Decibel Calculator

What is a Decibel?

The decibel (dB) is a logarithmic ratio unit used to compare power, voltage, or intensity levels. Because human hearing spans an enormous range (from a whisper to a jet engine — a 10 trillion-fold difference in power), the logarithmic dB scale compresses this to a manageable 0–140 dB range.

The Formulas

Power ratio: dB = 10 × log₁₀(P₂/P₁) Voltage/SPL ratio: dB = 20 × log₁₀(V₂/V₁)

Note: factor 10 for power (intensity), factor 20 for amplitude (voltage, sound pressure). A 3dB power change doubles or halves power. A 6dB voltage change doubles or halves voltage.

Sound Pressure Level References

| Sound | dB SPL | |-------|--------| | Threshold of hearing | 0 dB | | Whisper | 30 dB | | Normal conversation | 60 dB | | Traffic | 80 dB | | Concert | 110 dB | | Jet engine | 140 dB |

How to Use This Calculator

Enter two power or voltage values to compute the dB ratio, or enter a dB value to find the ratio. Also calculates audio SPL (dBSPL) from reference pressure.

Practical Examples

Example 1: Amplifier with 100W output vs 50W output. dB = 10 × log₁₀(100/50) = 10 × 0.301 = +3.01 dB (perceived as barely louder).

Example 2: Doubling voltage: dB = 20 × log₁₀(2) = +6.02 dB.

Example 3: Reducing power to 1/4: dB = 10 × log₁₀(0.25) = −6.02 dB.