dB Gain Calculator

What Are Decibels (dB)?

Decibels express a logarithmic ratio between two quantities. In electronics and acoustics, dB gain compares output to input, making large ratios easier to read than raw multiplication factors.

dB Gain Formulas

For voltage (or current) ratios:

$$\text{dB} = 20 \log_{10}\left(\frac{V_\text{out}}{V_\text{in}}\right)$$

For power ratios:

$$\text{dB} = 10 \log_{10}\left(\frac{P_\text{out}}{P_\text{in}}\right)$$

Example: doubling voltage gives $20 \log_{10}(2) \approx 6.02$ dB. Ten times the power gives $10 \log_{10}(10) = 10$ dB.

Real-World Applications

dB gain is used in audio amplifiers, RF transmitters, antenna systems, and signal chains. Engineers stack stage gains in dB because logarithmic values add instead of multiply.

Frequently Asked Questions

Why is voltage gain 20 log and power gain 10 log?

Power is proportional to voltage squared ($P \propto V^2$), so a factor of 2 in voltage is a factor of 4 in power. The 20 and 10 factors keep dB definitions consistent with power.

What does negative dB mean?

Negative dB indicates attenuation (loss). For example, −3 dB means the output is about half the input power.

Can I use this for sound pressure level?

Yes, SPL uses the same logarithmic concept, though reference levels differ. This calculator compares two arbitrary input and output values you provide.

What if Vin or Pin is zero?

Logarithms require positive ratios. Enter values greater than zero for meaningful dB results.

How do I convert dB back to a ratio?

For voltage: ratio = $10^{\text{dB}/20}$. For power: ratio = $10^{\text{dB}/10}$.

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What Are Decibels (dB)?

dB Gain Formulas

Real-World Applications

Frequently Asked Questions

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