Decibel Calculator
Compute decibel ratio: 20·log10(P/Pref) for power or 10·log10(I/Iref) for intensity.
dB = —
Decibel: a logarithmic ratio scale
A decibel (dB) measures the ratio between two quantities on a logarithmic scale. When you're dealing with power, the formula is dB = 10·log10(P/P_ref). For amplitude values like voltage or sound pressure, you use dB = 20·log10(A/A_ref) instead. Sound pressure level (SPL) takes p_ref = 20 µPa as its reference, which is roughly the quietest sound a person can hear. Worth memorizing: +10 dB is 10× the power, yet your ear only registers it as about twice as loud, and +3 dB ≈ 2× the power. For a sense of scale, a library sits around 30 dB, conversation 60, traffic 80, a rock concert 110, and a jet on takeoff 140. Anything above 120 dB risks permanent hearing loss. The Brazilian NR-15 occupational limits allow 85 dB for 8 h and 88 dB for 4 h, with the permitted dose cut in half for every extra 3 dB.
Applications
You'll find decibels in audio engineering (mixing and gain staging), acoustic engineering, and occupational health, where NR-15 makes hearing protection mandatory at 85 dB or above. Telecom uses dB to work out link budgets, antenna gain shows up as dBi or dBd, and imaging reports signal-to-noise ratio in dB as well.
FAQ
Why use 10·log for power and 20·log for amplitude? Power scales with the square of amplitude (P ∝ A²). Take the log of a squared term and the exponent comes down as a factor of 2, so the amplitude form lands on the exact same dB value.
Is 0 dB silence? Not at all. 0 dB SPL is the reference threshold of hearing, not the absence of sound. A negative dB value just means the level falls below that reference.
What's dBA? A-weighted decibels run the signal through a filter that mimics how loud each frequency actually sounds to us. That weighting is what environmental and occupational noise measurements rely on.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.