Decibel (dB) Converter
Convert between dB and power or voltage ratios, and between dBm, watts and volts.
Formulas
For power, dB = 10·log10(P2)/(P1). For voltage, dB = 20·log10(V2)/(V1). So 3 dB is about twice the power and 6 dB is about twice the voltage. dBm is absolute power referenced to 1 mW: 0 dBm is 1 mW and 30 dBm is 1 W.
Try it: oscilloscope view
A sine or square wave as a scope screen shows it. Change frequency, amplitude and offset and the trace and measurements follow.
- Peak to peak Vpp
- 4 V
- Max / min
- 2 V / −2 V
- Mean (DC level)
- 0 V
- RMS (AC + DC)
- 1.41 V
- AC rms
- 1.41 V
- AC rms in dBV
- 3.01 dBV
- Period T
- 1 ms
A scope plots voltage up the screen (V/div) against time across it (time/div). This screen has 8 × 10 divisions; the marker on the left edge is 0 V and the dashed line is the mean. Amplitude here is the peak value Vp, so the trace spans 2·Vp from top to bottom. Offset adds a DC level that moves the whole trace up or down; a real scope set to AC coupling would remove it.
A square wave sits at its peak the whole time, so its rms equals the peak: twice the power of a sine with the same peak, or 3 dB more. With an offset, the AC + DC rms adds the two in quadrature, the way a true-rms meter on DC + AC does.
Worked example: 1 mW through 20 dB of gain
- An input of 1 mW is 0 dBm.
- After a 20 dB amplifier it is 0 + 20 = 20 dBm.
- 20 dBm = 10^(20 ÷ 10) × 1 mW = 100 mW: 100× the power and 10× the voltage.
Decibel conversion chart
| dB | Power ratio | Voltage ratio |
|---|---|---|
| −40 dB | ×0.0001 | ×0.01 |
| −30 dB | ×0.001 | ×0.03162 |
| −20 dB | ×0.01 | ×0.1 |
| −10 dB | ×0.1 | ×0.3162 |
| −6 dB | ×0.2512 | ×0.5012 |
| −3 dB | ×0.5012 | ×0.7079 |
| −1 dB | ×0.7943 | ×0.8913 |
| 0 dB | ×1 | ×1 |
| +1 dB | ×1.259 | ×1.122 |
| +3 dB | ×1.995 | ×1.413 |
| +6 dB | ×3.981 | ×1.995 |
| +10 dB | ×10 | ×3.162 |
| +20 dB | ×100 | ×10 |
| +30 dB | ×1,000 | ×31.62 |
| +40 dB | ×10,000 | ×100 |
dBm to power chart
| dBm | Power | Vrms (50 Ω) |
|---|---|---|
| −30 dBm | 1 µW | 7.07 mV |
| −20 dBm | 10 µW | 22.4 mV |
| −10 dBm | 100 µW | 70.7 mV |
| 0 dBm | 1 mW | 224 mV |
| 10 dBm | 10 mW | 707 mV |
| 13 dBm | 20 mW | 999 mV |
| 20 dBm | 100 mW | 2.24 V |
| 27 dBm | 501 mW | 5.01 V |
| 30 dBm | 1 W | 7.07 V |
| 40 dBm | 10 W | 22.4 V |
Checked on our bench: reading a channel mismatch in dB
The numbers below are computed from values the site owner recorded in lab classes. Measured values are left exactly as recorded.
In the lab one function generator was clipped to both scope channels at once and the Vpp read off. It is one signal, so the two readings should match. Turning the ratio into dB shows at a glance how far apart they are.
| Setting | CH1 Vpp | CH2 Vpp | Voltage ratio | dB (20 log) |
|---|---|---|---|---|
| SettingDefault | CH1 Vpp4.015 V | CH2 Vpp2.975 V | Voltage ratio0.741 | dB (20 log)−2.60 dB |
| SettingDC coupling | CH1 Vpp3.995 V | CH2 Vpp2.985 V | Voltage ratio0.747 | dB (20 log)−2.53 dB |
| SettingAC coupling | CH1 Vpp4.020 V | CH2 Vpp2.990 V | Voltage ratio0.744 | dB (20 log)−2.57 dB |
| SettingMoved | CH1 Vpp4.005 V | CH2 Vpp3.125 V | Voltage ratio0.780 | dB (20 log)−2.16 dB |
| Setting10 kHz | CH1 Vpp4.080 V | CH2 Vpp3.435 V | Voltage ratio0.842 | dB (20 log)−1.49 dB |
- At 1 kHz CH2 sat at −2.6 to −2.2 dB, about 26% low in voltage. That is as big as a −3 dB cutoff, far too large to shrug off as reading error.
- At 10 kHz the gap shrank to −1.5 dB. A ratio that changes with frequency rules out a simple ×1/×10 attenuation slip, which would show as exactly −20 dB.
Why dB helps: put two readings in dB and you can subtract them directly, then match the result against familiar figures like −20 dB (a tenth), −6 dB (half) and −3 dB (0.707) to guess the cause. The diagnosis is in the oscilloscope basics guide.
Working in decibels
Converting in the right direction
- Choose what you have: a dB value, a power ratio, a voltage ratio or an absolute level in dBm.
- Enter it and read the other forms side by side.
- For a chain of stages, add the gains and losses in dB, then convert the total back to a ratio once.
Power dB versus voltage dB
- Using 10 log for voltages. Power ratios use 10 log; voltage and current ratios use 20 log. A voltage gain of 10 is 20 dB, not 10 dB.
- Comparing voltages across different impedances. The 20 log rule assumes both voltages are across the same impedance. Otherwise convert to power first.
- Mixing dBV and dBu. 0 dBV is 1 V RMS, while 0 dBu is 0.775 V RMS (1 mW into 600 Ω). The two differ by about 2.2 dB.
Numbers worth remembering
3 dB is about twice the power, 6 dB about twice the voltage, 10 dB ten times the power and 20 dB ten times the voltage. 0 dBm is 1 mW; 30 dBm is 1 W; −30 dBm is 1 µW. In a 50 Ω system 0 dBm is about 0.224 V RMS. Negative dB simply means a loss, so a filter at −3 dB passes half the power.
Frequently asked questions
How much is 3 dB?
About twice the power (×1.995), or about 1.41 times the voltage. −3 dB is half the power, which is why filter cutoffs are defined at −3 dB.
What is the difference between dB and dBm?
dB is a ratio between two values and has no unit. dBm is an absolute power referenced to 1 mW, so 20 dBm is exactly 100 mW.