# RF power converters and calculators

## 1) dBm to mW (milliwatt)

Formula: P(mW) = 1mW * 10^(P(dBm)/ 10)

## 2) mW (milliwatt) to dBm

Formula: P(dBm) = 10 * log(P(mW))

dBm to mW conversion table with sample values

Power (dBm) | Power (mW) |

-25 dBm | 0.003 mW |

-20 dBm | 0.01 mW |

-15 dBm | 0.03 mW |

-10 dBm | 0.1 mW |

-5 dBm | 0.3 mW |

0 dBm | 1 mW |

5 dBm | 3 mW |

10 dBm | 10 mW |

15 dBm | 30 mW |

20 dBm | 100 mW |

Examples of common devices working in the 2 GHz frequency range:

Max transmit power of a typical laptop, wifi: 30mW = 15 dBm

Max transmit power of a typical cordless DECT phone: 85mW = 19 dBm

Transmit power of a typical wifi router: 100mW = 20 dBm

Max transmit power of a typical 4G phone: 1000mW = 30 dBm

## 3) Power density for omnidirectional antennas

All consumer wifi devices and 4G mobile phones have approximately Isotropic Antennas (also known as an omnidirectional antennas). An Isotropic antenna emits the signal uniformly in all directions. You can look-up the emitted RF power based on the FCC-id printed on the device. This can then be used to caluclate the power density. Power density is used for human safty exposure limits such as:

Note that 1 W/m^{2} = 1000 mW/m^{2} = 1000000 μW/m^{2}. In other words there is a factor 1000000 (10^{6} = one million) difference between the levels that the Canadian government regulator considers safe and what that company making the safe-and-sound monitor considers safe.

For easier comparison with the above exposure limit tables the results are shown in both W/m^{2} and μW/m^{2}.

Formula: S = P/(4 * pi * r^{2})

S = power density

P = emitted RF power

For an antenna that is not omnidirectional you would have to multiply the result by the antenna gain factor.
Manufactures provides antenna gains usually in units of dBi.

Antenna gain factor=10^{gain_in_dBi/10}

A typical rectangular box shaped 4G cell tower antenna has a gain of 15dBi. This corresponds to a gain factor of 32. Thus you would multiply the results calculated by the above calculator with the factor 32.

## 4) RF power decrease over distance

This calculator does not consider atmospheric losses (e.g due to water vapor) and it does not work
for array antennas that support beam forming.

Formula: P(in mW at distance A)*square(A) = P(in mW at distance B)*square(B)

A = distance from the transmitting antenna to point A

B = distance from the transmitting antenna to point B

distance can be measured in inch, feet, cm or meter but it must be the same unit for A and B

**Neither A or B can be zero**

The power in milliwatt is related to the square of the distance. In other words if you double the distance then the power goes down to a quarter of the value.

© Guido Socher, License: GPL,