dB to Ratio Converter
A change of 3 dB is about double the power and 1.41 times the voltage.
Quick answer: For power divide the dB by 10, for voltage divide by 20, then raise 10 to that power. For example, 3 dB is 1.995, 10 dB is 10 and -10 dB is 0.1.
The dB to ratio formula
Power ratio equals 10 to the power of dB divided by 10.
Amplitude ratio equals 10 to the power of dB divided by 20.
Take 3 dB. 10^(3 ÷ 10) gives 1.995.
Take 10 dB. 10^(10 ÷ 10) gives 10.
A dB is a ratio on a log scale
The decibel compares two values on a logarithmic scale. A power ratio uses 10 times the log, and an amplitude ratio such as voltage or pressure uses 20 times the log (Engineering ToolBox: Decibel).
This page runs that backward, from the dB figure to the plain ratio.
How to convert dB to ratio step by step
- Read the level change in dB.
- Divide by 10 for a power ratio, or by 20 for an amplitude ratio.
- Raise 10 to that power.
- Read the ratio. A number below 1 is a loss.
Example 1: 3 dB
- Start with 3 dB.
- 10^(3 ÷ 10) = 1.995.
- The ratio is 1.995.
3 dB = 1.995
Example 2: 10 dB
- Start with 10 dB.
- 10^(10 ÷ 10) = 10.
- The ratio is 10.
10 dB = 10
Example 3: -10 dB
- Start with -10 dB.
- 10^(-10 ÷ 10) = 0.1.
- The ratio is 0.1.
-10 dB = 0.1
The three examples below use common sizes.
Each one shows the sum in full.
dB to ratio conversion table
| Level change | Power ratio | Amplitude ratio |
|---|---|---|
| -40 dB | 0.0001 | 0.01 amplitude |
| -20 dB | 0.01 | 0.1 amplitude |
| -10 dB | 0.1 | 0.3162 amplitude |
| -6 dB | 0.2512 | 0.5012 amplitude |
| -3 dB | 0.5012 | 0.7079 amplitude |
| 0 dB | 1 | 1 amplitude |
| 1 dB | 1.259 | 1.122 amplitude |
| 3 dB | 1.995 | 1.413 amplitude |
| 6 dB | 3.981 | 1.995 amplitude |
| 10 dB | 10 | 3.162 amplitude |
| 20 dB | 100 | 10 amplitude |
| 40 dB | 10,000 | 100 amplitude |
The highlighted row is the default of the calculator. The last column gives amplitude.
A quick mental shortcut for dB to ratio
Remember three steps. 3 dB is about twice the power, 6 dB is about twice the voltage, and 10 dB is ten times the power.
Add the steps to build others. 13 dB is 10 plus 3, so about 20 times the power.
The rules of thumb
Doubling a power adds about 3 dB. Doubling an amplitude adds about 6 dB, which is a fourfold power. A tenfold power adds 10 dB, and a tenfold amplitude adds 20 dB (Engineering ToolBox: Decibel).
These cover most quick checks.
Power ratio or amplitude ratio
Power goes with the square of the voltage, so a voltage ratio uses 20 in the formula and a power ratio uses 10 (Wikipedia: Decibel).
The two columns above show both at the same dB.
Negative dB
A negative level change is a loss. Minus 3 dB leaves about half the power, which is a ratio of 0.501, and minus 10 dB leaves one tenth.
The ratio never goes negative.
Quick conversion answers
| Conversion | Result |
|---|---|
| 3 dB | 1.995 |
| 6 dB | 3.981 |
| 10 dB | 10 |
| 20 dB | 100 |
Where this conversion is used
Engineers turn a gain or loss in dB into a plain multiplier.
Students practise log and power relations.
Common mistakes to avoid
- Using 10 for voltage. Voltage and pressure use 20.
- Using 20 for power. Power uses 10.
- Treating 3 dB as exactly 2. It is 1.995.
- Ignoring the sign. A negative dB is a ratio below 1.
Related converters
More level changes
2 dB is 1.585. 4 dB is 2.512. 5 dB is 3.162.
9 dB is 7.943. 12 dB is 15.85. 15 dB is 31.62.
30 dB is 1,000. 50 dB is 100,000. 60 dB is 1,000,000.
Doubling the first number
4 dB is 2.512. 8 dB is 6.31. 10 dB is 10.
18 dB is 63.1. 24 dB is 251.2. 30 dB is 1,000.
60 dB is 1,000,000. 100 dB is 10,000,000,000. 120 dB is 1,000,000,000,000.
The 3, 6, 10 and 20 dB steps
3 dB is 1.995. 6 dB is 3.981. 10 dB is 10.
20 dB is 100.
More worked examples
1 dB is a power ratio of 1.259 and an amplitude ratio of 1.122. 2 dB is 1.585 in power and 1.259 in amplitude.
9 dB is 7.943 in power and 2.818 in amplitude. 12 dB is 15.85 in power and 3.981 in amplitude.
15 dB is 31.62 in power and 5.623 in amplitude.
Going from a ratio to dB
To go back, take the log of the ratio and multiply by 10 for power or 20 for amplitude. A power ratio of 4 is 6.02 dB, and an amplitude ratio of 4 is 12.04 dB.
A power ratio of 0.5 is minus 3.01 dB, and a power ratio of 100 is 20 dB.
A quick check
Square the amplitude ratio and you should get the power ratio. For 6 dB, 1.995 squared is about 3.98, which matches the power column.
If the two columns do not fit that rule, one of them was read from the wrong row.
Reading the table
Rows above 1 are gains and rows below 1 are losses. At 0 dB both ratios are exactly 1, which means no change.
At 40 dB the power ratio is 10,000 and the amplitude ratio is 100.
Which column to use
Use the power column for watts and other power quantities. Use the amplitude column for volts, amps and sound pressure.
If you are unsure, ask whether the quantity would be squared to get a power.
Frequently asked questions
How do I convert dB to a ratio?
Divide by 10 for power or 20 for voltage, then raise 10 to that power.
What is 3 dB as a ratio?
About 1.995 for power and 1.413 for voltage.
What is 10 dB as a ratio?
10 for power and 3.162 for voltage.
What is minus 3 dB?
A power ratio of 0.501.
Why are there two ratios?
Power goes with the square of voltage.
Can the ratio be negative?
No. Only the dB value can be negative.
Sources
- Engineering ToolBox: Decibel (engineeringtoolbox.com)
- Wikipedia: Decibel (en.wikipedia.org)
