Decibel (dB) Converter

Decibel (dB) Converter

Sound Level Reference Table

dB LevelExamplePerceived Loudness
0 dBThreshold of hearingBarely audible
20 dBRustling leavesVery quiet
40 dBLibrary, quiet roomQuiet
60 dBNormal conversationModerate
80 dBCity trafficLoud
100 dBJackhammer (nearby)Very loud
120 dBThreshold of painPainful
140 dBJet engine (close)Dangerous

Decibel (dB) Converter — Power, Voltage, and Sound

The decibel (dB) is a logarithmic unit used to express ratios of power, voltage, amplitude, or intensity. It is used across audio engineering, telecommunications, acoustics, electronics, and signal processing. This converter lets you convert any power or voltage ratio to decibels and back, with a reference table of common sound pressure levels.

What Is a Decibel?

The decibel is one tenth of a Bel (named after Alexander Graham Bell). Because the human ear perceives loudness on a logarithmic scale — a sound ten times more intense sounds roughly twice as loud — the logarithmic decibel scale naturally matches human perception. A 10 dB increase represents a 10× power increase, while a 20 dB increase represents a 100× power increase.

Power vs. Voltage Decibels

There are two standard decibel formulas. For power ratios: dB = 10 × log₁₀(P2/P1). For voltage or amplitude ratios: dB = 20 × log₁₀(V2/V1). The factor of 20 in the voltage formula arises because power is proportional to voltage squared (P = V²/R), so a 2× voltage ratio corresponds to a 4× power ratio, or 6 dB in both cases.

Key Reference Points

  • +3 dB — approximately double the power (+6 dB doubles the voltage)
  • +6 dB — approximately double the amplitude/voltage
  • +10 dB — exactly 10× the power; perceived as roughly twice as loud
  • 0 dB — unity gain (output equals input)
  • −3 dB — the standard filter cutoff frequency (half power point)

Applications in Engineering

In audio engineering, amplifier gain and speaker sensitivity are specified in dB. In telecommunications, signal attenuation along cables is measured in dB/km. In RF engineering, antenna gain is expressed in dBi (dB relative to an isotropic antenna). Signal-to-noise ratios (SNR) in audio equipment and communications systems are given in dB.

Frequently Asked Questions

Why do we use logarithmic (dB) scale instead of linear?
Human perception of loudness, brightness, and other sensory inputs follows a logarithmic law (the Weber-Fechner law). The logarithmic dB scale also compresses enormous ranges — from the faintest audible sound to jet engine noise — into a manageable 0–140 dB range instead of a 10-trillion-to-1 linear range.
What is 0 dB SPL?
0 dB SPL (Sound Pressure Level) is the threshold of human hearing — the quietest sound a healthy young person can detect, defined as 20 micropascals (20 μPa) of sound pressure. All other sound levels are measured relative to this reference.
Can decibels be negative?
Yes. Negative dB values simply mean the output is less than the reference. For example, −20 dB means the signal is 1/10 the reference voltage or 1/100 the reference power. A −3 dB filter passes half the power at the cutoff frequency.
What is the difference between dB, dBm, and dBu?
dB is a relative ratio. dBm is power relative to 1 milliwatt. dBu is voltage relative to 0.775 V (the voltage across 600 Ω dissipating 1 mW). dBV is voltage relative to 1 V. These absolute references make measurements independent of the source and load impedances.
How loud is too loud for hearing damage?
Sustained exposure above 85 dB can cause hearing damage over time. Sounds above 120 dB can cause immediate pain and damage. The safe exposure time decreases rapidly with level: roughly 2 hours at 91 dB, 30 minutes at 97 dB, and only a few minutes at 103 dB.