation is as follows:

\scriptsize \begin{align*} \mathrm{EIRP} =\ &\mathrm{Tx\, power\,(dBmW)} \\ &- \mathrm{Cable\, loss\,(dB)} \\ &- \mathrm{Connectors \, loss\,(dB)} \\ &+ \mathrm{Antenna\,gain\,(dBi)} \end{align*}

So, what is ERP?

ERP (effective radiated power) is the total power radiated by an actual antenna relative to a half-wave dipole rather than a theoretical isotropic antenna. A dipole antenna radiates most of its energy horizontally but very little vertically. If you want to know more about dipole antennas, check out our dipole calculator. The ERP equation is very similar to the EIRP one:

\scriptsize \begin{align*} \mathrm{ERP} =\ &\mathrm{Tx\, power\,(dBmW)} \\ &- \mathrm{Cable\, loss\,(dB)} \\ &- \mathrm{Connectors \, loss\,(dB)} \\ &+ \mathrm{Antenna\,gain\,(dBd)} \end{align*}

As you can see, the only difference between the two equations lies in the units of the antenna gain — dBi and dBd:

• dBi (i for isotropic) refers to the antenna gain with respect to an isotropic antenna; and
• dBd (d for dipole) refers to the antenna gain with respect to a reference 1/2λ dipole antenna.

The conversion between dBd and dBi is as follows:

$\footnotesize \mathrm{dBi = dBd + 2.15}$

According to this conversion, a gain of 0 dBi is equivalent to a loss of 2.15 dBd.

But what does it mean for EIRP and ERP calculations?

Well, we can simply rewrite the relationship between the EIRP and the ERP as follows:

$\scriptsize \mathrm{EIRP (dBmW) = ERP (dBmW) + 2.15}$

Thus, you can use our EIRP calculator as an ERP calculator by simply subtracting 2.15 from the final result (when expressed in dBmW).

FAQs

### How do I calculate EIRP?

To calculate the EIRP (effective isotropic radiated power) of a system consisting of a transmitter, a cable, and an antenna, use the following formula:

EIRP = Transmitter power − Cable and connectors losses + Antenna gain

The transmitter output power is expressed in dBmW, the antenna gain in dBi, and the cable and connectors losses in dB.

### What is the EIRP?

EIRP, effective isotropic radiated power or equivalent isotropic radiated power, is defined as the power that a hypothetical isotropic antenna would have to radiate (evenly in all directions) to obtain an identical signal level in the direction of maximum radiation from a specific antenna.

### What is the EIRP of a transmitter with an output power of 15 dBmW?

25 dbmW. Let's assume that the transmitter emits 15 dBmW of power through a cable that adds 3 dB of loss. The antenna used has a gain of 12 dBi. To calculate the EIRP:

EIRP = Transmitter power − Cable loss + Antenna gain
EIRP = 15 dBmW − 3 dB + 13 dBi
EIRP = 25 dBmW

### What is the EIRP limit?

In the US, systems operating under FCC (Federal Communications Commission) regulations are limited to 36 dBmW EIRP (effective isotropic radiated power), but exceptions exist. Regulations may vary from state to state. If you want to know what your EIRP limit is, it's best to check your local regulations.