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Voltage Magnitude Ratio & Decibel Transfer

Express a nonzero output-to-input voltage magnitude ratio as a linear ratio or logarithmic level.

Formula & worked example
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How to use this calculator

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

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Formula and method

Changing from 10 V input to 1 V output gives a magnitude ratio of 0.1 and a 20-log voltage gain of −20 dB. Equal voltage magnitudes give 0 dB.

Voltage gain in dB = 20 log₁₀(|output voltage / input voltage|)

Worked example

Enter these known values and leave the other values blank.

Input voltage: 10 V
Output voltage: 1 V

Output/input voltage magnitude transfer: -20 dB (20 log₁₀)

Assumptions and limitations

Input and output voltages must be nonzero. The forward result depends on their magnitudes; opposite signs do not change it. Phase and polarity are not determined by the ratio magnitude.
The default 20-log gain is negative for attenuation. Positive insertion loss uses the opposite sign. The optional 10-log display applies ten times the logarithm to the same amplitude ratio; it is not automatically a power gain.
When solving a missing voltage, the retained inverse chooses the same sign as the supplied voltage. An opposite-sign voltage has the same magnitude ratio. Relating voltage gain to power gain requires matching impedances or another justified square-law relationship.

Common questions

Is −20 dB a tenfold or hundredfold voltage decrease?

It is a tenfold decrease in voltage magnitude. Under matching resistive impedances, the corresponding power is one hundredth.

Why is attenuation shown as a negative number?

This field reports output-over-input gain. A smaller output gives negative gain; a positive attenuation-loss convention reverses that sign.

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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