The gain corresponding to 20 dB is 100. This means when a signal is amplified by 20 decibels, its power increases by a factor of 100.
Decibels (dB) measure ratios logarithmically, so converting dB to gain requires exponentiation. The gain is the linear scale equivalent of the logarithmic dB value, showing how much the power has multiplied.
Conversion Tool
Result in gain:
Conversion Formula
The formula to convert decibels (dB) to gain is:
Gain = 10^(dB / 10)
This works because decibels express power ratios on a logarithmic scale, with base 10. When you want to find the linear gain, you raise 10 to the power of the dB divided by 10.
Example: To convert 20 dB to gain, calculate:
- Divide 20 by 10, getting 2.
- Raise 10 to the power of 2: 10² = 100.
- Resulting gain is 100, meaning power is multiplied by 100.
Conversion Example
- 15 dB to gain:
- 15 ÷ 10 = 1.5
- 10^1.5 = 31.6228
- Gain is approximately 31.62 times power increase.
- 0 dB to gain:
- 0 ÷ 10 = 0
- 10^0 = 1
- Gain equals 1, meaning no change in power.
- -3 dB to gain:
- -3 ÷ 10 = -0.3
- 10^-0.3 ≈ 0.5012
- Gain is about 0.5, power is halved approximately.
- 10 dB to gain:
- 10 ÷ 10 = 1
- 10^1 = 10
- Gain equals 10 times the power.
- 5 dB to gain:
- 5 ÷ 10 = 0.5
- 10^0.5 ≈ 3.1623
- Gain is roughly 3.16 times increase.
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 |
To use the chart, find the dB value in the left column, then see the gain value on the right. Gain shows how much the power multiplies from the dB value given.
Related Conversion Questions
- What is the gain value for 20 dB in linear scale?
- How do you convert 20 decibels to gain manually?
- Is a 20 dB gain equal to 100 times the power?
- What does 20 dB mean in terms of signal amplification?
- How to calculate gain from 20 dB for audio signals?
- Can 20 dB be directly converted to voltage gain?
- Why is 20 dB gain equal to 100 in power ratio?
Conversion Definitions
dB (decibel): A logarithmic unit used to express the ratio between two values, commonly power or intensity. It quantifies levels relative to a reference, compressing wide ranges into manageable numbers, based on powers of ten. Decibels are unitless but describe relative differences.
Gain: The factor by which a signal’s power or amplitude is increased. In linear terms, gain shows how much the output is multiplied compared to input. Gain can be expressed in linear scale or logarithmic dB values, relating to signal amplification or attenuation.
Conversion FAQs
Why does converting dB to gain involve exponentiation?
Decibels are logarithmic, meaning they represent powers of ten. To reverse this, converting back to a linear scale, exponentiation with base 10 is needed. This raises 10 to the dB value divided by 10, undoing the logarithmic compression.
Can gain values be less than 1 when converted from dB?
Yes, when dB values are negative, gain becomes less than 1. This means the signal power decreases or attenuates. For example, -3 dB equals about 0.5 gain, halving the power.
Is gain always a power ratio or can it be voltage ratio?
Gain can refer to power, voltage, or current ratios. When expressed in dB, power gain uses 10*log10, but voltage gain uses 20*log10 because power is proportional to voltage squared. The formula here applies to power gain.
How accurate is the gain calculation from dB?
Gain calculated from dB using 10^(dB/10) is exact in mathematical terms. Practical measurements might vary due to device imperfections, but the formula accurately represents theoretical ratios.
What happens if the dB value is zero?
A 0 dB value corresponds to a gain of 1, meaning no change in power. The signal’s strength remains the same, serving as a reference point in conversions.