The decibel (dB) is a logarithmic unit that expresses the ratio between two physical quantities — most commonly power, voltage, current, or sound pressure. Named after Alexander Graham Bell, this unit was originally developed to measure signal attenuation across telegraph lines. Because the human auditory system perceives loudness on a logarithmic scale, the decibel became the universal standard for acoustic measurements as well.

Decibel Formulas

For power ratios, the formula is: dB = 10 × log₁₀(P₂ / P₁). A +3 dB gain represents approximately doubled power; +10 dB means 10× the power. For voltage or current ratios: dB = 20 × log₁₀(V₂ / V₁). Here +6 dB doubles the voltage, and +20 dB means a 10× voltage increase. The factor of 20 (vs 10) arises because power is proportional to the square of voltage (P = V²/R).

Practical Examples

  • Power amplifier gain: An amplifier delivering 100 W from a 10 W input has a gain of 10 dB.
  • Voltage attenuator: A signal reduced from 1 V to 0.1 V has been attenuated by −20 dB.
  • RF signal level: A WiFi router transmitting at 20 dBm outputs exactly 100 mW.
  • Sound level: Normal conversation at 1 m is approximately 60 dBSPL; a pneumatic drill at 1 m is about 100 dBSPL.

dBm, dBu, and dBV Reference Levels

dBm references power to 1 mW: dBm = 10 × log₁₀(P_mW). It is the standard unit in RF engineering, WiFi, and cellular networks. dBu references voltage to 0.7746 V (the voltage that delivers 1 mW into 600 Ω) and is widely used in professional audio. dBV references voltage to 1 V and is common in consumer electronics. Understanding the difference between these referenced units prevents costly measurement errors when interconnecting equipment.

Sound Pressure Level (dBSPL)

dBSPL measures acoustic sound pressure relative to the threshold of human hearing (20 µPa): dBSPL = 20 × log₁₀(P / 20µPa). Typical reference points include: 0 dBSPL (threshold of hearing), 30 dBSPL (quiet library), 60 dBSPL (normal conversation), 90 dBSPL (lawnmower), and 120 dBSPL (threshold of pain). Extended exposure above 85 dBSPL can cause permanent hearing damage.

Adding and Subtracting dB Values

Because dB is logarithmic, gains and losses in a signal chain simply add or subtract: a pre-amplifier with +20 dB gain followed by a 3 dB attenuator and an amplifier with +10 dB gain produces a net gain of +27 dB. This additive property is one of the main reasons engineers prefer the dB scale for system-level design work.