Decibel Calculator

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.