What Is a Decibel (dB)? The Logarithmic Scale Explained

A decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity — most commonly sound pressure, sound intensity, or sound power — relative to a fixed reference value. It is defined as one-tenth of a bel (B), a much larger and less practical unit named after Alexander Graham Bell. In acoustics, the decibel is the standard way to compress an enormous range of audible sound pressures — from the faintest detectable whisper to the roar of a jet engine, a ratio of about 10 million to 1 — into a manageable scale running roughly from 0 to 140.

Because the decibel is a ratio, not an absolute physical unit like the meter or the pascal, a decibel value is only meaningful once you know what quantity is being measured (pressure, intensity, power, voltage) and what reference value it is being compared against. This is exactly why you will see labels like dB SPL, dB SWL, or dBV in technical literature — the letters after “dB” tell you which reference is in use. This article focuses on the acoustic case: dB SPL (Sound Pressure Level), the everyday decibel of loudness measurement, standardized in ISO 80000-8 (Quantities and Units — Acoustics) and measured according to IEC 61672 (Electroacoustics — Sound Level Meters).

Why Is the Decibel Scale Logarithmic?

The decibel scale is logarithmic because human hearing itself responds to sound logarithmically, not linearly, and because the range of pressures the ear can detect is too vast to express conveniently on a linear scale.

The human ear can detect sound pressures spanning roughly 20 micropascals (µPa) — the quietest sound a healthy young ear can perceive — up to over 20 pascals (Pa) before the onset of pain, a ratio of about 1,000,000:1 in pressure, or roughly 10,000,000,000,000 (10 trillion) to 1 in intensity (since intensity scales with the square of pressure). Trying to plot that range on a linear axis — say, from 1 to 10,000,000,000,000 — would be useless for any practical chart or instrument dial. A logarithmic scale compresses this entire range into a set of numbers from about 0 dB to 194 dB (the theoretical maximum sound pressure level in Earth’s atmosphere before waveform clipping occurs).

There is also a deep physiological reason for this choice, described by the Weber-Fechner law: the perceived intensity of many stimuli — including sound loudness, brightness of light, and other sensory phenomena — grows roughly in proportion to the logarithm of the physical stimulus, not the stimulus itself. A logarithmic decibel scale therefore tracks how loudness is actually experienced far more closely than a linear pressure or intensity scale would. This is one reason the decibel, though invented as an engineering convenience for telephone-line signal loss (its precursor, the “transmission unit” or TU, was developed at Bell Telephone Laboratories in the 1920s), turned out to map naturally onto human hearing when it was adopted for acoustics.

How Is a Decibel Calculated? The Sound Pressure Level Formula

For sound pressure level (SPL), the formula is:

Lp = 20 · log₁₀(p / p₀) dB

Where:
– Lp = sound pressure level, in decibels (dB)
– p = the measured root-mean-square (RMS) sound pressure, in pascals (Pa)
– p₀ = the reference sound pressure = 20 micropascals (20 µPa = 2 × 10⁻⁵ Pa)

The reference value of 20 µPa is not arbitrary: it approximates the quietest sound pressure a healthy young human ear can detect at 1,000 Hz under laboratory conditions — the nominal threshold of hearing. This reference is fixed by international agreement (ISO 1683 and ISO 80000-8) precisely so that every sound level meter, hearing test, and acoustic report in the world uses the same zero point.

For sound intensity and sound power, a different (but related) formula applies, using a factor of 10 rather than 20:

LI = 10 · log₁₀(I / I₀) dB (sound intensity level, reference I₀ = 1 × 10⁻¹² W/m²)

LW = 10 · log₁₀(W / W₀) dB (sound power level, reference W₀ = 1 × 10⁻¹² W)

Why 20·log for Pressure but 10·log for Intensity and Power?

This is one of the most common points of confusion in acoustics, and the answer comes down to a simple physical relationship: intensity is proportional to pressure squared (I ∝ p²). Sound pressure is a “field quantity” (it can be positive or negative, oscillating above and below atmospheric pressure), while intensity and power are “power-like quantities” (always positive, representing energy flow).

Substituting p² for I in the intensity formula shows why the factor changes:

LI = 10 · log₁₀(p² / p₀²) = 10 · 2 · log₁₀(p / p₀) = 20 · log₁₀(p / p₀)

In other words, the factor of 20 for pressure is mathematically identical to applying the factor of 10 to the corresponding intensity (which is proportional to pressure squared). This convention — factor of 10 for power-like quantities, factor of 20 for field-like quantities — is a general rule across all decibel applications, not just acoustics; it applies equally to voltage (dBV), electrical power (dBW), and signal amplitude in audio engineering. The rule guarantees that a measurement expressed in dB gives the same numerical result whether you calculate it from pressure or from the intensity that pressure produces.

What Is 0 dB? And Can Decibels Be Negative?

0 dB SPL is not “no sound” or absolute silence — it is simply the reference point of the scale, corresponding to a sound pressure of exactly 20 µPa (roughly the nominal threshold of human hearing at 1 kHz). Because 0 dB is a fixed benchmark rather than the absence of pressure, decibel values below the reference are mathematically negative, and negative dB SPL readings are real and occur in practice.

Any sound quieter than 20 µPa produces a value where p/p₀ < 1, and the logarithm of a number less than 1 is negative — so Lp comes out negative. This happens inside extremely quiet spaces such as high-performance anechoic chambers. For example, Microsoft’s anechoic chamber in Building 87, Redmond, Washington, was measured at approximately -20.6 dBA, certified as a Guinness World Record for the quietest place on Earth in 2015 — a reading so far below the nominal hearing threshold that the residual noise floor is dominated by the listener’s own blood flow and breathing rather than any external sound. (Orfield Laboratories in Minneapolis has since been measured even quieter, at about -24.9 dBA.) This demonstrates clearly that “0 dB” is a reference marker, not a physical floor: sound pressure itself can never truly reach zero (that would require a perfect vacuum), but the decibel value representing it can go below zero once pressure drops under the 20 µPa benchmark.

How Much Louder Is 10 dB? Loudness, Intensity, and the Logarithmic Jump

Because the decibel scale is logarithmic, the relationship between a change in decibels and the resulting change in physical intensity is exponential, not linear — and the relationship between physical intensity and perceived loudness is a separate, additional layer on top of that.

The three benchmark relationships every acoustics reference should state precisely are:

• +3 dB = a doubling of sound power or intensity. Since 10 · log₁₀(2) ≈ 3.01, an increase of 3 dB corresponds almost exactly to twice the acoustic energy.
• +6 dB = a doubling of sound pressure. Since 20 · log₁₀(2) ≈ 6.02, a 6 dB increase in SPL corresponds to twice the pressure amplitude (which, consistent with the formula above, also equals a 4× increase in intensity, since intensity ∝ pressure²).
• +10 dB = a 10-fold increase in intensity/power, and is widely used by hearing-health and psychoacoustics literature (including NIOSH and OSHA training materials) as the practical benchmark for a perceived doubling of loudness. This “10 dB ≈ twice as loud” rule is an empirical approximation rooted in psychoacoustic loudness research (related to Stevens’ power law for loudness), not an exact physical law — individual perception varies with frequency, sound level, and listener — but it is the standard rule of thumb used across hearing-conservation and audio-engineering training.

This table is the single most important reference for understanding amplitude and loudness relationships: notice that the physical intensity ratio and the perceived loudness ratio diverge sharply as dB increases, which is precisely the point of using a logarithmic scale — it maps an enormous physical range onto a compact perceptual one.

How Do You Add Two Decibel Levels Together?

Because decibels are logarithmic, you cannot add sound levels the way you add ordinary numbers. Two machines each producing 60 dB do not combine to 120 dB — that would represent a trillion-fold increase in intensity, an absurd result. Decibels must first be converted back to their linear intensity (or pressure-squared) values, summed, and then converted back to decibels.

The correct formula for combining two incoherent (unrelated/uncorrelated) sound sources is:

Ltotal = 10 · log₁₀(10^(L₁/10) + 10^(L₂/10))

For two equal sources, each at level L, this simplifies to:

Ltotal = L + 10 · log₁₀(2) ≈ L + 3 dB

So two sources at 60 dB each combine to produce 60 + 3 = 63 dB, not 120 dB. This follows directly from the “+3 dB = doubling of intensity” rule above: two equal sources double the total acoustic intensity, and a doubling of intensity is, by definition, a 3 dB increase. For n identical sources each at level L, the general rule is:

Ltotal = L + 10 · log₁₀(n)

So four identical 60 dB sources produce 60 + 10·log₁₀(4) ≈ 60 + 6 = 66 dB; ten identical 60 dB sources produce 60 + 10·log₁₀(10) = 70 dB. This logarithmic addition rule is essential for noise-impact assessments — for example, predicting the combined noise level of multiple traffic lanes, several identical HVAC units, or a bank of machines on a factory floor — and it is a direct, practical consequence of the same math that defines the decibel scale itself.

What Are Typical Decibel Levels of Everyday Sounds?

The following table gives representative, commonly cited dB SPL ranges for everyday environments and sources (measured at a typical listening distance; actual readings vary with distance, per the inverse square law, and with the specific source). For a fuller reference chart, see Decibel Levels of Everyday Sounds.

These figures are representative averages drawn from commonly cited references (CDC/NIOSH noise exposure charts, ANSI-based acoustic textbooks); real-world values vary with distance, equipment, and measurement method — always use ranges, not single fixed numbers, when communicating real-world sound levels.

Myth vs Fact: Is 80 dB Twice as Loud as 40 dB?

Myth: “80 dB is twice as loud as 40 dB, because 80 is double 40.”

Fact: This is false, and it’s the single most common misunderstanding about the decibel scale. Decibels do not work like a ruler where doubling the number doubles the quantity. Going from 40 dB to 80 dB is a 40 dB increase, which — using the +10 dB ≈ doubling-of-loudness rule from the table above — represents four successive doublings of loudness (10, 20, 30, 40 dB = four steps of +10 dB each), or roughly 16 times louder, not 2 times louder. In terms of raw physical intensity, the jump is even larger: a 40 dB increase equals 10⁴ = 10,000 times more intensity. The lesson: never compare two decibel values by simple arithmetic ratio (e.g., “80/40 = 2×”); always convert the difference in dB using the logarithmic relationships above.

What Is the Difference Between dB and dB(A)?

Plain “dB” (or dB SPL) measures raw acoustic energy across all frequencies equally — it is a purely physical measurement. However, the human ear does not perceive all frequencies as equally loud; we are far more sensitive to sounds in the 1,000–4,000 Hz range than to very low or very high frequencies. To account for this, sound level meters apply frequency-weighting filters — most commonly A-weighting, producing readings in dB(A) or dBA — that adjust the raw measurement to better approximate perceived loudness. Nearly all hearing-health regulations (OSHA, NIOSH) and environmental noise ordinances are expressed in dB(A) rather than unweighted dB. See dB(A) vs dB(C) vs dB(Z): Frequency Weighting Explained for the full comparison of weighting curves and when each is used.

Why Does the Decibel Scale Matter for Hearing Health?

Because the decibel scale is logarithmic, small-looking numeric increases represent large real-world increases in acoustic energy and correspondingly large increases in risk of hearing damage. This is why occupational-safety exposure limits are expressed as a combination of level and duration rather than a single number: the U.S. National Institute for Occupational Safety and Health (NIOSH) recommends an exposure limit of 85 dB(A) averaged over 8 hours, using a 3 dB exchange rate — meaning every 3 dB increase in level cuts the safe exposure time in half (consistent with 3 dB representing a doubling of acoustic energy). The Occupational Safety and Health Administration (OSHA) uses a permissible exposure limit of 90 dB(A) over 8 hours with a less conservative 5 dB exchange rate. Full detail, including exposure-time tables, is covered in How Loud Is Too Loud? Safe Decibel Levels.

Is the Decibel Only Used for Sound?

No. The decibel is a general-purpose logarithmic ratio unit defined in ISO 80000-8 and used throughout physics and engineering — not just acoustics. It appears in electrical engineering (dBW, dBm for power ratios; dBV for voltage ratios), telecommunications (signal-to-noise ratio, cable attenuation — its original 1920s application at Bell Labs), optics, and RF engineering. Whenever a quantity spans an enormous dynamic range and benefits from logarithmic compression, decibels tend to be the unit of choice. In every case the same 10·log (power-like quantity) vs. 20·log (field-like quantity) convention explained above applies.

Frequently Asked Questions

Is a higher decibel number always louder?
Yes, for the same weighting and measurement method, a higher dB value always represents greater sound pressure or intensity. However, comparing dB(A) to unweighted dB, or comparing readings taken at different distances, can be misleading — always confirm the weighting curve and measurement conditions before comparing two figures directly.

How many decibels is a whisper compared to a shout?
A whisper at close range measures around 30 dB, while a loud shout can reach 90 dB or more — a 60 dB difference, which corresponds to roughly 1,000,000 times more sound intensity (since 60 dB = six steps of 10 dB, i.e., 10⁶).

Why is 20 micropascals used as the reference instead of a rounder number?
20 µPa (2 × 10⁻⁵ Pa) was chosen because it closely approximates the quietest sound pressure a healthy young human ear can just detect at 1,000 Hz — making 0 dB SPL correspond meaningfully to the practical threshold of hearing rather than an arbitrary round figure.

Can a decibel meter reading be wrong if it doesn’t specify a weighting?
Yes. A “dB” figure without an A, C, or Z weighting label, and without a stated measurement standard (such as IEC 61672 for the meter’s accuracy class), is scientifically incomplete — it is comparable to quoting a temperature without stating Celsius or Fahrenheit. See dB(A) vs dB(C) vs dB(Z) for how this affects real measurements.

Does doubling the distance from a sound source halve the decibel level?
No — doubling distance from a point source reduces sound pressure level by approximately 6 dB (not 50% of the dB number), a direct consequence of the inverse square law applied to sound propagation in free field conditions.

What’s the difference between sound pressure level and sound power level?
Sound pressure level (dB SPL) is what a microphone or ear measures at a specific location and depends on distance and environment; sound power level (dB SWL) is a fixed property of the source itself, describing total radiated acoustic energy regardless of where you stand. See Sound Power vs Sound Pressure for the full comparison.

Related Reading

Understanding the decibel is foundational to nearly every other topic in acoustic measurement. Explore the broader physics context in Sound & Acoustics Fundamentals: The Complete Guide, or continue with related concepts: how sound pressure relates to amplitude and the sound pressure level formula in more depth, how sound intensity differs from pressure, why the human hearing range shapes which frequencies matter most, and how everyday levels stack up on the full decibel chart.