Decibel Calculator
dB
10
How it works
The decibel (dB) is a logarithmic unit expressing ratios. For power ratios: dB = 10 × log₁₀(P₂/P₁). For amplitude ratios (voltage, pressure, current): dB = 20 × log₁₀(A₂/A₁). The factor of 20 (vs. 10) arises because power ∝ amplitude².
**Common decibel values** +3 dB: double power (+6 dB for double amplitude). -3 dB: half power (−3 dB point defines filter cutoff frequencies). +10 dB: 10× power. +20 dB: 100× power (10× amplitude). -60 dB: one part in 10⁶. +120 dB: 10¹² power ratio.
**Absolute reference levels** dBm: power relative to 1 milliwatt (P_ref = 1 mW). Used in RF and fiber optics. dBW: relative to 1 watt. dBu (audio): voltage relative to 0.775V (the voltage that produces 1 mW in a 600Ω load). dBFS: decibels relative to full scale in digital audio — 0 dBFS is the maximum digital level. dBA: A-weighted sound pressure level for human hearing sensitivity.
**Adding signals in dB** Two equal-power uncorrelated signals sum to +3 dB total. Two equal-power coherent (same phase) signals sum to +6 dB. General case: convert to linear, add, convert back to dB. You cannot directly add dB values representing different signals — only ratios in the same dB chain can be added/subtracted (gain stages in series: total gain = sum of individual gains in dB).
**Human hearing and dB SPL** 0 dB SPL: threshold of hearing (20 μPa reference). 60 dB: normal conversation. 85 dB: OSHA 8-hour exposure limit. 120 dB: pain threshold. 140 dB: permanent hearing damage. Each 10 dB increase is perceived roughly as doubling of loudness (Weber-Fechner law).
Frequently Asked Questions
- P (dBm) = 10 × log₁₀(P_watts / 0.001) = 10 × log₁₀(P_milliwatts). To convert back: P_watts = 0.001 × 10^(dBm/10). Common values: 0 dBm = 1 mW, 10 dBm = 10 mW, 20 dBm = 100 mW, 30 dBm = 1 W, 40 dBm = 10 W. Wi-Fi transmit power: typically 20 dBm = 100 mW. Smartphone cellular: up to 33 dBm = 2 W. Phone at ear: 0–10 dBm. The dBm scale compresses the enormous power range in communications — from -120 dBm (femtowatts at a radio receiver) to +60 dBm (1 MW transmitter) into a manageable 180 dB range.
- In a cascaded signal chain, dB values add algebraically: total gain = G1 (dB) + G2 (dB) + G3 (dB) - L1 (dB) - L2 (dB)... Example: antenna 3 dBi gain → coaxial cable -2 dB loss → LNA amplifier +15 dB gain → filter -3 dB loss → receiver. Total = 3 - 2 + 15 - 3 = 13 dB net gain. If signal enters at -100 dBm, it exits at -100 + 13 = -87 dBm. This additive property is why dB is used in RF engineering — avoiding multiplications of very large and small numbers.
- The -3 dB point (also called the half-power point or corner frequency) is where power response drops to half: 10log(0.5) = -3.01 dB. For filters: the -3 dB frequency defines the boundary between the passband (signals pass with minimal loss) and the stopband (signals are attenuated). A low-pass filter with -3 dB at 1 kHz: signals below 1 kHz pass, signals above 1 kHz are attenuated. Amplitude response at -3 dB point is 1/√2 = 0.707 of the passband level — this corresponds to a 45° phase shift in a first-order filter.
- Decibels are defined as a power ratio: dB = 10log(P2/P1). Power ∝ V² (for constant impedance): P = V²/R. Therefore: dB = 10log(V2²/V1²) = 10 × 2 × log(V2/V1) = 20log(V2/V1). The factor of 20 appears only for amplitude quantities (voltage, current, pressure) when expressing power ratios. Misusing 10log for voltage gives wrong answers — doubling voltage is +6 dB (power quadruples = +6 dB), not +3 dB. Always check: is the quantity a power/intensity, or an amplitude/field quantity? Same for acoustic pressure: sound pressure level = 20log(P/P_ref), not 10log.