Decibel Calculator | dB, Power & Sound Level
Convert between decibels, power ratios, and amplitude ratios. Combine multiple sound sources, compute distance attenuation, and see NIOSH hearing safety limits with an SPL reference meter.
What Is the Decibel Calculator | dB, Power & Sound Level?
The decibel (dB) is a logarithmic unit used to express the ratio between two quantities, most commonly power, voltage, or sound pressure. Because human perception of loudness is itself logarithmic (a sound must be 10× more powerful to seem twice as loud), the decibel scale maps naturally onto how we actually hear.
The factor of 10 vs 20 in the formula comes from the relationship between power and amplitude. Since power is proportional to the square of voltage or pressure (P ∝ V²), doubling the voltage quadruples the power. To keep the dB value consistent between power and amplitude measurements: dB(power) = 10·log₁₀(P₂/P₁), and since log(x²) = 2·log(x), dB(amplitude) = 20·log₁₀(A₂/A₁).
Combining sound sources from separate speakers or machines cannot be done by simple addition. A second identical source adds only 3 dB, not double. Ten identical sources add 10 dB. The logarithmic combine formula accounts for the fact that acoustic energy (power) adds linearly while dB levels do not.
Formula
Core Decibel Formulas
Power ratio → dB:
dB = 10 · log₁₀(P₂ / P₁)
Amplitude / Voltage / Pressure → dB:
dB = 20 · log₁₀(A₂ / A₁)
Inverse (dB → ratio):
Power ratio = 10^(dB / 10)
Amplitude ratio = 10^(dB / 20)
Combining Sources & Distance Attenuation
Combine N sources:
L_total = 10 · log₁₀(10^(L₁/10) + 10^(L₂/10) + … + 10^(Lₙ/10))
Distance attenuation (point source):
L₂ = L₁ − 20 · log₁₀(d₂ / d₁)
Every doubling of distance → −6 dB
Distance attenuation (line source):
L₂ = L₁ − 10 · log₁₀(d₂ / d₁)
Every doubling of distance → −3 dB
| Symbol | Meaning | Example |
|---|---|---|
| P₁, P₂ | Reference and measured power (watts) | 1 W, 100 W → +20 dB |
| A₁, A₂ | Reference and measured amplitude (volts, Pa) | 1 V, 10 V → +20 dB |
| dB | Decibels, logarithmic ratio of two quantities | 20 dB = 100× power, 10× amplitude |
| dB SPL | Sound pressure level re. 20 μPa | 60 dB SPL = normal conversation |
| dBm | Power level re. 1 milliwatt (telecom/RF) | 0 dBm = 1 mW into 50 Ω load |
| dBV | Voltage level re. 1 volt (audio) | 0 dBV = 1 V RMS |
| dBu | Voltage level re. 0.7746 V (pro audio) | 0 dBu = 0.7746 V (√0.6W/600Ω) |
How to Use
- 1Choose a mode: "Ratio ↔ dB" converts between power/amplitude ratios and decibels. "Combine Sources" adds multiple dB levels correctly. "Distance" applies the inverse square law for sound attenuation.
- 2Select type (Ratio mode): Choose Power (10·log) for watts, intensity, or power ratios. Choose Amplitude (20·log) for voltage, pressure, or SPL comparisons.
- 3Choose direction: "Ratio → dB" converts a ratio like 100× into decibels. "dB → Ratio" tells you how much larger a +20 dB signal is in actual ratio terms.
- 4Enter your value: Type the ratio or dB number. Results appear after clicking Calculate or pressing Enter.
- 5Read the SPL meter: The level meter shows where your result sits relative to real-world sound levels, and flags hearing damage risk using NIOSH guidelines.
- 6Try Distance mode: Enter SPL at a known reference distance, then set a target distance. See SPL across a full distance table with +/− changes shown.
Example Calculation
Example 1, Amplifier Gain (Power)
- ›An amplifier takes a 0.1 W input and produces 100 W output.
- ›Power ratio = 100 / 0.1 = 1,000.
- ›Gain in dB = 10 · log₁₀(1,000) = 10 × 3 = 30 dB.
- ›Inverse check: 10^(30/10) = 10³ = 1,000× power ratio ✓
- ›Use the Power ratio mode with ratio → dB direction.
Example 2, Two Speakers at 85 dB Each
- ›Each speaker produces 85 dB SPL at the listening position.
- ›Total = 10 · log₁₀(10^(85/10) + 10^(85/10)) = 10 · log₁₀(2 × 10^8.5).
- ›Result: 85 + 10·log₁₀(2) ≈ 85 + 3.01 = 88.01 dB.
- ›Two identical sources always add exactly 3.01 dB, not 170 dB.
- ›Use Combine Sources mode: enter 85 and 85, get 88 dB.
Example 3, Sound Level at Distance (Inverse Square Law)
- ›A generator produces 100 dB SPL at 1 m (reference distance).
- ›At 10 m: 100 − 20·log₁₀(10/1) = 100 − 20 = 80 dB.
- ›At 100 m: 100 − 20·log₁₀(100/1) = 100 − 40 = 60 dB.
- ›Every 10× increase in distance subtracts 20 dB for a point source.
- ›Every doubling of distance subtracts exactly 6.02 dB.
Understanding Decibel | dB, Power & Sound Level
Common Sound Pressure Levels
| dB SPL | Sound source | Relative loudness | Safety |
|---|---|---|---|
| 0 | Threshold of hearing | 1× (reference) | Safe |
| 20 | Rustling leaves | 4× louder than 10dB | Safe |
| 30 | Quiet library | Very quiet | Safe |
| 60 | Normal conversation at 1m | 1,000× louder than 0dB | Safe |
| 70 | Vacuum cleaner at 3m | 10,000,000× | Safe |
| 85 | Heavy traffic, busy café | 316 million× | 8hr limit |
| 100 | Jackhammer at 15m | 10 billion× | 15min limit |
| 110 | Rock concert (near PA) | 100 billion× | 2min limit |
| 120 | Threshold of pain | 1 trillion× | Harmful |
| 140 | Rifle muzzle blast | 100 trillion× | Instant damage |
dB in Audio Engineering
In professional audio, decibels are used to measure virtually every signal in the chain, from microphone sensitivity to amplifier gain, speaker sensitivity to room acoustics. Signal chains typically work at nominal levels around 0 dBu or −18 dBFS with “headroom” reserved above to avoid clipping.
- ›Microphone sensitivity: A good condenser microphone might have a sensitivity of −30 dBV/Pa, meaning it outputs −30 dBV for a 1 Pascal input. 94 dB SPL = 1 Pa, so the output is 94 + (−30) = 64 dBV (0.002 V).
- ›Amplifier gain: A preamp with 60 dB of gain amplifies the signal by a voltage ratio of 10^(60/20) = 1,000×.
- ›Room acoustics: A well-treated studio has an RT60 (time for sound to decay by 60 dB) of 0.2–0.4 seconds. Live concert halls target RT60 of 1.5–2.5 seconds.
- ›Noise floor: Professional audio equipment has noise floors of −100 to −120 dBu, 10 to 100 billion times below the signal level.
Frequently Asked Questions
Why is the decibel scale logarithmic instead of linear?
- ›Human hearing perceives loudness logarithmically, we need a sound to be 10× more powerful to perceive it as twice as loud.
- ›A linear scale would be impractical: the range from silence to pain spans a power ratio of 10¹³ (10 trillion).
- ›The dB scale compresses this to a 0–130 range that reflects actual perceptual experience.
- ›This logarithmic compression is not a limitation, it mirrors how the ear's basilar membrane physically responds to pressure.
- ›The same principle explains why musical pitch (octaves) is logarithmic: A3=220 Hz, A4=440 Hz, A5=880 Hz.
What is the difference between dB, dB SPL, dBm, dBV, and dBu?
- ›Plain "dB" is a unitless ratio between two quantities, it means nothing without a reference.
- ›dB SPL: Sound Pressure Level re. 20 μPa (the threshold of human hearing). 60 dB SPL = normal speech.
- ›dBm: Power level relative to 1 milliwatt. Used in RF, telecom, and optical fiber. 0 dBm = 1 mW.
- ›dBV: Voltage level relative to 1 volt RMS. Common in consumer audio equipment.
- ›dBu: Voltage level relative to 0.7746 V RMS (= √(0.6 W into 600 Ω)). Standard in professional audio.
- ›dBFS: "Full Scale", used in digital audio. 0 dBFS is the maximum level before clipping.
Why do two identical sound sources add only 3 dB instead of doubling?
- ›Decibels measure power ratios on a log scale. Doubling the power adds 10·log₁₀(2) ≈ 3.01 dB.
- ›Two speakers each at 80 dB produce 80 + 3 = 83 dB total, not 160 dB.
- ›To add 10 dB (perceived as twice as loud), you need 10 identical sources.
- ›This is why PA engineers use many speakers: each speaker doubles the power, adding 3 dB.
- ›Practical implication: a second amplifier or generator adds far less than you might expect to the measured level.
At what dB level does hearing damage occur?
- ›NIOSH (National Institute for Occupational Safety and Health) guidelines:
- ›85 dB: safe for up to 8 hours. The most cited "action level" for workplace noise.
- ›91 dB: safe for up to 2 hours. Each 3 dB increase halves the safe exposure time.
- ›100 dB: safe for only 15 minutes.
- ›115 dB and above: no exposure without hearing protection is considered safe.
- ›Damage is cumulative, repeated exposure at 85 dB over years causes permanent hearing loss.
- ›The EU Noise at Work Directive sets similar limits: 80 dB(A) action level, 87 dB(A) exposure limit.
How does the inverse square law apply to sound?
- ›For a point source (loudspeaker, engine, instrument) in a free field (outdoors, no reflections):
- ›Sound intensity decreases with the square of distance: I ∝ 1/d².
- ›In dB terms: every doubling of distance drops SPL by 6 dB.
- ›1 m → 2 m: −6 dB. 1 m → 10 m: −20 dB. 1 m → 100 m: −40 dB.
- ›Line sources (long traffic streams, train lines) follow a 1/d law: −3 dB per doubling.
- ›Indoors, reflections from walls/floors/ceilings cause the level to drop more slowly, "reverberant field".
What is the difference between power ratio and amplitude ratio in dB?
- ›Power quantities (watts, intensity): use 10·log₁₀(ratio). +3 dB = 2× power, +10 dB = 10× power.
- ›Amplitude quantities (voltage, current, pressure): use 20·log₁₀(ratio). +6 dB = 2× amplitude, +20 dB = 10× amplitude.
- ›The factor of 2 difference exists because power is proportional to the square of amplitude (P ∝ V²).
- ›Example: a signal with 2× the voltage has 4× the power, both represent the same +6 dB change.
- ›Mixing the two formulas is a common error, always confirm whether you're measuring power or amplitude.
What is 0 dB? Can sound be below 0 dB?
- ›0 dB represents a ratio of 1:1, the measured value equals the reference value.
- ›For dB SPL: 0 dB SPL is the threshold of hearing (20 μPa RMS), the quietest sound most young adults can detect.
- ›Yes, sound can be below 0 dB SPL. Values like −5 dB SPL or −10 dB SPL exist and are below the hearing threshold.
- ›In digital audio, 0 dBFS is the ceiling (maximum level). All digital audio levels are negative: −18 dBFS, −6 dBFS, etc.
- ›The meaning of 0 dB always depends on the reference standard being used.
How do noise-cancelling headphones work in dB terms?
- ›Active noise cancellation (ANC) generates an inverted sound wave that destructively interferes with incoming noise.
- ›Good ANC headphones achieve 20–35 dB of attenuation for low-frequency noise (engine hum, HVAC).
- ›25 dB attenuation reduces power by a factor of 10^(25/10) ≈ 316×, perceived as roughly 5× quieter.
- ›ANC is less effective above ~1 kHz (shorter wavelengths are harder to cancel in real time).
- ›Passive isolation (ear cups, foam seals) adds another 15–30 dB of high-frequency attenuation.
- ›Combined, a good headphone system can achieve 35–45 dB total isolation across the audible range.
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