Decibel to Ratio Converter: Sound and Signal Levels

The decibel (dB) is a logarithmic unit expressing the ratio of one value to a reference. Decibels compress extremely large ranges (sound can span 13 orders of magnitude) into manageable numbers. A 20 dB increase in sound doesn't mean twice as loud — it means 10 times the pressure ratio. Understanding the conversion between decibels and linear ratios is essential in acoustics, electronics, and communications.

The Formula

For pressure or amplitude ratios:

Decibels = 20 × log₁₀(Ratio)
Ratio = 10^(Decibels / 20)

For power or intensity ratios:

Decibels = 10 × log₁₀(Ratio)
Ratio = 10^(Decibels / 10)

The difference is because power is proportional to amplitude squared, so the factor changes from 20 to 10.

Worked Example: Sound Pressure

A sound is measured at 94 dB (a motorcycle). What is the pressure ratio relative to the reference (20 micropascals, threshold of human hearing)?

Ratio = 10^(94 / 20) = 10^4.7 = 50,118

The sound pressure is about 50,000 times higher than the reference level.

Common Decibel Values

Every 6 dB increase roughly doubles amplitude; every 10 dB roughly doubles power.

Sound Level Examples

The scale is logarithmic, so each step up represents exponential increases in actual sound energy.

Attenuation and Gain

In electronics, positive dB indicates amplification (gain), negative dB indicates reduction (attenuation):

• +20 dB gain: Signal 10× larger
• -20 dB attenuation: Signal 1/10 the original
• -3 dB: Signal reduced to about 70% (half the power)

Tips

Remember the 3-6-10 rule: 3 dB ≈ √2 (1.4×), 6 dB ≈ 2×, 10 dB = 10×. For sound, account for the fact that subjective loudness doesn't match the decibel scale — 10 dB louder than a whisper doesn't make a motorcycle 10× "louder" perceptually; it's much more dramatic.

Use our Decibel to Ratio Converter to convert between decibels and linear ratios instantly.