This decibel calculator converts sound intensity to decibel level, finds the dB difference between two intensities or powers, and adds two sound sources correctly (logarithmically, never by adding dB numbers).

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dB = 10·log₁₀(I/I₀) — a Logarithmic Ruler for a Logarithmic Ear

Hearing spans a trillion-fold intensity range; the decibel compresses it into 0–130. The waves being measured travel per our Wave Speed Calculator. Part of our Physics Calculators collection.

Worked Examples (Verified)

  • I = 10⁻⁶ W/m² (defaults): 10·log₁₀(10⁶) = 60 dB — conversation level; I = 10⁻³ → 90 dB, the motorcycle/lawn-mower band
  • Two 80 dB machines together: 83 dB, not 160 — addition mode’s whole sermon in one example
  • Ratio mode: a 100 W amp vs a 10 W amp is +10 dB electrically but perceived as roughly “twice as loud” (≈ +10 dB perceptual rule of thumb) — physics and psychoacoustics shake hands there
  • Distance rule (inverse square): doubling distance quarters intensity → −6 dB per doubling in free field

Decibel Discipline

  • dB is meaningless without its reference: dB SPL (re 20 µPa), dBm (re 1 mW), dBV, dBFS — same surname, different currencies.
  • A-weighting (dBA) mimics the ear’s frequency sensitivity; occupational limits (85 dBA/8 h) use it.
  • +3 dB = double the power but a just-noticeable step; +10 dB ≈ double the perceived loudness.
  • Never average decibels arithmetically — convert to intensities, average, convert back.

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Frequently Asked Questions

How do you convert intensity to decibels?

dB = 10·log₁₀(I / 10⁻¹² W/m²). I = 10⁻⁶ gives 60 dB (conversation); 10⁻³ gives 90 dB. Each factor of 10 in intensity adds exactly 10 dB — the logarithm’s whole design.

Why do two 80 dB sources make 83 dB, not 160?

Decibels are logarithms; intensities add, labels don’t. Two equal incoherent sources double the intensity: 10·log₁₀(2) ≈ +3 dB. This calculator’s add mode does the conversion honestly for any pair of levels.

When is it 10·log and when 20·log?

10·log for power-like quantities (power, intensity); 20·log for amplitude-like quantities (voltage, sound pressure) because power ∝ amplitude², and log pulls the square out as a 2. Both describe identical decibel differences.

How much louder is +10 dB?

Physically 10× the intensity; perceptually, roughly twice as loud (the sone scale’s rule of thumb). +3 dB (2× power) is barely noticeable; +1 dB is the lab-grade just-noticeable difference for trained listeners.

What dB level damages hearing?

Risk accumulates with level × time: occupational standards use 85 dBA for 8 hours, halving allowed time per +3 dB (88 dBA → 4 h, 100 dBA → 15 min). Sudden impulses above ~140 dB peak can injure instantly. The calculator’s anchors put 90 dB in the protect-your-ears band for sustained exposure.

Is this decibel calculator free?

Yes — free, instant, no sign-up.