20 Db to Gain – Full Calculation Guide

The gain corresponding to 20 dB is 100. This means a signal amplified by 20 decibels results in a gain factor of 100 times the original amplitude.

The conversion from decibels (dB) to gain involves using the formula gain = 10^(dB/20). Decibels express ratios on a logarithmic scale, so converting back to linear gain requires exponentiation. For 20 dB, raising 10 to the power of (20 divided by 20) gives 10¹, which equals 100.

Conversion Tool

Conversion Formula

The formula to convert decibels (dB) to gain is:

gain = 10^(dB / 20)

This works because decibels represent a logarithmic measure of power or amplitude ratios. When measuring voltage or amplitude, the factor is 20 instead of 10 in the denominator, reflecting the squared relationship between power and voltage.

For example, converting 20 dB:

• Divide 20 by 20: 20 / 20 = 1
• Calculate 10^1 = 10
• Therefore, gain = 10

Note: The example above is for voltage gain, which uses 20 in the denominator. If referencing power gain, the denominator would be 10.

Conversion Example

• 15 dB to gain:
  • Divide 15 by 20: 15 / 20 = 0.75
  • Calculate 10^0.75 ≈ 5.623
  • Gain is approximately 5.623 times
• 0 dB to gain:
  • Divide 0 by 20: 0 / 20 = 0
  • Calculate 10^0 = 1
  • Gain equals 1, meaning no amplification
• -10 dB to gain:
  • Divide -10 by 20: -10 / 20 = -0.5
  • Calculate 10^-0.5 ≈ 0.316
  • Gain is roughly 0.316, indicating attenuation
• 30 dB to gain:
  • Divide 30 by 20: 30 / 20 = 1.5
  • Calculate 10^1.5 ≈ 31.622
  • Gain equals about 31.622 times

Conversion Chart

The chart lists decibel values in the first, third, and fifth columns with corresponding gain values beside them. You can use it to quickly find gain factors for common dB levels without calculation.

Related Conversion Questions

• How much gain does 20 dB represent in linear scale?
• What is the formula to convert 20 dB to gain?
• Is gain of 20 dB equal to 100 or 10?
• How to calculate gain from 20 dB in audio systems?
• What does 20 dB gain mean for amplifier output?
• Can you convert 20 dB to voltage gain easily?
• How does 20 dB translate into numeric gain value?

Conversion Definitions

db: Decibel (dB) is a logarithmic unit used to express ratios between two values, commonly power or intensity levels. It compresses large ranges of values into manageable scales, which helps in measuring signals, sound, and electronic gains with more convenience.

gain: Gain is the factor by which a signal is amplified or attenuated, expressed as a ratio of output to input. It can be linear or logarithmic, and in electronics, gain shows how much a device boosts signal strength or amplitude relative to its original level.

Conversion FAQs

Why do we divide dB by 20 when converting to gain?

The division by 20 arises because decibels measure amplitude ratios on a logarithmic scale, and power is proportional to the square of amplitude. Since power calculations use 10 in the denominator, amplitude (or voltage gain) requires doubling that to 20. This ensures correct scaling between logarithmic and linear domains.

Can gain values be less than 1 after converting from dB?

Yes, when the dB value is negative, it means the signal is attenuated, producing a gain less than 1. For example, -6 dB corresponds to a gain of approximately 0.5, which halves the amplitude of the input signal.

Is the gain from dB conversion always a positive number?

Gain itself is a ratio and always positive, but the dB value might be negative to indicate attenuation. When converting, the result is positive but less than 1 for negative dB values, reflecting a decrease in signal amplitude.

Why does the formula use 10 raised to the power of (dB/20)?

Because dB scales are logarithmic, converting back requires exponentiation. The base 10 is used since decibels are defined as 10 times the logarithm base 10 of the power ratio. For amplitude or voltage, the exponent divides dB by 20 to accommodate the squared relationship between power and amplitude.

Does the gain conversion apply the same way for power and voltage?

No, for power ratios, the formula uses gain = 10^(dB/10), while for voltage or amplitude, it uses gain = 10^(dB/20). The difference is due to power being proportional to the square of voltage, so voltage gain requires the factor 20 in denominator.