Case 1
- First power
- 100W
- Second power
- 1W
20.0000dB
Open with these valuesDecibel Calculator
20.0000dB
Result: 20.0000 dBTen times the base-ten logarithm of one power divided by the other. Ten times the power is 10 dB, a hundred times is 20 dB, and merely doubling it is 3.01 dB. Only the ratio matters, so 50 W against 25 W reads the same as 2 W against 1 W.
Worked examples
Case 2
- First power
- 2W
- Second power
- 1W
3.0103dB
Open with these valuesCase 3
- First power
- 1W
- Second power
- 100W
-20.0000dB
Open with these valuesHow it's calculated
dB = 10 × log₁₀(P₁ ÷ P₂)
- StepEnter the power you are measuring.
- StepEnter the power you are comparing it against.
- ResultRead the difference in decibels; a negative value means quieter.
Reference table
| Two powers (W) | Ratio | Difference (dB) |
|---|---|---|
| 1, 1 | Equal | 0 |
| 2, 1 | Twice the power | 3.0103 |
| 10, 1 | Ten times | 10 |
| 100, 1 | A hundred times | 20 |
| 1000, 1 | A thousand times | 30 |
| 50, 25 | Twice again, larger numbers | 3.0103 |
| 1, 100 | A hundredth | -20 |
Questions
How do I calculate decibels?
Divide the two powers, take the base-ten logarithm and multiply by ten. A ratio of 100 gives 20 dB.
Why does doubling the power give only 3 dB?
Because the scale is logarithmic, and log₁₀(2) is 0.301. Ten times that is 3.01 dB, which is roughly the smallest change most people notice.
When is the factor 20 instead of 10?
For field quantities such as voltage, sound pressure or current, which enter power as a square. That case has its own calculator in this set.
What does a negative result mean?
The first power is the smaller one. A hundredth of the power is −20 dB, the exact mirror of a hundred times.
Do I need a reference level?
Not here. A decibel is a ratio, so any reference cancels out; absolute levels such as dB SPL are a separate matter that needs a fixed reference.
Sources and last check
Information, not professional advice.