dB (Power)

dB = 10 × log₁₀(P2/P1)

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Result
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Formula

dB = 10 × log₁₀(P2 / P1)

Description

The decibel is a logarithmic unit for expressing the ratio between two power levels. It was originally developed by Bell Telephone Laboratories to quantify signal loss in telephone cables. The logarithmic scale is used because human perception of loudness and signal strength is approximately logarithmic, and because it converts multiplication and division of gains into simple addition and subtraction. A gain of +3dB means the power has doubled, +10dB means a tenfold increase, and -3dB means the power has halved. Cascaded amplifier stages can be analyzed by simply adding their individual dB gains.

Variables

  • dB — Power ratio in decibels
  • P1 — Reference power in watts (W)
  • P2 — Measured power in watts (W)

Practical Notes

Key landmarks: 0dB = no change, +3dB = 2x power, +10dB = 10x power, +20dB = 100x power, +30dB = 1000x power. Negative values indicate attenuation. Both P1 and P2 must be positive for the logarithm to be defined.

Related Formulas

dB (Voltage) dBm to Watts dBV (Voltage Level) dBu (Voltage Level) dBm to dBW Conversion Receiver Noise Floor

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