Associated Topics || Dr. Math Home || Search Dr. Math

### Converting mW to dB

```
Date: 06/14/2001 at 21:45:44
From: Jeff Carson
Subject: Conversion of mW to dB

4x10-12mW = -114dBm

How does it equate? What is the math that performs this conversion?
```

```
Date: 06/15/2001 at 12:04:22
From: Doctor Peterson
Subject: Re: Conversion of mW to dB

Hi, Jeff.

According to my favorite source on units, How Many? A Dictionary of
Units of Measurement, by Russ Rowlett:

http://www.unc.edu/~rowlett/units/

dB m, dB W
logarithmic units of power used in electronics. These units
measure power in decibels above the reference level of 1
milliwatt in the case of dB m and 1 watt in the case of dB W.
A power of n watts equals 10 log n dB W; conversely, a power
of p dB W equals 10^(p/10) watts. The same formulas link dB m
to milliwatts. An increase of 10 dB m or 10 dB W represents a
10-fold increase in power. Since 1 watt = 1000 milliwatts, 0
dB W = 30 dB m.

(Look up decibel and bel there, too.)

Another source I found, a column by Ron Hranac in the April 2000 issue
of Communications Technology:

Broadband DBmV: Power in Terms of Voltage
http://www.cabletoday.com/ct2/archives/0400/0400col1.htm

says that dBm is read as "decimal milliwatt," and gives the same
formula:

dBm = 10log(P/1 mW), where P is a power level in milliwatts

Note that a bel is the base-ten logarithm of any ratio; in this case
the ratio is that of the given power to a 1 mW output. A decibel is
1/10 of a bel, accounting for the factor of ten.

So in your example, with P = 4x10^-12 mW, we get

10 log(4x10^-12) = 10 (log(4) - 12) = -113.98

which agrees with what you read, rounded appropriately.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Logs
High School Physics/Chemistry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search