Calibration and dBFS

Every level this library reports is only as trustworthy as the one number this page produces: the sensitivity factor that converts digital units into pascals. The page covers both reference frames a recording can be analyzed in: physical dB SPL, obtained by calibrating the chain against an IEC 60942 acoustic calibrator, and digital dBFS, levels relative to full scale with no physical claim attached.

Choosing between them is a question about your measurement chain, not about preference. Work in dB SPL whenever the result faces a physical criterion (a noise limit, an exposure threshold, any acoustics standard); that requires a calibrator recording made through the same, untouched chain as the measurement. Work in dBFS when the signal never had a calibrated analog front end (loudness normalization, codec and interface tests, file-only analysis) or when no calibration tone exists, in which case absolute SPL statements are simply out of reach.

The workflow around the factor matters as much as the formula: derive it before and re-check it after each session, verify meter and calibrator periodically in the laboratory (IEC 61672-3 and IEC 60942; Bies, Hansen & Howard 2017, §3.4), and treat the pre/post difference as your drift bound. The field, laboratory and drift section below turns that into concrete rules, and the Build a sound level meter walkthrough starts from exactly this step before any level is computed.

Why calibrate? The theory

A digital recording only knows numbers: a full-scale sine wave is ±1.0 regardless of whether it was a whisper or a jet engine. To report physical sound pressure levels the chain microphone → preamplifier → ADC must be characterised by a single number, the sensitivity factor $S$, that converts digital units into pascals:

$$p(t)=Sx(t)S=\frac{p_{\text{ref}}\cdot 10^{L_{\text{cal}}/20}}{{\tilde{x}}_{\text{ref}}}$$

where $L_{\text{cal}}$ is the calibrator’s level (typically 94 dB, i.e. 1 Pa), $p_{\text{ref}}=20\mu \text{Pa}$ and ${\tilde{x}}_{\text{ref}}$ is the RMS of the recorded calibration tone in digital units. sensitivity() is exactly that equation. The factor is valid as long as nothing in the chain changes: touch the gain knob and you must recalibrate.

Calibrating a recording, end to end

The three steps below are the whole physical-SPL workflow: a calibrator take, one call to sensitivity(), and the factor handed to a level function. Both recordings must come from the same chain with nothing touched in between. The same factor works across the whole library: octave_filter and OctaveFilterBank take it inside LevelCalibration(factor=...), and leq, laeq and ln_levels as calibration_factor=.

import numpy as np
from phonometry import filters, metrology

# 1. Record your 94 dB calibrator signal (1 kHz, 1 Pa RMS = 94 dB SPL)
fs = 48000
# calibrator_recording: your recorded 1 kHz calibrator tone (1 Pa RMS = 94 dB SPL).
#   Synthesized here so the guide runs; in a real measurement, record your calibrator.
#   Five seconds, as the coupling procedure below asks for.
calibrator_recording = np.sqrt(2) * np.sin(2 * np.pi * 1000 * np.arange(5 * fs) / fs)
# recording: the mic capture you want to calibrate, same input chain (Pa after calibration).
#   Synthesized here; in a real measurement this is your recorded signal.
recording = 0.2 * np.sin(2 * np.pi * 1000 * np.arange(fs) / fs)

# 2. Calculate the sensitivity factor
calibration_factor = metrology.sensitivity(calibrator_recording, target_spl=94.0, fs=fs)

# 3. Apply calibration to your measurements
spl, freq = filters.octave_filter(
    recording, fs,
    calibration=filters.LevelCalibration(factor=calibration_factor))
# spl is now in dB SPL re 20 µPa
print(f"S = {calibration_factor:.3f} Pa per digital unit")   # 1.002
print(f"1 kHz band: {spl[freq.index(1000.0)]:.1f} dB SPL")   # 77.0

Both numbers are worth reading rather than skipping. The synthetic calibrator take has an RMS of exactly 1.0 digital unit, so $S=20\mu \text{Pa}\cdot 10^{94/20}/1.0=1.002$ Pa per digital unit: one digital unit is one pascal, which is what a chain whose full scale sits just above the calibrator level looks like. The measurement record has amplitude 0.2, hence an RMS of 0.141 digital units, hence 0.142 Pa, hence $20{\log }_{10}(0.142/2\times 10^{-5})=77.0$ dB SPL — which is the 1 kHz band the snippet prints.

That gives the sanity rule for every later session. $S$ is the pascal-per-unit scale of the chain, so $94-L_{\text{cal,dBFS}}$ — the calibrator level minus the RMS level of the calibrator take in dBFS — is the sound pressure level that would drive the converter to a digital RMS of 1.0. If that number is not within a few decibels of the loudest level the chain was set up for, something is wrong with the take: a clipped or half-scale recording, a target_spl left at 94.0 for a 114 dB calibrator, or a gain change between the two recordings. A factor wrong by exactly 20 dB is the usual outcome of the second mistake, and no later step will reveal it.

Coupling the calibrator

The snippet is three lines; the step it hides is the one that goes wrong. The specified level of a sound calibrator is the level at the diaphragm of the inserted microphone (IEC 60942:2017, 5.3.1.2), so the mechanical assembly is part of the measurement, not a preliminary to it. Six steps:

1. Set the gain for the loudest level you expect, and lock it. $S$ is valid only while the chain stays exactly as calibrated, and a gain knob moved after the check shifts every level by an amount nothing downstream can detect.
2. Disable every automatic process on the interface — gain riding, limiting, noise suppression, “voice” enhancement — and record at 24 bit. Any of them makes the chain non-linear, and the calibrator take is the one signal on which that is invisible, because it is a single steady tone.
3. Take the windscreen off and fit the adaptor supplied with the calibrator. An adaptor is an integral part of the sound calibrator (5.1.1), and where the manual gives adaptor design data it also gives the insertion distance and the minimum microphone diameter at which sealing occurs (6.3 u). Check that your microphone model and configuration — with or without the protective grid — is in the manual’s list (6.3 a): the specified level holds for the models and configurations stated there (5.3.1.3), and the manual states how much the level moves with the effective load volume of the inserted microphone (6.3 k), the air volume bounded by the reference plane, the diaphragm and the capsule wall (3.13).
4. Insert the capsule fully to the reference plane — the plane of contact between microphone and calibrator (3.12) — hold the assembly still and let it settle. The manual states two settling times: the calibrator’s own, which may not exceed 30 s (5.1.10), and the time the microphone-and-calibrator combination needs after they are coupled (6.3 e).
5. Do the check away from the running source. The cavity is not a sound isolator. IEC 60942 makes this quantitative for its own tests: with the microphone coupled and the calibrator switched off, the level the microphone reads must be at least 30 dB below the level being measured for periodic testing (B.4.2), and 40 dB below for pattern evaluation (A.5.3). For a 94 dB calibrator that is a background below 64 dB at the capsule — a number you can record and check in ten seconds, and the one that decides whether narrowband=True is optional (see the figure below).
6. Record 5 to 10 s of settled tone, trim the handling noise at both ends, and pass the rest to sensitivity(ref, fs=fs). The standard measures the generated level as an average over 20 s to 25 s (A.5.5.1) and the short-term fluctuation over 60 s sampled at least 30 times (5.3.3); a few settled seconds is enough for the RMS to converge, and the stability check below is what tells you the tone really was settled.

Pressure field in the cavity, free field in the measurement. The coupler drives the diaphragm with a pressure excitation: the cavity is far smaller than a wavelength, so the sound pressure is uniform over it and no diffraction around the capsule takes place. The microphone you are calibrating is normally rated for a free field, where its own body and the grid raise the response at high frequency. The two ratings differ by tenths of a decibel below about 2 kHz and by several decibels near 10 kHz, which is why IEC 60942 confines the principal frequency of a sound calibrator to the 160 Hz to 1250 Hz range (5.4.1.1): there the pressure and free-field sensitivities of a measurement capsule coincide closely enough that no correction is applied. It also means $S$ is a single-frequency anchor. The shape of the chain’s response away from the calibrator frequency comes from the microphone’s own free-field data, not from this check — the three sensitivities and where each applies are laid out in Microphones. Put the windscreen back on before measuring, and remember it has its own insertion loss of a few tenths of a decibel at high frequency, which the calibration did not see.

Calibrator assumptions (IEC 60942)

sensitivity assumes the reference recording comes from an acoustic calibrator as specified by IEC 60942 (classes LS, 1 and 2):

• The default target_spl=94.0 matches the common 94 dB @ 1 kHz calibrator output. Clause 5.3.1.3 requires the principal level to be at least 90 dB re 20 µPa when the calibrator is applied to the microphone models and configurations specified in its instruction manual; 94 dB and 114 dB are the usual choices, and the principal frequency must lie between 160 Hz and 1.25 kHz (5.4.1.1).
• The resulting sensitivity inherits the calibrator’s own level tolerance, and that number takes one step to obtain. IEC 60942:2017 deliberately does not print tolerance limits: Table 2 gives the acceptance limit on the generated level (0.25 dB for a class 1 calibrator from 160 Hz to 1.25 kHz, 0.40 dB for class 2, 0.10 dB for class LS) and Table A.1 the maximum-permitted uncertainty of the laboratory measurement that demonstrates it (0.15 dB for class 1 over the same range); Annex D, Figure D.1 places the tolerance limit at their sum. ±0.4 dB is therefore the class 1 figure to carry into an uncertainty budget at 1 kHz, and it is a tolerance, not a measured error. Add the RMS estimation error of your own recording on top of it.
• IEC 60942 measures the generated level as an average over 20 s to 25 s (A.5.5.1): record a few seconds of stable tone (excluding handling noise at the start/end) for the RMS estimate to converge.
• Environmental corrections, and which calibrators need them. The generated level is specified at the reference conditions of Clause 4: 23 °C, 101.325 kPa and 50 % relative humidity. Table 2 still applies without any correction over a band around them (97 kPa to 105 kPa, 20 °C to 26 °C, 40 % to 65 % RH, clause 5.3.2), and outside that band a calibrator must stay inside the wider limits of Tables 5 and 6 over its whole operating range, which for class 1 is 65 kPa to 108 kPa, −10 °C to +50 °C and 25 % to 90 % RH (5.5). Only pistonphones that need a static-pressure correction to meet their class carry the letter M in their designation (class LS/M, class 1/M, 5.1.5 and Table 1); they are supplied with a barometer, or their manual specifies one (5.1.8), and the manual states the correction and its uncertainty (6.3 i, 6.3 m). A pistonphone generates a fixed volume displacement, so its output follows the ambient static pressure — of order a tenth of a decibel for ordinary weather and around −1 dB at 1000 m above sea level. Every other calibrator, by 5.1.7, must meet its class with no environmental correction at all. When a correction is required, apply it to the target level and not to the results:

p_correction_db = 0.0  # from the calibrator manual and the barometer reading
cal_corrected = metrology.sensitivity(
    calibrator_recording, target_spl=94.0 + p_correction_db, fs=fs)

The correction enters $S$ directly, so it moves every level of the session by the same amount.

Automatic stability validation

When you pass the sample rate (and validate=True, the default), sensitivity(ref, fs=fs) checks the recording the way IEC 60942:2017 checks the calibrator itself (5.3.3): the short-term level fluctuation, the absolute difference between each of the maximum and minimum F-time-weighted levels and the mean level, must not exceed the Table 2 class 1 limit for the calibrator’s nominal frequency. Table 2 gives three disjoint rows, and they must not be read as overlapping ranges:

Nominal frequency	Class 1 limit
160 Hz to 16 kHz	0.07 dB	the strict row, and the one a 1 kHz calibrator is judged on
above 63 Hz to below 160 Hz	0.10 dB
31.5 Hz to 63 Hz	0.20 dB	where the F time weighting itself ripples on the tone

Table 2 spans 31.5 Hz to 16 kHz and specifies nothing outside it, so a frequency below 31.5 Hz or above 16 kHz falls back to the strict 0.07 dB rather than to the relaxed low-frequency rows. Pass frequency= to select the right row for non-1 kHz calibrators. A CalibrationWarning flags badly coupled microphones or handling noise before they silently corrupt every calibrated level. The recording must be at least 2 s long (1 s for the F-integrator to settle plus 1 s of settled envelope); shorter recordings get a warning instead of an unreliable verdict. Without fs the check is skipped. Override the limit with max_fluctuation_db or disable with validate=False.

The check catches exactly what ruins field calibrations (a loose coupler, wind, handling noise):

The check is a decision, and the figure shows how far from marginal it is. The stable tone wanders between +0.003 and −0.004 dB about its mean, a twentieth of the 0.07 dB Table 2 class 1 limit. Three per cent of amplitude modulation — a coupler that is not quite seated, a hand on the microphone — takes it to +0.142 and −0.143 dB, twice the limit, while sounding identical and reading the same mean level. The mean is what the sensitivity uses; only the fluctuation says whether it can be trusted.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np
from phonometry import filters

fs = 48000
t = np.arange(int(fs * 6.0)) / fs
stable = 0.5 * np.sin(2 * np.pi * 1000 * t)
# 3 % amplitude modulation at 2 Hz: ~0.14 dB of wobble, clearly over
unstable = stable * (1 + 0.03 * np.sin(2 * np.pi * 2.0 * t))

plt.figure(figsize=(9, 5))
skip = fs                     # discard the F-integrator attack (~8 tau)
for x, label in ((stable, "Stable tone (good coupling)"),
                 (unstable, "3% AM tone (loose coupling)")):
    env = filters.time_weighting(x, fs, mode="fast")[skip:]
    level = 10 * np.log10(np.maximum(env, np.finfo(float).eps))
    plt.plot(t[skip:], level - level.mean(), label=label)
for lim in (0.07, -0.07):
    plt.axhline(lim, linestyle="--", color="gray")
plt.xlabel("Time [s]")
plt.ylabel("F-weighted level re mean [dB]")
plt.legend()
plt.show()

Broadband noise in the take, and what it costs

The RMS of the calibrator recording is the denominator of $S$, so anything in the take that is not the tone inflates it and shrinks the factor — and every level derived from that factor then reads low, by $-10{\log }_{10}(1+1/\mathrm{SNR})$ with SNR the tone-to-noise power ratio in the recording. Passing narrowband=True replaces the full-band RMS with a coherent Goertzel detector locked to the tone, which rejects the incoherent part:

Sensitivity error against the signal-to-noise ratio of the calibrator take, measured by calling sensitivity() on a 1 kHz tone plus broadband noise. The full-band RMS estimator lands exactly on the closed form; it costs 0.41 dB at 10 dB SNR, 0.05 dB at 20 dB and spends the whole class 1 acceptance limit of 0.25 dB below 12.3 dB SNR. The Goertzel estimator stays inside 0.02 dB everywhere. The 30 dB background margin the coupling procedure asks for (B.4.2) therefore puts the plain RMS estimator at 0.004 dB, which is why narrowband=False is a sane default and narrowband=True is the repair for a take you could not make quiet enough.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np

# metrology comes from the first snippet on this page.
fs = 48000
t = np.arange(int(fs * 6.0)) / fs
tone = np.sqrt(2) * np.sin(2 * np.pi * 1000 * t)     # 1 Pa RMS on 1.0 digital
s_true = 2e-5 * 10 ** (94 / 20)
noise = np.random.default_rng(7).standard_normal(t.size)
noise /= np.sqrt(np.mean(noise ** 2))

snr_db = np.arange(0.0, 40.5, 1.0)
rms, goertzel = [], []
for snr in snr_db:
    x = tone + noise * 10 ** (-snr / 20)
    # validate=False: the noisy takes deliberately fail the stability check,
    # which is a second, independent reason not to accept them.
    rms.append(
        20 * np.log10(metrology.sensitivity(x, fs=fs, validate=False) / s_true))
    goertzel.append(20 * np.log10(
        metrology.sensitivity(x, fs=fs, narrowband=True, validate=False) / s_true))

plt.figure(figsize=(9, 5))
plt.axhspan(-0.25, 0.25, alpha=0.15)
plt.plot(snr_db, rms, label="narrowband=False")
plt.plot(snr_db, -10 * np.log10(1 + 10 ** (-snr_db / 10)), "k:",
         label="closed form")
plt.plot(snr_db, goertzel, label="narrowband=True")
plt.xlabel("Coupler signal-to-noise ratio [dB]")
plt.ylabel("Sensitivity error [dB]")
plt.legend()
plt.show()

sensitivity() parameters

Parameter	Type / shape	Units	Range / default	Notes
ref_signal	1D/2D array	digital units	non-empty, non-silent	Recording of the calibration tone only (trim handling noise)
target_spl	float	dB re 20 µPa	default 94.0	The calibrator’s nominal level (114 dB calibrators: pass 114.0)
ref_pressure	float	Pa	default 2e-5	Reference pressure $p_0$; rarely changed
fs	int, optional	Hz	> 0; default None	Required for the stability validation; omit to skip it
validate	bool	—	default True	Emit CalibrationWarning on unstable/short recordings
max_fluctuation_db	float, optional	dB	default None → Table 2 class 1	Explicit override of the stability limit
frequency	float	Hz	default 1000.0	Calibrator’s nominal frequency; selects the IEC 60942 Table 2 row
narrowband	bool	—	default False	Estimate the tone with a coherent Goertzel detector near frequency (needs fs) instead of full-band RMS; rejects broadband hum/noise that otherwise inflates the RMS and shrinks every later level (−0.41 dB at 10 dB SNR, −0.04 dB at 20 dB; see the figure above). Enable for noisy coupler recordings

Returns the sensitivity factor (float) to pass as calibration_factor= to leq, laeq, ln_levels, lc_peak, sel and the dose functions, and as calibration=LevelCalibration(factor=...) to octave_filter.

What the factor also tells you: the measurable range

$S$ is not only a conversion, it is the chain’s scale, and both ends of the measurable range fall straight out of it.

The ceiling. A signal whose digital RMS reaches 1.0 corresponds to $20{\log }_{10}(S/p_0)$ dB, which is also the calibrator level minus the dBFS level of the calibrator take. A full-scale sine has an RMS of $1/\sqrt{2}$, so it reads 3.01 dB lower, $L_{\text{FS}}=20{\log }_{10}(S/(\sqrt{2}{p}_0))$. That is the highest sine level the converter can carry without clipping; compare it against the microphone’s own overload sound pressure level, which is a capsule-and-preamplifier property and not a converter one (see Microphones), and keep the smaller of the two at least 10 dB above the loudest event you expect. A clipped event does not announce itself: it reads low, and plausibly so.

The floor. Record 30 s with the capsule in a quiet enclosure — the closed calibrator cavity with the drive switched off does nicely, which is the same take the coupling step already asks for — and run it through the same factor. That level is the chain’s inherent noise, microphone plus preamplifier plus converter. A measured level within 3 dB of it is not a measurement of the source; one within 10 dB needs the background correction that the emission and environmental guides apply.

# Continues from the first snippet: calibration_factor and fs are already bound.
ceiling = 20 * np.log10(calibration_factor / (np.sqrt(2) * 2e-5))
quiet = 1e-4 * np.random.default_rng(0).standard_normal(30 * fs)  # your 30 s take
floor = 20 * np.log10(np.sqrt(np.mean((quiet * calibration_factor) ** 2)) / 2e-5)
print(f"full-scale sine {ceiling:.1f} dB SPL, noise floor {floor:.1f} dB SPL")

Without a calibrator: from the rated sensitivity

A calibrator is the only route to a normative level, but it is not the only route to a number. If the microphone datasheet states a sensitivity and the interface a full-scale input voltage, the chain gain is a product of three numbers you can read off, and $S$ can be assembled arithmetically:

$$S=\frac{V_{\text{FS}}}{MG}$$

where $M$ is the capsule’s rated free-field sensitivity in volts per pascal at the reference frequency, $G$ the linear voltage gain of preamplifier plus interface, and $V_{\text{FS}}$ the input voltage amplitude that drives the converter to $\pm 1.0$. Note the trap in the last one: an interface datasheet normally quotes its maximum input level as the RMS of the sine that just reaches full scale, so $V_{\text{FS}}=\sqrt{2}$ times that figure.

Worked through for a 12.5 mV/Pa half-inch capsule, +20 dB of gain and an input whose maximum level is 1.0 V RMS: $M=0.0125$ V/Pa, $G=10$, $V_{\text{FS}}=1.414$ V, so $S=11.31$ Pa per digital unit. One pascal (94 dB) then lands at $MG/V_{\text{FS}}=0.0884$ digital units RMS, that is −21.1 dBFS, and the ceiling derived above is $20{\log }_{10}(11.31/(\sqrt{2}\cdot 2\times 10^{-5}))=112.0$ dB SPL. Both numbers are checkable against the chain in a few seconds, which is the point of the route.

Beware the word sensitivity: it means reciprocal things on the two pages. Here $S$ is pascals per digital unit; on the Microphones page $M$ is volts per pascal, exposed as sensitivity_mv_per_pa, and the free-field, pressure and random-incidence ratings are three different numbers for the same capsule — use the free-field one at the reference frequency.

What the route costs: it inherits the capsule’s individual deviation from its rated value (a few tenths of a decibel for a laboratory microphone with an individual calibration chart, but a nominal figure on a low-cost capsule can be a couple of decibels out), the repeatability of the gain setting, and the interface’s own full-scale tolerance. Budget about a decibel against the few tenths of a calibrator check, and note what it cannot do at all: it cannot detect a damaged capsule, a leaking preamplifier or a changed gain, because nothing in it is measured. Use it for dBFS-adjacent work, for sanity-checking a calibrator result, and never for a level that faces a limit. And once the numbers are read, the gain must stay exactly where it was.

Field checks, laboratory verification and drift

Calibration lives at three time scales:

• Every session: the field check. Couple the calibrator and derive the sensitivity before each measurement series, and check it again at the end. Normative methods make the second check mandatory and use the pre/post difference as a validity gate (a common criterion invalidates the series when the two differ by more than 0.5 dB). Whatever the threshold, the difference is your drift bound for everything captured in between; carry it into the uncertainty budget rather than assuming zero.
• Periodically: laboratory verification. A field check only compares the chain against the calibrator; it cannot see an error the calibrator and meter share, and it says nothing about the response away from 1 kHz. IEC 61672-3 defines the periodic tests for the meter (weightings, level linearity and ballistics spot-checked against the class limits), and IEC 60942 the corresponding tests for the calibrator itself; typical laboratory intervals are one to two years.
• Between checks: drift. Microphone sensitivity moves with temperature, humidity and capsule aging; electronics with battery voltage. A healthy class 1 chain drifts a few hundredths of a dB over a session, which is why a pre/post difference of half a decibel signals damage rather than weather. The largest “drift” of all is a touched gain knob: the factor $S$ is valid only while the chain stays exactly as calibrated.

What a calibration must record to be reportable

The pre/post pair and the calibrator’s class tolerance are the two Type B inputs that the uncertainty budget of a level consumes. A check that was not written down cannot be propagated, so record, at the time of the check:

• calibrator make, model, serial number, class designation (including the letter M if present) and the date of its last laboratory verification;
• microphone and preamplifier model and serial number, and the microphone configuration used (with or without the protective grid);
• the adaptor fitted, if any;
• the sensitivity obtained before the series, the one obtained after it, and their difference — the drift bound;
• sample rate, bit depth and the gain setting, exactly as locked;
• air temperature, static pressure and relative humidity, plus any static pressure correction applied to target_spl and where it came from;
• the background level read by the coupled capsule with the calibrator off;
• the resulting factor $S$ and the tolerance assumed for it.

One more class subtlety: tolerances chain. A class 1 measurement requires a class 1 (or LS) calibrator and a class 1 meter; calibrating a class 1 chain with a class 2 calibrator silently downgrades every derived level to class 2 accuracy, because the calibrator’s wider level tolerance enters $S$ directly.

Digital analysis (dBFS)

If you are working with digital audio files (e.g., WAV, FLAC) and want to analyze levels relative to Full Scale rather than physical pressure, you can use the dbfs=True parameter.

In this mode:

• 0 dBFS corresponds to a numeric signal level of 1.0 (RMS or Peak).
• The calibration factor does not apply (dBFS is relative to digital full scale).
• Useful for analyzing headroom, digital mastering, or normalized signals.

import numpy as np
from phonometry import filters

fs = 48000
# recording: the mic capture you want to calibrate, same input chain (Pa after calibration).
#   Synthesized here; in a real measurement this is your recorded signal.
recording = 0.2 * np.sin(2 * np.pi * 1000 * np.arange(fs) / fs)

# Assume 'recording' is normalized between -1.0 and 1.0
spl_dbfs, freq = filters.octave_filter(
    recording, fs, calibration=filters.LevelCalibration(dbfs=True))
# Results will be negative (e.g., -20 dBFS)

The convention differs from AES17 by 3.01 dB

This is the RMS-referenced convention: a signal whose RMS is 1.0 reads 0 dBFS, so a full-scale sine, whose RMS is 0.707, reads −3.01 dBFS in mode='rms'. AES17 — and the meters, DAWs and loudness tools that follow it — normalise a full-scale sine to 0 dBFS instead, so the same file measured by two tools differs by exactly 3.01 dB with neither of them wrong. Note that mode='peak' with dbfs=True reads 0 dBFS for that same sine, because its peak is 1.0: the RMS-versus-peak choice below and the convention question are the same question asked twice. Any dBFS number quoted outside the library should carry its convention with it.

What survives the loss of a physical reference

Half of what this library computes does not care which frame it is in, and the other half is silently meaningless without $S$. The dividing line is whether the quantity is built from a ratio or a shape — invariant — or from an absolute value — not.

Frame-invariant (the same number in dBFS as in dB SPL): reverberation times and decay slopes, transfer functions and coherence, correlation and delay, spectral slopes and shapes, band-to-band differences, and any A-minus-C or C-minus-Z difference. These are the quantities you can legitimately get from an uncalibrated recording, and most of signals/spectra lives here.

Frame-dependent (plausible, wrong, and silent without a calibration): $L_{Aeq}$ against a limit, SEL, noise dose and exposure, the percentile levels $L_N$, every psychoacoustic quantity anchored to 20 µPa (loudness in sones, sharpness, the ECMA-418-2 chain), the peak criteria of hearing-conservation rules, and every conformance verdict in the library. None of these functions refuses uncalibrated samples — they cannot tell — so the frame is a decision the analyst has to record beside the result.

Left: one record, two frames. The dBFS spectrum is the dB SPL spectrum shifted by a constant, here 106.04 dB, which is exactly the calibrator level minus the dBFS level of the calibrator take — the dBFS frame changes the origin and nothing else, which is why every shape-based quantity above survives it. Right: the onset of a 1 kHz tone burst after the octave filter, drive amplitude 0.5. The band signal overshoots to 0.582 before settling, so mode='peak' reads 1.32 dB above the steady tone.

RMS versus peak levels

Levels can be read two ways, and both are in use in commercial analysers:

• RMS (mode='rms') integrates energy over the frame, which is what every standardized level ($L_{eq}$, $L_{Aeq}$, $L_N$) is defined on.
• Peak (mode='peak') holds the largest instantaneous value in the frame, which is what impact and peak-limit criteria such as $L_{Cpeak}$ are checked against. Note that the band peak returned here is band-limited and unweighted, so it is not itself $L_{Cpeak}$.

import numpy as np
from phonometry import filters

fs = 48000
# recording: the mic capture you want to calibrate, same input chain (Pa after calibration).
#   Synthesized here; in a real measurement this is your recorded signal.
recording = 0.2 * np.sin(2 * np.pi * 1000 * np.arange(fs) / fs)

# Measure peak-holding levels for impact analysis
spl_peak, freq = filters.octave_filter(recording, fs, mode='peak')

Note

mode='peak' measures the absolute maximum of the filtered band signal, which includes the filter’s onset transient (overshoot). Signals that start abruptly may read about 1 dB high — 1.32 dB for the tone burst drawn in the right-hand panel above. This is inherent to IIR band filters (an analog sound level meter behaves the same way), not a processing artifact.

Integer audio input

Integer signals (e.g. int16 from scipy.io.wavfile.read) are converted to float64 internally before any squaring. The conversion is a dtype cast, not a rescaling: an int16 sample of +32767 enters as 32767.0, not as 1.0. That is harmless as long as the calibrator recording and the measurement are in the same format, because sensitivity then returns a factor 32768 times smaller and the two cancel exactly — a tone that reads 87.958 dB from float arrays reads 87.958 dB from the int16 arrays of the same recordings. It is not harmless otherwise: the same tone read uncalibrated is 87.94 dB as float and 172.14 dB as int16, a $20{\log }_{10}(32768)=90.3$ dB offset, and applying a float-derived sensitivity to an integer-read measurement (or the reverse) carries that offset straight into the result with no symptom. Either keep both recordings in one format, or divide both by the full-scale value (x / 32768.0 for int16) before anything else.

What this guide covers

• Covered

  IEC 60942:2017 as far as it constrains the sensitivity factor: the principal calibrator level that target_spl assumes, the Table 2 and Table A.1 class tolerances quoted in the uncertainty discussion above, and the short-term level-fluctuation check of clause 5.3.3 against the class 1 limits of Table 2, which sensitivity(ref, fs=fs) runs on the reference recording.

• Not covered

  The conformance tests of the calibrator itself (generated level, frequency, distortion, and the environmental corrections for static pressure and temperature) are not implemented, so pass an already corrected target_spl when the calibrator’s manual asks for one. The IEC 61672-3 periodic tests are cited as laboratory practice, not run: nothing here verifies a sound level meter or assigns it a class. The dBFS half of the page sits outside any standard and makes no physical claim.

See also

• Build a sound level meter: the walkthrough that starts from this calibration step and ends at a class-checked instrument.
• Levels: every metric that consumes the calibration_factor derived here.
• Multichannel and Performance: one sensitivity per channel when the channels differ.
• GUM uncertainty: propagating the calibrator tolerance and drift bound into a level’s uncertainty.
• API reference: metrology.calibration and phonometry.

Quick answers

What calibrator level should I use to calibrate my measurement chain?

The usual choice is 94 dB SPL at 1 kHz (1 Pa RMS), which is what sensitivity() assumes with its default target_spl=94.0; for a 114 dB calibrator pass 114.0. IEC 60942 requires the principal level to be at least 90 dB re 20 µPa. Record a few seconds of stable tone, because the standard specifies the generated level as a 20 s average.

How much drift between the pre and post calibration checks is acceptable?

Derive the sensitivity before each measurement series and check it again at the end: a common criterion invalidates the series when the two differ by more than 0.5 dB. A healthy class 1 chain drifts a few hundredths of a dB over a session, so a half-decibel pre/post difference signals damage rather than weather. Whatever the threshold, carry the difference into the uncertainty budget rather than assuming zero.

Can I calibrate a class 1 chain with a class 2 calibrator?

You can, but the tolerances chain: a class 1 measurement requires a class 1 (or LS) calibrator per IEC 60942 and a class 1 meter, so a class 2 calibrator silently downgrades every derived level to class 2 accuracy, because its wider level tolerance enters the sensitivity factor $S$ directly. For reference, the class 1 tolerance limit is ±0.4 dB between 160 Hz and 1.25 kHz: the 0.25 dB acceptance limit of IEC 60942:2017 Table 2 plus the 0.15 dB maximum-permitted measurement uncertainty of Table A.1, combined as Annex D describes.

References

• Audio Engineering Society. (2020). AES standard method for digital audio engineering — Measurement of digital audio equipment (AES17-2020). The full-scale-sine dBFS convention, which differs from this page's RMS-referenced convention by 3.01 dB.
• Bies, D. A., Hansen, C. H., & Howard, C. Q. (2017). Engineering noise control (5th ed.). CRC Press. https://doi.org/10.1201/9781351228152Sections 3.1.5 and 3.4 (microphone field effects and sound level meter calibration: the electrical and acoustic calibration practice this page's workflow follows). ISBN 978-1-4987-2405-0.
• International Electrotechnical Commission. (2013). Electroacoustics — Sound level meters — Part 3: Periodic tests (IEC 61672-3:2013). The laboratory verification procedure behind the recommended periodic checks.
• International Electrotechnical Commission. (2017). Electroacoustics — Sound calibrators (IEC 60942:2017). The calibrator level and class assumptions behind sensitivity() (the principal level of clause 5.3.1.3, the Table 2 acceptance limits with the Table A.1 maximum-permitted uncertainties they combine with under Annex D) and the short-term level-fluctuation stability check of the reference recording (clause 5.3.3, Table 2 class 1 limits per nominal frequency).