2.2 Decibels: SPL, HL, SL

The decibel is the audiologist’s unit. Every measurement in the field — pure-tone thresholds, speech-recognition levels, hearing-aid gain prescriptions, noise dosimetry, OAE levels, evoked-potential amplitudes — is reported in dB. But “dB” by itself is ambiguous: there are at least four scales in routine clinical use, and the same physical sound has different decibel values on each. Confusing them is one of the more common sources of misinterpretation in audiology.

This lesson develops the four scales — dB SPL, dB HL, dB SL, dB(A) — and how to convert between them. The conversion table that ties them together is the RETSPL (Reference Equivalent Threshold Sound Pressure Level), which we develop properly in the worked example.

The decibel, recapped

The decibel is a logarithmic ratio of two quantities, defined as

L \;=\; 10\, \log_{10}\!\left( \frac{Q}{Q_0} \right)

for a power-like quantity $Q$ , or

L \;=\; 20\, \log_{10}\!\left( \frac{A}{A_0} \right)

for an amplitude-like quantity $A$ (since power scales as amplitude squared). The factor of 20 is what makes pressure-domain decibels (acoustic pressure, voltage, current) work out correctly: doubling the pressure adds 6 dB; doubling the power adds 3 dB. For more on the underlying motivation see Sound 5.5 — The decibel, motivated.

The decibel is always relative to a reference. The reference is the “0 dB” point. Different fields choose different references; each choice produces a distinct decibel scale.

The four scales

dB SPL — sound pressure level

The physics scale. Reference: $p_0 = 20\,\mu\mathrm{Pa}$ — historically chosen as the approximate threshold of human hearing at 1 kHz. The sound pressure level is

L_p \;=\; 20\, \log_{10}\!\left( \frac{p_\text{rms}}{20\,\mu\mathrm{Pa}} \right).

This is the ground-truth physical measurement. A calibrated microphone reads dB SPL directly. Every other decibel scale in audiology is a transformation of dB SPL.

Useful landmarks:

0 dB SPL — approximate threshold of audibility at 1 kHz for a normal-hearing young adult
20 dB SPL — leaf rustle, very quiet bedroom
60 dB SPL — normal conversational speech at 1 m
85 dB SPL — start of noise-induced hearing loss with prolonged exposure
120 dB SPL — threshold of pain
140 dB SPL — instantaneous damage threshold; jet engine at 30 m

dB HL — hearing level

The audiometric scale. Reference: the normal-hearing threshold at each frequency, called the RETSPL. The hearing level is

L_\text{HL}(f) \;=\; L_p \;-\; \text{RETSPL}(f).

So 0 dB HL at 1 kHz corresponds to about 7 dB SPL; 0 dB HL at 250 Hz corresponds to about 25 dB SPL; 0 dB HL at 4 kHz corresponds to about 9.5 dB SPL. The RETSPL absorbs all the frequency dependence of normal hearing sensitivity into the y-axis of the audiogram, so a healthy ear plots as a horizontal line at 0 dB HL.

This is the scale the audiogram uses, exclusively. The audiometer’s level dial is calibrated in dB HL.

dB SL — sensation level

The patient-specific scale. Reference: the individual patient’s threshold at that frequency. The sensation level is

L_\text{SL}(f) \;=\; L_\text{HL}(f) \;-\; \text{patient threshold at } f.

dB SL is what the patient actually experiences in terms of how far above their own threshold the sound sits. It’s particularly useful when comparing patients with different hearing losses on equal footing — a “50 dB SL” stimulus is 50 dB above threshold for both the normal-hearing and the impaired listener, even though the absolute SPLs differ. Speech audiometry and OAE protocols often specify stimulus levels in dB SL for this reason.

dB(A) — A-weighted SPL

The occupational / environmental scale. Reference: $p_0 = 20\,\mu\mathrm{Pa}$ (same as dB SPL), but the measurement is filtered by the A-weighting curve before integration. The A-weighting is a fixed frequency-dependent attenuation that mimics the ear’s reduced sensitivity to low frequencies and very high frequencies at moderate listening levels (close to the inverted 40-phon equal-loudness contour).

The conversion from dB SPL to dB(A) at a single frequency is just

L_A(f) \;=\; L_p(f) \;+\; W_A(f),

where $W_A$ is the A-weighting filter’s value at that frequency:

$f$ (Hz)	$W_A$ (dB)
125	−16.1
250	−8.6
500	−3.2
1000	0.0
2000	+1.2
4000	+1.0
8000	−1.1

For a broadband signal, the A-weighted level is computed by applying the A-weighting filter to the signal spectrum and integrating; the resulting single number is dB(A). This is the unit used in occupational-health regulations (OSHA, NIOSH) and most environmental-noise standards. A noise-exposure limit of 85 dB(A) for an 8-hour day is the universal occupational reference.

A consistency example

For a 1-kHz tone at 60 dB SPL:

dB SPL = 60 (by definition)
dB HL = 60 − 7 = 53 (using RETSPL at 1 kHz = 7 dB)
dB SL for a patient with 25 dB HL threshold = 53 − 25 = 28
dB(A) = 60 + 0 = 60 (A-weighting is 0 at 1 kHz)

The same physical sound is 60 on one scale, 53 on another, 28 on a third, and 60 again on a fourth. None of the values is wrong; each answers a different question.

frequency:

dB SPL = 60.0 dB HL = 53.0

dB SL = 28.0 (over patient threshold) patient threshold = 25 dB HL

Four scales, one underlying physical level. dB SPL is the acoustic pressure (re 20 µPa) — the ground truth. dB HL subtracts the frequency-dependent RETSPL so that "0 dB HL" means "at threshold for a normal-hearing young adult at this frequency"; this is what the audiogram displays. dB SL further subtracts an individual's measured threshold, giving "how far above the patient's own threshold the sound sits" — useful for stimuli that must be presented at a fixed sensation level. dB(A) applies a frequency-dependent weighting that approximates human perception of loudness at moderate levels — used in occupational and environmental noise measurements. Sliding any one updates all four; switching the test frequency re-anchors the RETSPL and A-weight offsets.

Pick a frequency and slide any one of the four scales. The others update via the conversions above. The sidebar shows the RETSPL for the chosen frequency (the y-axis offset between dB SPL and dB HL) and the A-weighting (the y-axis offset between dB SPL and dB(A)). Switching frequencies re-anchors both — 0 dB HL at 250 Hz is not the same SPL as 0 dB HL at 1 kHz.

Worked example: RETSPL from the equal-loudness contour

▶ Where the RETSPL table comes from

The RETSPL is, at root, the minimum-audible threshold of a normal-hearing population. The standard procedure is:

Recruit a representative sample of otologically-normal young adults (typically aged 18–25, no history of ear disease or excessive noise exposure, normal otoscopy, normal tympanometry).
Measure their pure-tone thresholds at each audiometric frequency, using a specified earphone (TDH-39 / TDH-49 supra-aural, or insert earphone, or circumaural) coupled to an artificial ear that simulates the average human ear-canal acoustic impedance.
Average the sample medians of threshold across subjects. The average is reported in dB SPL at the earphone’s reference coupler.
Round to the nearest 0.5 dB and publish in the standard (ANSI S3.6 in the US, ISO 389 internationally).

The current ANSI S3.6-2018 values for a TDH-39 supra-aural earphone (the most common clinical earphone):

Frequency (Hz)	RETSPL (dB SPL)
125	45.0
250	25.5
500	11.5
750	7.5
1000	7.0
1500	6.5
2000	9.0
3000	10.0
4000	9.5
6000	15.5
8000	13.0

A few observations:

The U-shape — RETSPL is high at low frequencies (humans are less sensitive there), reaches minimum around 1–3 kHz, then rises again at very high frequencies. This is the familiar equal-loudness contour shape, restricted to the threshold-of-audibility curve.
The 250-Hz value is high (25.5 dB SPL) — partly true low-frequency insensitivity, partly the earphone’s poor low-frequency response when coupled to the ear with the standard pressure method.
Different earphones have different tables. Insert earphones (EARtone 3A, etc.) have a different RETSPL set because they couple to the ear canal differently; the audiometer must be calibrated to whichever earphone is in use.

When a patient’s threshold is recorded as “30 dB HL at 2 kHz,” what is physically present at the earphone’s output is approximately $30 + 9 = 39$ dB SPL. The audiogram value is the clinical number; the SPL is the physical number; the conversion is the RETSPL at that frequency.

Which scale to use when

In day-to-day clinical work:

The audiogram uses dB HL, exclusively.
Speech testing uses dB HL for SRTs and dB SL for word-recognition presentation levels above the patient’s SRT.
OAE testing uses dB SPL (the in-ear-canal pressure is the relevant quantity).
Evoked-potential testing uses dB nHL (“normal HL” — like dB HL but referenced to a click stimulus rather than a pure tone) or dB peSPL (peak-equivalent SPL, for transient stimuli).
Hearing-aid fitting uses dB SPL (the target output at the eardrum is what matters), with prescription targets specified in dB SPL at each frequency.
Noise-exposure measurements use dB(A) for the time-weighted average and dB(C) for peak measurements.

In published research:

Psychoacoustic studies almost always use dB SPL or dB SL (laboratory rigour).
Clinical-population studies almost always use dB HL (because that’s what the audiometer reads).
Environmental studies use dB(A).

Knowing which scale is in play is half of correctly interpreting any measurement that arrives with “dB” attached.

What’s next

The next lesson, 2.3 — Air and bone conduction, introduces the second axis of the audiogram: bone-conduction thresholds, the air-bone gap, and the conductive / sensorineural / mixed taxonomy that the audiogram makes diagnosable.