The gain corresponding to 20 dB is 100. This means that a 20 dB increase represents a hundredfold increase in power ratio.
Decibels (dB) measure ratios in logarithmic scale, so converting dB to gain involves reversing that logarithmic relationship. Gain here means the linear multiplier of power or amplitude.
Conversion Tool
Result in gain:
Conversion Formula
The formula to convert decibels (dB) to gain is:
Gain = 10^(dB / 10).
This formula works because decibels express ratios logarithmically, so to get the actual linear gain value, you must raise 10 to the power of the dB value divided by 10.
Example with 20 dB:
- Divide 20 by 10: 20 ÷ 10 = 2
- Raise 10 to the power of 2: 10² = 100
- Gain equals 100, meaning the linear gain is hundred times the original power.
Conversion Example
- 10 dB to gain:
- Divide 10 by 10 = 1
- 10¹ = 10
- Gain = 10
- 3 dB to gain:
- 3 ÷ 10 = 0.3
- 10^0.3 ≈ 1.995
- Gain ≈ 1.995
- 0 dB to gain:
- 0 ÷ 10 = 0
- 10^0 = 1
- Gain = 1 (no change)
- -3 dB to gain:
- -3 ÷ 10 = -0.3
- 10^-0.3 ≈ 0.501
- Gain ≈ 0.501 (power is halved approximately)
Conversion Chart
| dB | Gain |
|---|---|
| -5.0 | 0.3162 |
| 0.0 | 1.0000 |
| 5.0 | 3.1623 |
| 10.0 | 10.0000 |
| 15.0 | 31.6228 |
| 20.0 | 100.0000 |
| 25.0 | 316.2278 |
| 30.0 | 1000.0000 |
| 35.0 | 3162.2777 |
| 40.0 | 10000.0000 |
| 45.0 | 31622.7766 |
This chart shows the gain values for dB numbers between -5 and 45. To use it, find the dB value in left column, read across to see the corresponding linear gain multiplier in the right. It helps quickly estimate gain without calculator.
Related Conversion Questions
- What gain value does 20 dB represent in linear scale?
- How do I convert 20 dB into a power gain?
- Is 20 dB equivalent to 100 times gain?
- What formula converts 20 decibels to gain?
- How much does a 20 dB increase amplify the signal?
- What’s the linear gain for a 20 dB signal boost?
- Can 20 dB be converted directly to gain without logarithms?
Conversion Definitions
dB: Decibel is a logarithmic unit used to express the ratio between two power quantities, or amplitude levels. It quantifies relative changes in signal strength or intensity on a scale where 10 dB corresponds to tenfold power change.
Gain: Gain is the linear factor that represents amplification of power or amplitude in a system. It shows how much a signal increases compared to its original level, often expressed as a multiplier without logarithmic scaling.
Conversion FAQs
Why is the gain calculated as 10^(dB/10) and not another exponent?
The decibel scale is based on a logarithm of power ratios using base 10, where 10 dB equals a tenfold increase in power. Since the dB value is defined as 10 times the log of gain, reversing that requires raising 10 to the power of dB divided by 10 to get the linear gain.
Can negative dB values convert to gain?
Yes, negative dB values represent a reduction in power. When converted, gain becomes a fraction less than 1, indicating signal attenuation rather than amplification. For example, -3 dB corresponds to about 0.5 gain, which halves the power.
Is this conversion applicable to voltage gain as well?
For voltage gain, the formula differs because voltage relates to power squared. Voltage gain (linear) converts from dB by 10^(dB/20), not 10^(dB/10). The 10^(dB/10) formula applies strictly to power gain calculations.
How accurate is the conversion using this formula?
The formula gives precise theoretical gain from dB values. Real-world measurements might vary due to device imperfections, but mathematically this conversion is exact for ideal power ratios.
Does this gain conversion apply to all types of signals?
This gain conversion applies to power-related signals where dB is used to express ratio. For other quantities like voltage or sound pressure, different conversion or reference levels might be necessary to interpret gain properly.