dB to mW: Convert dBm to Milliwatts and dBW to Watts
A direct dB to mW or dB to W conversion is not possible from a plain dB value alone. Plain dB expresses a power ratio, while dBm and dBW express power relative to stated reference levels. For a usable power result, the reference must be known.
dBm uses 1 mW as its reference, and dBW uses 1 W. The formulas below convert each logarithmic level to linear power and back, including negative, zero, and positive values.
dB to mW: Why dB, dBm, and dBW are different
Plain dB describes the ratio between two power levels:
Power ratio = 10^(dB/10)
For example, a 10 dB increase means the output power is 10 times the input power, while a -10 dB change means the output power is one-tenth of the input power. Because dB is a ratio, it does not identify an absolute number of milliwatts or watts without a reference power.
With a known reference, the absolute output power can be calculated as:
Output power = Reference power × 10^(dB/10)
For example, a 6 dB gain applied to a 2 mW input produces approximately 7.96 mW:
2 mW × 10^(6/10) = 2 × 3.981 = 7.96 mW
dBm is an absolute power level referenced to 1 mW:
- 0 dBm = 1 mW
- 10 dBm = 10 mW
- -10 dBm = 0.1 mW
dBW is an absolute power level referenced to 1 W:
- 0 dBW = 1 W
- 10 dBW = 10 W
- -10 dBW = 0.1 W
Therefore, a plain dB value should not be labeled as a power level. A statement such as “-3 dB equals 0.5 W” is incomplete unless the reference power is supplied. A statement such as “-3 dBm equals approximately 0.501 mW” is complete because dBm already defines its reference.
Convert dBm to milliwatts with the right formula
Forward conversion: dBm to mW
To convert dBm to milliwatts, use:
Power (mW) = 10^(power (dBm)/10)
The result is in milliwatts because the dBm reference is 1 mW. The exponent is the dBm value divided by 10.
- Negative value: -20 dBm = 10^(-20/10) = 10^-2 = 0.01 mW, or 10 µW.
- Zero value: 0 dBm = 10^(0/10) = 1 mW.
- Positive value: 10 dBm = 10^(10/10) = 10 mW.
- Higher positive value: 20 dBm = 10^(20/10) = 100 mW.
Another useful example is -3 dBm:
10^(-3/10) = 10^-0.3 ≈ 0.501 mW
For levels expressed in dBm but needed in watts, first calculate milliwatts and divide by 1,000. A direct formula is also available:
Power (W) = 10^((power (dBm) – 30)/10)
For example, 30 dBm equals:
10^((30 – 30)/10) = 1 W
Reverse conversion: mW to dBm
To convert milliwatts back to dBm, use the base-10 logarithm:
Power (dBm) = 10 × log10(power (mW))
- Negative result: 0.01 mW gives 10 × log10(0.01) = -20 dBm.
- Zero result: 1 mW gives 10 × log10(1) = 0 dBm.
- Positive result: 10 mW gives 10 × log10(10) = 10 dBm.
For a non-power-of-ten value, 2 mW converts as follows:
10 × log10(2) ≈ 3.01 dBm
Similarly, 0.5 mW is approximately -3.01 dBm. The logarithm automatically produces a negative dBm value for any power below 1 mW and a positive value for any power above 1 mW.
dB to W: Convert dBW to watts
Forward conversion: dBW to W
To convert dBW to watts, use:
Power (W) = 10^(power (dBW)/10)
Because dBW is referenced to 1 W, a dBW value of zero represents exactly 1 W.
- Negative value: -20 dBW = 10^(-20/10) = 0.01 W, or 10 mW.
- Zero value: 0 dBW = 10^(0/10) = 1 W.
- Positive value: 10 dBW = 10^(10/10) = 10 W.
- Higher positive value: 20 dBW = 10^(20/10) = 100 W.
For a value that is not a multiple of 10, -3 dBW converts to:
10^(-3/10) = 10^-0.3 ≈ 0.501 W
The direct conversion from dBW to milliwatts is:
Power (mW) = 1,000 × 10^(power (dBW)/10)
For example, 0 dBW equals 1 W, which is 1,000 mW. Likewise, -30 dBW equals 0.001 W, which is 1 mW.
Reverse conversion: W to dBW
To convert watts back to dBW, use:
Power (dBW) = 10 × log10(power (W))
- Negative result: 0.01 W gives 10 × log10(0.01) = -20 dBW.
- Zero result: 1 W gives 10 × log10(1) = 0 dBW.
- Positive result: 10 W gives 10 × log10(10) = 10 dBW.
For 0.5 W:
10 × log10(0.5) ≈ -3.01 dBW
For 100 W:
10 × log10(100) = 20 dBW
As with dBm, a wattage below the reference level produces a negative logarithmic value, while a wattage above the reference produces a positive value.
Worked examples: decibels to watts, reverse conversions, and the 30 dB offset
Negative, zero, and positive examples
The following examples show how the two reference systems behave at common values:
- -30 dBm: 10^(-30/10) = 0.001 mW = 1 µW.
- -10 dBm: 10^(-10/10) = 0.1 mW.
- 0 dBm: 10^(0/10) = 1 mW.
- 10 dBm: 10^(10/10) = 10 mW.
- 30 dBm: 10^(30/10) = 1,000 mW = 1 W.
- -30 dBW: 10^(-30/10) = 0.001 W.
- -10 dBW: 10^(-10/10) = 0.1 W.
- 0 dBW: 10^(0/10) = 1 W.
- 10 dBW: 10^(10/10) = 10 W.
- 30 dBW: 10^(30/10) = 1,000 W.
For reverse conversions, 0.001 mW is -30 dBm, 1 mW is 0 dBm, and 1,000 mW is 30 dBm. In watts, 0.001 W is -30 dBW, 1 W is 0 dBW, and 1,000 W is 30 dBW.
How the 30 dB dBm-to-dBW offset works
dBm and dBW use different reference powers: 1 mW and 1 W. Since 1 W equals 1,000 mW, and:
10 × log10(1,000) = 30 dB
the two scales have a fixed 30 dB offset:
Power (dBm) = Power (dBW) + 30
Power (dBW) = Power (dBm) – 30
Examples include:
- 0 dBW = 30 dBm: both represent 1 W.
- -10 dBW = 20 dBm: both represent 0.1 W, or 100 mW.
- -30 dBW = 0 dBm: both represent 1 mW.
- 10 dBW = 40 dBm: both represent 10 W.
The offset changes only the numerical label, not the physical power. A conversion involving plain dB still requires a reference. For example, a gain of 30 dB applied to 1 mW produces 1 W, but the same 30 dB gain applied to 10 mW produces 10 W.