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Decibel Gain from Power or Voltage Ratios

Convert positive power ratios and positive voltage-magnitude ratios to independent decibel gains.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Increasing power from 2 W to 20 W is a 10 dB gain. Increasing voltage magnitude from 2 V to 20 V is a 20 dB amplitude gain.

Power gain = 10 log₁₀(P₂/P₁); voltage gain = 20 log₁₀(V₂/V₁)

Worked example

Enter these known values and leave the other values blank.

Initial power
2 W
Final power
20 W
Initial voltage magnitude
2 V
Final voltage magnitude
20 V
Power-ratio gain in dB
10 dB
Voltage-ratio gain in dB
20 dB

Assumptions and limitations

  • The power and voltage groups are independent. Every power and voltage magnitude must be strictly positive; a zero endpoint would require an unbounded logarithm.
  • Voltage gain uses a factor of 20. Equating it to power gain requires matching resistive impedances or another justified square-law relationship.
  • Gains can be negative, zero or positive. These are ratios, not absolute dBm or dBV levels, and no phase is calculated.

Common questions

Why do the formulas use different multipliers?

Power ratios use 10 log₁₀. An amplitude ratio uses 20 log₁₀ because power is proportional to amplitude squared under the relevant fixed-impedance conditions.

What is a negative gain?

It means the final magnitude is lower than the initial magnitude. For example, one tenth the initial power is −10 dB.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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