Decibel Calculator (dB ↔ Ratio, dB SPL Summation)
Convert between decibels and linear ratios for voltage/SPL (20·log) or power (10·log), sum dB SPL sources, and look up dBV, dBu, dBm and dBFS.
| 0 dB | Threshold of hearing (1 kHz, healthy ear) |
| 10 dB | Calm breathing, sound studio |
| 30 dB | Whisper, quiet bedroom |
| 45 dB | Quiet office |
| 60 dB | Normal conversation at 1 m |
| 70 dB | Vacuum cleaner, busy traffic |
| 85 dB | OSHA workplace 8-hour limit |
| 90 dB | Lawnmower, motorcycle at 7 m |
| 100 dB | Subway train, hand drill |
| 110 dB | Rock concert front row |
| 120 dB | Threshold of pain, jet at 30 m |
| 140 dB | Jet engine close, instant hearing damage |
| dBV | 1 V RMS | voltage relative to 1 V |
| dBu | 0.7746 V RMS (~600 Ω, 1 mW) | pro audio line level |
| dBm | 1 mW into 50 Ω (RF) or 600 Ω (audio) | RF / telecom power |
| dBFS | digital full scale | always ≤ 0; 0 dBFS = clipping |
| dB SPL | 20 µPa RMS in air | acoustic loudness |
| dBW | 1 W | absolute power |
| dBi | isotropic radiator | antenna gain |
Voltage/SPL uses 20·log₁₀ (amplitudes). Power uses 10·log₁₀ (true power). dB SPL summation is incoherent (assumes uncorrelated sources).
How to use
- Pick 'Voltage / SPL (20·log)' for amplitudes (volts, sound pressure, field strength) or 'Power (10·log)' for true power (watts, intensity).
- Enter a dB value to see the linear ratio, or a ratio to see the equivalent dB.
- In the summation panel, paste a list of dB SPL values (one per line) to get their logarithmic sum — the actual combined level of multiple incoherent sources.
- Click any row in the reference table to load that dB value into the converter.
About this tool
ShowHide
Decibels look simple but trip up almost everyone the first time, because the factor between dB and ratio depends on what you're measuring. Voltage, sound pressure, and field strength use 20·log₁₀(ratio); power uses 10·log₁₀(ratio). This tool gives you both formulas with a single toggle, converts in both directions, shows how many doublings the value corresponds to (≈ 6.02 dB per voltage doubling, ≈ 3.01 dB per power doubling), and includes a logarithmic-sum panel for combining multiple incoherent dB SPL sources — useful for room acoustics, noise dose work, and HVAC. A reference panel lists everyday dB SPL values from threshold of hearing (0) to instant hearing damage (140), and a second panel defines the standard absolute references: dBV (1 V), dBu (0.7746 V), dBm (1 mW), dBFS (digital clipping), dB SPL (20 µPa), dBW (1 W) and dBi (isotropic antenna).
Frequently asked questions
Why does +3 dB sometimes mean 'double' and other times mean 'about 1.4× louder'?
Because dB is always relative to a quantity. For power (watts, intensity, energy), 3 dB is exactly a doubling: 10^(3/10) ≈ 2. For voltage or sound pressure (an amplitude), 3 dB is only √2 ≈ 1.41× the level. Doubling the voltage is +6 dB. The trick: when you double the voltage, the power quadruples — and 10·log₁₀(4) = 6 dB. Both rules describe the same physics; they just measure different things.
How are multiple dB SPL sources added?
They're added as power, not as decibels. Two identical 60 dB sources give 63 dB, not 120 dB. The formula is dB_total = 10·log₁₀(Σ 10^(dBᵢ/10)). Two equal sources always add 3.01 dB; ten equal sources add 10 dB; a hundred add 20 dB.
What's the difference between dBV, dBu and dBm?
dBV is voltage relative to 1 V RMS — common in consumer audio. dBu is voltage relative to ~0.7746 V RMS (the voltage that delivers 1 mW into 600 Ω) — the standard in pro audio. dBm is true power relative to 1 mW — used in RF and telecom (with 50 Ω as the implicit impedance). 0 dBV ≈ +2.22 dBu; 0 dBu ≈ −2.22 dBV.
Why is dBFS always negative?
Digital full scale (0 dBFS) is the loudest sample a fixed-point audio format can represent — any louder and you clip. Real audio always sits some dB below it (a peak of −1 dBFS is typical for mastering). Positive dBFS values exist only as theoretical values in floating-point intermediate buses.
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