Decibels to Linear Gain
Convert a decibel gain back to a linear amplitude factor.
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Example
L=6 dB: G = 10^{0.3} ≈ 2×
How it works
Decibels are a logarithmic way to express ratios, so converting back to linear gain means undoing that logarithm with a power of 10. For amplitude quantities such as voltage or sound pressure, the factor is 20 in the denominator because power is proportional to the square of amplitude. This formula tells you the actual multiplicative change in signal size that corresponds to a given dB value.
When to use it
Use this when you have an amplifier gain, filter boost, or attenuation written in decibels and need the actual amplitude multiplier. It is also useful in audio, communications, and instrumentation when converting dB specifications into signal ratios.
Worked example, step by step
Given L = 12 dB Step 1: Substitute into the formula: G = 10^(L/20) Step 2: Compute the exponent: 12/20 = 0.6 Step 3: Evaluate: G = 10^0.6 Step 4: Calculate: G ≈ 3.98 Final answer: the linear gain is about 4×
Common mistakes to avoid
- Using 10^(L/10) for voltage or amplitude gain instead of 10^(L/20)
- Forgetting that negative dB values produce gains less than 1
- Confusing linear gain with dB and reporting the exponent result as the final answer
Did You Know?
Turning a fader up 6 dB doubles the signal amplitude — a handy mental shortcut for mixing.
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