Decibel (dB) & Sound Level Calculator

Decibels and Sound Guide

The Decibel Scale

The decibel (dB) is a logarithmic unit. dB = 10 × log₁₀(I/I₀), where I₀ = 10⁻¹² W/m² (threshold of human hearing). Because it is logarithmic: +10 dB = 10× more power/intensity. +3 dB ≈ 2× more power. +6 dB ≈ 4× more power. Common levels: 0 dB (threshold of hearing), 30 dB (quiet bedroom), 60 dB (normal conversation), 85 dB (heavy traffic), 100 dB (nightclub), 120 dB (jet engine at 100m), 140 dB (threshold of pain).

Combining Sound Levels

Two identical sound sources at 90 dB together produce 93 dB — not 180 dB. This is the logarithmic addition: total = 10 × log₁₀(10^(dB1/10) + 10^(dB2/10)). Two levels equal produce 3 dB more. Two levels 10 dB apart: the combined level is essentially the louder one (within 0.4 dB). This is why adding a second violin to an orchestra makes very little difference to overall volume — the orchestra's background noise dominates.

Hearing Damage and Safe Exposure

The Health and Safety Executive (UK) sets noise action levels: 80 dBA: employers must provide hearing protection if requested. 85 dBA: employers must supply and workers must use hearing protection. 87 dBA: absolute limit at ear (cannot be exceeded even with protection). Safe daily exposure times (approximately): 85 dB = 8 hours, 88 dB = 4 hours, 91 dB = 2 hours, 94 dB = 1 hour, 100 dB = 15 minutes, 110 dB = 2 minutes. Noise-induced hearing loss is permanent and cumulative — concert-going, power tools, and loud headphone use are among the most common everyday sources of preventable hearing damage.

Inverse Square Law

Sound intensity decreases with the square of distance: if you double your distance from a source, intensity reduces by 6 dB. At 1m from a speaker at 100 dB: at 2m = 94 dB, at 4m = 88 dB, at 10m = 80 dB, at 100m = 60 dB. This is why standing back from speakers at events reduces hearing damage risk dramatically. The inverse square law applies to point sources in open spaces — indoors, reflections mean sound does not decrease as rapidly with distance.

What should I know about Sound Intensity Level vs Sound Pressure Level?

The decibel scale is logarithmic by design because human hearing itself responds roughly logarithmically to sound energy. Sound intensity level uses IL = 10 log₁₀(I/I₀), comparing power per unit area to a reference intensity I₀ = 10⁻¹² W/m² (the threshold of human hearing at 1 kHz). Because intensity is proportional to pressure squared, the equivalent sound pressure level uses SPL = 20 log₁₀(p/p₀) with reference pressure p₀ = 20 µPa — the factor of 20 instead of 10 exactly accounts for the squared relationship, so both formulas give the same dB reading for the same real sound.

What do I need to know about Decibels in Electronics?

Electronics engineers reuse the same logarithmic dB idea to express gain or attenuation: power gain in dB = 10 log₁₀(P_out/P_in), or equivalently voltage gain in dB = 20 log₁₀(V_out/V_in) when input and output impedances match. A gain of +3 dB roughly doubles power; +10 dB means exactly ten times the power. This is why amplifier and filter specifications are almost always quoted in dB rather than as raw ratios — it turns multiplying gains through a chain of stages into simple addition, and compresses enormous dynamic ranges into manageable numbers.

Common Everyday Sound Levels

The numbers in the decibel scale only become meaningful once they're pinned to familiar real-world sounds. The reference table below lists well-established, widely-cited typical levels — actual readings vary with distance and source, but these are the standard figures used in acoustics and occupational-health guidance.

Because the scale is logarithmic, the gap between any two rows represents a far bigger real difference than the numbers suggest at a glance — the jump from normal conversation (60 dB) to a nightclub (105 dB) is not '1.75 times louder', it's roughly 30,000 times more sound intensity, even though it feels only a few times louder to the ear.

Why +10 dB Means 10× the Intensity but Only 'Twice as Loud'

This is the single most counter-intuitive thing about decibels, and it comes from the difference between physical sound intensity (energy) and perceived loudness (what the ear and brain report). By definition, +10 dB always means exactly 10× more sound intensity — that's built directly into the formula dB = 10 × log₁₀(I/I₀), since log₁₀(10) = 1. But human hearing does not perceive loudness linearly with intensity; extensive psychoacoustic research (dating back to Fletcher and Munson's original equal-loudness work in the 1930s and refined many times since) has established that a 10 dB increase is judged, on average, as being about 'twice as loud' subjectively, even though it represents ten times the actual sound energy hitting the ear. This is why a chainsaw at 110 dB doesn't feel '11 times louder' than a quiet office at 50 dB, despite being 10⁶ (one million) times more intense — it feels roughly 2⁶ = 64 times louder, which still sounds dramatic, but is a completely different number from the million-fold intensity increase. The practical takeaway: when using this calculator to combine or compare levels, trust the dB-to-intensity-ratio math for anything involving energy, exposure, or equipment specifications, but don't expect a straight-line relationship between the dB number and how loud something will subjectively feel.

dBA vs dBC vs Unweighted dB — Why Weighting Matters

A raw decibel reading on its own doesn't say whether the measurement reflects what a human ear actually experiences, which is why almost every real-world noise regulation specifies a weighting curve alongside the dB figure. dBA (A-weighting) is by far the most common: it filters the raw sound pressure to match the sensitivity of average human hearing, which is much less sensitive to very low and very high frequencies than to mid-range ones (roughly 500 Hz-6 kHz) — this is why UK HSE noise-at-work limits, hearing protection ratings, and most environmental noise laws are specified in dB(A). dBC (C-weighting) applies a much flatter filter across the frequency range, barely reducing bass frequencies at all, which makes it the preferred scale for assessing bass-heavy or impulsive noise — gunfire, explosions, and heavy machinery peaks — where A-weighting would understate how much low-frequency energy is actually present. Unweighted (sometimes labelled dBZ or 'linear') applies no frequency filter at all and is mainly used for lab-grade acoustic measurement rather than everyday compliance work. A sound with a lot of bass can show a noticeably higher dBC reading than dBA reading for the identical physical sound — that gap is itself diagnostic information about the sound's frequency content, not a measurement error.

OSHA vs HSE Exposure Limits — The 5 dB vs 3 dB Exchange Rate

The earlier safe-exposure figures on this page (85 dB = 8 hours, down to 100 dB = 15 minutes) follow the UK/EU convention of a 3 dB exchange rate, where every 3 dB increase halves the permitted exposure time, because 3 dB corresponds closely to a doubling of sound energy. The US OSHA standard (29 CFR 1910.95) instead uses a 90 dBA reference level for an 8-hour day with a 5 dB exchange rate, which is noticeably more permissive at higher levels because it halves allowed time every 5 dB rather than every 3 dB.

The practical consequence: at 100 dBA, OSHA's rule allows 2 hours of exposure, while the HSE/EU 3 dB-exchange approach used earlier on this page allows only about 15 minutes at the same level — both are legitimate, officially published standards, they simply model hearing-damage risk with different exchange rates, so always check which jurisdiction's rule applies before relying on either figure for compliance purposes.

Subtracting Background Noise from a Measurement

A practical problem that comes up constantly for anyone measuring real sound with an SPL meter: the reading always includes both the source you care about and whatever background noise was already present, and because dB is logarithmic you can't just subtract the two dB figures directly. The correct method converts both readings back to raw intensity ratios, subtracts those, then converts the result back to dB. Worked example: a measurement with a noisy machine running reads 70 dB total; switching the machine off, the background alone reads 65 dB. Converting to intensity ratios (I/I₀ = 10^(dB/10)): total = 10⁷, background = 10^6.5 ≈ 3,162,278. Subtracting: 10,000,000 − 3,162,278 = 6,837,722. Converting back: 10 × log₁₀(6,837,722) ≈ 68.3 dB — so the machine alone, with the background noise mathematically removed, is actually producing about 68.3 dB, not the naive (and wrong) guess of 70 − 65 = 5 dB. This technique only works reliably when the source is at least a few dB louder than the background; once the two levels are within about 3 dB of each other, the subtraction becomes unreliable because the result is highly sensitive to small measurement errors in either reading.