dBm is a unit used to measure electrical power that is referenced to 1 milliwatt. The document defines dBm and provides formulas for converting between dBm, milliwatts, watts, and dBW. It also includes an example conversion calculation for each type of unit and ends with a conversion table listing common power levels in dBm, dBW, watts, and milliwatts.

1. dBm:- A mathematical Interpretation.
dBm definition
dBm or decibel-milliwatt is an electrical power unit in decibels (dB), referenced to 1
milliwatt (mW).
The power in decibel-milliwatts (P(dBm)) is equal to 10 times base 10 logarithm of the
power in milliwatts (P(mW)):
P(dBm) = 10 · log10( P(mW) / 1mW)
The power in milliwatts (P(mW)) is equal to 1mW times 10 raised by the power in decibel-
milliwatts (P(dBm)) divided by 10:
P(mW) = 1mW · 10(P(dBm) / 10)
1 milliwatt is equal to 0 dBm:
1mW = 0dBm
1 watt is equal to 30dBm:
1W = 1000mW = 30dBm
How to convert mW to dBm
How to convert power in milliwatts (mW) to dBm.
The power in dBm is equal to the base 10 logarithm of the power in milliwatts (mW):
P(dBm) = 10 · log10( P(mW) / 1mW )

2. For example: what is the power in dBm for power consumption of 100mW?
Solution:
P(dBm) = 10 · log10( 100mW / 1mW ) = 20dBm
How to convert dBm to mW
How to convert power in dBm to milliwatts (mW).
The power in milliwatts (P(mW)) is equal to 10 raised by the power in dBm (P(dBm)) divided
by 10?
P(mW) = 1mW · 10(P(dBm) / 10)
For example: what is the power in milliwatts for power consumption of 20dBm?
Solution:
P(mW) = 1mW · 10(20dBm / 10) = 100mW
How to convert Watt to dBm
How to convert power in watts (W) to dBm.
The power in dBm is equal to the base 10 logarithm of the power in watts (W) plus
30dB:
P(dBm) = 10 · log10( P(W) / 1W ) + 30
For example: what is the power in dBm for power consumption of 100W?
Solution:
P(dBm) = 10 · log10( 100W / 1W ) + 30 = 50dBm
How to convert dBm to Watt
How to convert power in dBm to watts (W).
The power in watts (P(W)) is equal to 10 raised by the power in dBm (P(dBm)) minus 30dB
divided by 10:
P(W) = 1W · 10( (P(dBm) - 30) / 10)
For example: what is the power in watts for power consumption of 40dBm?
Solution:

3. P(W) = 1W · 10( (40dBm - 30) / 10) = 10W
How to convert dBW to dBm
How to convert power in dBW to dBm.
The power in dBm is equal to the base 10 logarithm of the power in watts (W):
P(dBm) = P(dBW) + 30
For example: what is the power in dBm for power consumption of 20dBW?
Solution:
P(dBm) = 20dBW + 30 = 50dBm
How to convert dBm to dBW
How to convert power in dBm to dBW.
The power in dBW (P(dBW)) is equal to 10 raised by the power in dBm (P(dBm)) divided by
10:
P(dBW) = P(dBm) - 30
For example: what is the power in watts for power consumption of 40dBm?
Solution:
P(dBW) = 40dBm - 30 = 10dBW
dBm to Watt, mW, dBW conversion table
Power (dBm) Power (dBW) Power (watt) Power (mW)
-100 dBm -130 dBW 0.1 pW 0.0000000001 mW
-90 dBm -120 dBW 1 pW 0.000000001 mW
-80 dBm -110 dBW 10 pW 0.00000001 mW
-70 dBm -100 dBW 100 pW 0.0000001 mW
-60 dBm -90 dBW 1 nW 0.000001 mW
-50 dBm -80 dBW 10 nW 0.00001 mW
-40 dBm -70 dBW 100 nW 0.0001 mW
-30 dBm -60 dBW 1 μW 0.001 mW
-20 dBm -50 dBW 10 μW 0.01 mW
-10 dBm -40 dBW 100 μW 0.1 mW

4. -1 dBm -31 dBW 794 μW 0.794 mW
0 dBm -30 dBW 1.000 mW 1.000 mW
1 dBm -29 dBW 1.259 mW 1.259 mW
10 dBm -20 dBW 10 mW 10 mW
20 dBm -10 dBW 100 mW 100 mW
30 dBm 0 dBW 1 W 1000 mW
40 dBm 10 dBW 10 W 10000 mW
50 dBm 20 dBW 100 W 100000 mW
60 dBm 30 dBW 1 kW 1000000 mW
70 dBm 40 dBW 10 kW 10000000 mW
80 dBm 50 dBW 100 kW 100000000 mW
90 dBm 60 dBW 1 MW 1000000000 mW
100 dBm 70 dBW 10 MW 10000000000 mW