Decibel (dB) Calculator

Convert between decibels and linear ratios.

Calculate

Formula

Enter next fieldEsc clear

Formulas

dB = 10 × log10(P1/P2)

For voltage: dB = 20 × log10(V1/V2). 3dB = double power. 6dB = double voltage.

Decibel Scale

0 dB: reference level. 3 dB: 2x power. 10 dB: 10x power. 20 dB: 100x power. Sound: 0 dB threshold, 60 dB conversation, 85 dB harmful, 120 dB pain, 140 dB jet engine.

Understanding Decibels

The decibel is a logarithmic ratio used to express how much larger or smaller one power or signal level is than another. Because human perception of sound and many engineering quantities are logarithmic, decibels compress huge ranges into manageable numbers:

dB = 10 × log10(P1/P2)

For power ratios. For voltage or amplitude ratios, the multiplier is 20 instead of 10: dB = 20 × log10(V1/V2).

A positive dB value means a gain, a negative value means a loss, and 0 dB means the two levels are equal.

Worked Examples

Example 1 — Power gain

An amplifier raises 1 W to 100 W:

dB = 10 × log10(100/1) = 20 dB

Example 2 — Voltage ratio

A signal doubles in voltage:

dB = 20 × log10(2) = 6 dB

Decibel Reference Points

Change	Power ratio	Voltage ratio
3 dB	2×	1.41×
6 dB	4×	2×
10 dB	10×	3.16×
20 dB	100×	10×

Frequently Asked Questions

Why 10 for power but 20 for voltage?

Power is proportional to voltage squared. Taking the log brings the exponent down as a factor of 2, turning 10 into 20 for voltage/amplitude ratios.

What does 3 dB mean?

Roughly a doubling (or halving) of power. The −3 dB point is the standard definition of a filter's cutoff frequency.

What are dBm and dBW?

Absolute decibel scales referenced to 1 mW and 1 W respectively, used to express actual power levels rather than ratios.