The decibel — what it is and why the world of acoustics uses it
Sound spans an enormous range of pressures — from the threshold of hearing to the threshold of pain, a factor of roughly one million in pressure amplitude. The decibel is the unit that makes this range workable. This article explains what a decibel actually is, how it relates to sound pressure, and why logarithmic units are the natural choice for acoustics.
Why a logarithmic scale
Human hearing does not perceive loudness linearly. A sound that carries twice the acoustic power does not sound twice as loud — it sounds only marginally louder. Perceived loudness tracks the logarithm of intensity rather than its absolute value, a relationship described by the Weber-Fechner law. A unit system that mirrors this behaviour is more useful in practice than one based on linear ratios.
The decibel (dB) is a dimensionless unit expressing the ratio of two quantities on a logarithmic scale. It is not a unit of loudness, pressure, or power in isolation — it always expresses a ratio, either to a defined reference level or to another quantity in the same system.
Definition
For power or intensity ratios:
> L = 10 × log₁₀(P₁ / P₂) dB
For pressure or amplitude ratios (since power is proportional to pressure squared):
> L = 20 × log₁₀(p₁ / p₂) dB
The factor of 20 rather than 10 arises because power is proportional to the square of pressure: doubling pressure quadruples power, a 6 dB increase.
Sound pressure level
Sound pressure level (SPL) is the most common acoustic quantity expressed in decibels. It is defined as:
> L_p = 20 × log₁₀(p / p_ref) dB SPL
where p is the RMS sound pressure in pascals and p_ref = 20 μPa — the internationally agreed reference pressure, chosen to approximate the threshold of hearing for a young adult at 1 kHz.
At this reference, 0 dB SPL corresponds to a pressure of 20 μPa. This is not silence; it is the quietest sound a typical healthy human ear can detect under ideal conditions.
Common SPL values
Source & Approximate SPL
Threshold of hearing 0 dB SPL
Quiet bedroom at night 30 dB SPL
Normal conversation at 1 m 60 dB SPL
Busy road 80 dB SPL
Live music (front of house) 100–110 dB SPL
Pain threshold 120–130 dB SPL
A change of 3 dB corresponds approximately to a doubling of acoustic power. A change of 10 dB corresponds to a tenfold increase in power and is perceived as roughly a doubling of loudness.
Combining decibel values
Decibels do not add arithmetically. Two independent sources each producing 80 dB SPL produce 83 dB SPL together — not 160 dB. To combine incoherent sources:
> L_total = 10 × log₁₀(10^(L₁/10) + 10^(L₂/10))
For two equal sources, this simplifies to L + 3 dB. For sources differing by more than 10 dB, the quieter source contributes less than 0.5 dB to the total and can generally be ignored.
Frequency weighting
The ear's sensitivity varies with frequency. At low and high frequencies, a higher sound pressure level is required to produce the same perceived loudness as at mid frequencies. Frequency-weighted measurements apply a filter to the measured signal before calculating SPL, so that the result better reflects perceived loudness.
The most common weighting is A-weighting
(producing dBA values), which approximates the ear's sensitivity at moderate listening levels. A-weighting attenuates low frequencies significantly — 30 Hz is attenuated by approximately 39 dB relative to 1 kHz — and applies a modest attenuation at high frequencies. It is widely used in noise measurement, occupational health standards, and product datasheets.
C-weighting applies much less low-frequency attenuation and is used where low-frequency content is significant, such as in peak measurements and some environmental standards. Z-weighting (flat) applies no frequency correction.
dB in other contexts
The decibel appears throughout audio and electroacoustics with different reference levels:
dBu — voltage ratio relative to 0.775 V RMS. The professional audio standard line level is nominally +4 dBu.
dBV— voltage ratio relative to 1 V RMS. Consumer equipment often operates at −10 dBV.-
dBFS — digital level relative to full scale. 0 dBFS is the maximum value the digital system can represent; all values are negative.-
dB SPL — acoustic pressure relative to 20 μPa, as described above.
dBr — level relative to a specified reference level in a given system, used for describing gain, attenuation, and signal-to-noise ratio.
In all cases the unit is a ratio. The suffix specifies the reference.