Decibel Calculator
Calculate decibel difference between sound levels using dB = 10 log10(P2/P1).
Converts dB to intensity ratios and perceived loudness changes.
Decibels (dB) express ratios between power or intensity levels using a logarithmic scale. Because our hearing perceives loudness on an exponential curve, decibels align more naturally with human perception than linear measurements.
The unit is named after Alexander Graham Bell, who invented the telephone in 1876 in the United States. One bel equals a 10:1 power ratio; one decibel is one-tenth of a bel. The “deci-” sized unit caught on because whole-bel steps were too coarse for practical engineering work.
Power-based dB formula:
dB = 10 × log₁₀(P₁ / P₂)
Amplitude / voltage / pressure formula:
dB = 20 × log₁₀(A₁ / A₂)
Reverse: dB to ratio:
- Power ratio:
Ratio = 10^(dB / 10) - Amplitude ratio:
Ratio = 10^(dB / 20)
Worked example, power: Amplifier output increases from 10W to 100W:
- dB gain = 10 × log₁₀(100/10) = 10 × 1 = +10 dB
Worked example, sound pressure: Microphone signal doubles in amplitude:
- dB change = 20 × log₁₀(2) = 20 × 0.301 = +6.02 dB
Key dB relationships to memorize:
| Change | Power Effect | Perceived Loudness |
|---|---|---|
| +3 dB | ×2 power | Slightly louder |
| +6 dB | ×4 power | Noticeably louder |
| +10 dB | ×10 power | Twice as loud (perceptual) |
| −10 dB | ÷10 power | Half as loud |
Common sound pressure levels:
- 0 dB: Threshold of hearing (reference)
- 30 dB: Library whisper
- 60 dB: Normal conversation at 3 feet
- 85 dB: Heavy traffic (prolonged exposure causes hearing damage)
- 110 dB: Live music concert
- 130 dB: Threshold of pain
- 194 dB: Theoretical maximum in Earth’s atmosphere
OSHA exposure limits: At 90 dB, maximum safe exposure without protection is 8 hours. Every +5 dB halves the allowable exposure time.
Adding decibels — they don’t add the way numbers do
Because dB is logarithmic, you can’t just add dB values directly. Two identical sound sources together produce 3 dB more total, not double the dB. The correct formula is:
Total = 10 × log₁₀(10^(dB₁/10) + 10^(dB₂/10))
So two 80 dB sources together produce 83 dB, not 160 dB. Three identical sources combine to about +4.8 dB, four to +6 dB, ten to +10 dB. This is why a single noisy neighbor is almost as bad as several. Once one source dominates, adding more barely changes the total.
dBm and signal strength
dBm references signal power to 1 milliwatt: 0 dBm = 1 mW, +30 dBm = 1 W. Telecommunications, RF, and Wi-Fi gear use dBm because the dynamic range from a faint received signal (-90 dBm or lower) up to a strong transmitter (+30 dBm and above) spans 12 orders of magnitude, which is unwieldy in plain milliwatts.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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