Type a power value in watts to convert it to decibels (dBm). You can also run it in reverse to get watts from a dB figure.
Watts to dB Formula
The calculator uses one of three formulas depending on the selected mode.
Watts to dBm (reference: 1 mW):
dBm = 10 * log10(P / 1 mW)
Watts to dBW (reference: 1 W):
dBW = 10 * log10(P / 1 W)
Power gain (dB):
Gain (dB) = 10 * log10(P_out / P_in)
- P — power being converted, in watts (input is converted from mW or kW automatically).
- P_in — input power in watts.
- P_out — output power in watts.
- log10 — base-10 logarithm.
dBm and dBW are absolute power levels referenced to 1 mW and 1 W respectively. They differ by a fixed offset: dBm = dBW + 30. dB by itself is dimensionless and only makes sense as a ratio between two powers. Power must be greater than zero, since log10(0) is undefined.
Reference Tables
Use these to sanity-check a converted value.
| Power | dBm | dBW |
|---|---|---|
| 1 µW | -30 | -60 |
| 1 mW | 0 | -30 |
| 10 mW | 10 | -20 |
| 100 mW | 20 | -10 |
| 1 W | 30 | 0 |
| 10 W | 40 | 10 |
| 100 W | 50 | 20 |
| 1 kW | 60 | 30 |
| 1 MW | 90 | 60 |
Common gain ratios for the dB mode:
| P_out / P_in | Gain (dB) |
|---|---|
| 0.5 | -3 |
| 1 | 0 |
| 2 | +3 |
| 10 | +10 |
| 100 | +20 |
| 1,000 | +30 |
Example Problems
Example 1 — Wi-Fi router output to dBm. A router transmits at 0.1 W.
dBm = 10 × log10(100 mW / 1 mW) = 10 × log10(100) = 20 dBm.
Example 2 — 50 W transmitter to dBW.
dBW = 10 × log10(50 / 1) = 10 × 1.699 = 16.99 dBW (also 46.99 dBm).
Example 3 — Amplifier gain. Input 1 mW, output 2 W.
Gain = 10 × log10(2 / 0.001) = 10 × log10(2000) = 33.01 dB.
FAQ
Is dBm or dBW better? Neither. dBm is convenient for low-power radio and signal levels. dBW is convenient for transmitter and broadcast power. Convert between them with dBm = dBW + 30.
Why does watts use a factor of 10 instead of 20? The factor of 20 applies to amplitude ratios (voltage, current). Power is already a squared quantity, so the factor is 10.
Can power be negative in dB? Absolute levels (dBm, dBW) can be negative when the power is below the reference. The actual power in watts is always positive.
