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Decibel (dB) Converter

Convert between a power or voltage/amplitude ratio and decibels in either direction, and see the equivalent power and voltage ratios side by side for the same dB value.

Decibels (dB)
3.0103
Ratio
2
Equivalent power ratio
2×
Equivalent voltage/amplitude ratio
1.4142×

How it works

The decibel expresses a ratio on a logarithmic scale. For a power-like quantity (power, energy, intensity) the definition is dB = 10·log₁₀(P₂/P₁); for an amplitude-like quantity (voltage, current, sound pressure) it's dB = 20·log₁₀(V₂/V₁). The factor of 20 rather than 10 falls out because power is proportional to amplitude squared, and squaring a ratio doubles its logarithm. This calculator solves that identity in either direction: given a ratio, dB = k·log₁₀(ratio); given a dB value, ratio = 10^(dB/k), using k = 10 for power or k = 20 for voltage/amplitude.

Because those two conventions are tied together by that same squared relationship, every result also reports the equivalent power ratio (10^(dB/10)) and equivalent voltage ratio (10^(dB/20)) for the same dB figure — a single dB number implies both a power change and a voltage change at once (for example, 6.02 dB means power quadruples while voltage only doubles), which is a common point of confusion this makes explicit rather than requiring a second calculation.

FAQ

Why do engineers use decibels instead of plain ratios?

Signal levels in audio, RF, and optics often span many orders of magnitude — a ratio of a million to one is common. Decibels compress that huge range into small, easy-to-add numbers (doubling a ratio always adds the same fixed number of dB, regardless of the starting value), and because dB is logarithmic, cascading gains and losses through a signal chain becomes simple addition and subtraction instead of multiplication.

What do the classic '3 dB' and '6 dB' figures mean?

3 dB (more precisely 10·log₁₀(2) ≈ 3.01 dB) is the change in decibels for exactly doubling power — it's why halving a speaker's power output is often described as 'losing 3 dB.' 6 dB (20·log₁₀(2) ≈ 6.02 dB) is the change for doubling voltage or amplitude, which is also the change in decibels for quadrupling power, since power scales with amplitude squared.

Can a ratio be converted to decibels if it's negative or zero?

No — a logarithm is undefined for zero or negative numbers, and a power or voltage ratio of zero or less isn't physically meaningful as a straightforward before/after comparison, so this calculator requires a strictly positive ratio when solving for decibels. Decibel values themselves, however, can be negative (representing attenuation, a ratio less than 1) without any restriction.

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