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Convert decibels to power ratios, voltage ratios, and signal gain/loss. Calculate amplifier gain in dB, speaker sound pressure levels, RF signal attenuation, and audio signal chain analysis.
The decibel is an indispensable tool in electronics, acoustics, and telecommunications because human perception — of sound, light, and radio signal strength — is inherently logarithmic, not linear. Our brains perceive a tenfold increase in sound power as roughly doubling in loudness. The decibel scale naturally matches this human perceptual reality.
The decibel (dB) is a logarithmic unit expressing the ratio between two quantities — typically power or amplitude. Because human perception of sound and signal strength is logarithmic rather than linear, decibels are the natural unit for audio, RF, and telecommunications engineering. A 10 dB increase represents a 10× power increase but only sounds twice as loud to humans.
For power: dB = 10 × log₁₀(P2/P1). For voltage (or pressure): dB = 20 × log₁₀(V2/V1). The factor of 20 for voltage (vs 10 for power) comes from the relationship P = V²/R — doubling voltage quadruples power, which is 6 dB in voltage terms but also 6 dB in power terms (consistent).
| dB Level | Power Ratio | Notes |
|---|---|---|
| 0 dB | No change | 1:1 ratio |
| 3 dB | Power doubled | 1.414:1 voltage |
| 6 dB | Voltage doubled | 4:1 power |
| 10 dB | 10× power | Sounds twice as loud |
| 20 dB | 100× power | 10× voltage |
| 40 dB | 10,000× power | 100× voltage |
| 60 dB | 1,000,000× power | Loud conversation level |
| 120 dB | 1,000,000,000,000× | Threshold of pain |
The decibel scale appears across all branches of electronics and physics. Audio engineers use dB to describe signal levels and dynamic range. RF engineers use dBm and dBi for power levels and antenna gain. Telecommunications uses dB to specify cable losses and amplifier gains. Understanding dB allows rapid mental arithmetic across many orders of magnitude.
The standard reference level in professional audio is 0 dBu = 0.775V RMS. Consumer audio uses 0 dBV = 1V RMS. A mixing console shows levels in dBFS (full scale) for digital: 0 dBFS is maximum, and levels are always negative (e.g., -18 dBFS for nominal level). Dynamic range of 16-bit CD audio = 20 × log10(2^16) = 96 dB. Dynamic range of 24-bit = 144 dB.
dBm = 10 × log10(P/1mW). Common reference points: smartphone transmit power 23 dBm (200mW), WiFi router 20 dBm (100mW), strong received WiFi signal -60 dBm (1nW), minimum usable WiFi -95 dBm. Link budget calculation: TX power (dBm) + TX antenna gain (dBi) - cable loss (dB) - path loss (dB) + RX antenna gain (dBi) = received signal (dBm).
Thermal noise power at room temperature (Johnson-Nyquist noise): kTB where k = Boltzmann constant, T = temperature (K), B = bandwidth (Hz). At 25°C in 1 MHz bandwidth: N = -114 dBm. This sets the fundamental limit on receiver sensitivity. A receiver with 10 dB noise figure operating in 10 MHz bandwidth has noise floor = -114 + 10 + 10 = -94 dBm.