Decibel Calculator

A Logarithmic Scale for a Huge Range of Sound

The decibel exists because raw sound power spans an enormous range — the loudest tolerable sound is roughly a trillion times more powerful than the quietest audible one. Expressing that range in a linear unit would be unwieldy, so audio engineering compresses it logarithmically. This calculator converts between raw power or voltage ratios and their decibel equivalents in both directions.

The Formulas

Power Ratio: dB = 10 × log10(P2 / P1)
Voltage/Amplitude Ratio: dB = 20 × log10(V2 / V1)
dB to Power Ratio: P2 / P1 = 10^(dB / 10)
dB to Voltage Ratio: V2 / V1 = 10^(dB / 20)

The factor differs between power (10×) and voltage (20×) because power is proportional to the square of voltage or amplitude — squaring a ratio doubles its logarithm, which is why the voltage formula carries twice the multiplier.

Reference Points Worth Memorizing

Common ratios and their decibel values (computed from the formulas above)
Ratio	Power change	Voltage/amplitude change
2x	+3.01 dB	+6.02 dB
10x	+10.00 dB	+20.00 dB
0.5x (half)	−3.01 dB	−6.02 dB

These are the two figures every audio engineer ends up memorizing: doubling power is +3 dB, doubling voltage or amplitude is +6 dB.

Where This Gets Used

Amplifier and speaker specs — comparing rated power output between two amplifiers in dB terms rather than raw watts.
Gain staging — mixing engineers reason in dB when setting input trim, faders, and compressor thresholds because ear-perceived loudness tracks the log scale more closely than raw amplitude.
Signal-to-noise ratio — SNR is expressed in dB, calculated as a voltage or power ratio between signal and noise floor.
Attenuator and pad design — converting a target dB reduction back into the actual voltage or power ratio a circuit needs to deliver.

How to Use This Calculator

Choose a calculation type: Power Ratio to dB, Voltage/Amplitude Ratio to dB, dB to Power Ratio, or dB to Voltage/Amplitude Ratio.
For a ratio-to-dB conversion, enter the reference value (P1 or V1) and the measured value (P2 or V2).
For a dB-to-ratio conversion, enter the dB value and, optionally, a reference value (defaults to 1 if left blank).
Select Calculate to see the result and the full formula substitution.

Related Calculations

Once you have an output level in dB, size a speaker cable run with the Speaker Wire Gauge Calculator, or check total impedance with the Speaker Impedance Calculator.