Decibel Calculator
Convert a power or voltage ratio into decibels, or a decibel figure back into a ratio, using the correct 10× or 20× multiplier.
How it works
A decibel is a logarithmic ratio, not an absolute quantity. It always compares two values, which is why 'how many dB is this signal' has no answer without saying dB relative to what.
Power uses 10 × log10 of the ratio; voltage and current use 20 × log10. The factor of two is not a convention — it follows from power being proportional to voltage squared, and using the wrong one is the most common decibel mistake there is.
Two figures worth memorising: 3 dB is double the power, and 6 dB is double the voltage. 10 dB is ten times the power, 20 dB is ten times the voltage. Negative values mean attenuation rather than gain.
The formula
Power ratio to dB
dB = 10 × log10(P_out ÷ P_in)
Voltage ratio to dB
dB = 20 × log10(V_out ÷ V_in)
dB back to a power ratio
ratio = 10^(dB ÷ 10)
dB back to a voltage ratio
ratio = 10^(dB ÷ 20)
Worked examples
| Scenario | Working | Result |
|---|---|---|
| Power doubled | 10 × log10(2) | 3.01 dB |
| Voltage doubled | 20 × log10(2) | 6.02 dB |
| A −3 dB filter point | 10^(−3/10) | Half the power, 70.7% of the voltage |
When you'd use it
- Working out an amplifier's gain from input and output levels
- Reading a filter's roll-off from a datasheet
- Adding up gains and losses along a signal chain
- Converting an attenuator's dB rating into an actual ratio
Common questions
Why is it 10× for power but 20× for voltage?
Because power goes as voltage squared. Doubling the voltage into the same load quadruples the power, and log10(V²) is 2 × log10(V) — so the factor of 2 comes straight out of the algebra, not from convention.
Is 3 dB exactly double?
Not exactly. Doubling power is 3.0103 dB. The rounding to 3 dB is close enough for nearly all work, which is why the −3 dB point is the standard definition of a filter's cutoff.
What do dBm, dBu and dBV mean?
They are decibels against a fixed reference, which makes them absolute rather than relative: dBm is against 1 milliwatt, dBu against 0.775 V, dBV against 1 V. This calculator handles plain ratios — pick a reference first and the same maths applies.
Can I just add decibels along a chain?
Yes, and that is the main reason decibels are used. Gains and losses that would multiply as ratios simply add as dB, so a +20 dB amplifier after a −6 dB cable gives +14 dB overall.
Is anything I enter sent to a server?
No. Every calculation runs in your browser, so component values, circuit figures and measurements are never uploaded, logged or stored. There is no account and no record of what you typed.