Reverberation time

What reverberation is

When a sound source stops in an enclosed space, the sound does not disappear at once: it keeps bouncing between the surfaces, losing a fraction of its energy at each reflection, until it becomes inaudible. This sound tail is reverberation. Its duration is quantified by the reverberation time T60: the time for the sound level to decay by 60 dB from the steady state.

It is how the ear tells a “dry” room from a “boomy” one. A tiled bathroom, an empty gym, a church: they boom. A bedroom with rugs, curtains and a sofa: it is dry. The whole difference is in the T60.

It should not be confused with two neighbouring phenomena. Reverberation is not echo: an echo is a single reflection, distinguishable from the direct sound; the threshold beyond which it becomes audible as a separate event is of the order of tens of milliseconds for speech, but depends on the signal, the relative level of the reflection and the listener, and for impulsive transients can be far lower; reverberation is the continuous overlap of thousands of indistinguishable reflections. And it is not noise: even a single hand clap “booms” in a reverberant hall, with no noise source at all.

The concept originates with Wallace Clement Sabine, who around 1898 solved an intelligibility problem in a lecture room at Harvard’s Fogg Art Museum and empirically discovered the law linking T60, volume and absorption. From that discovery architectural acoustics was born as an engineering discipline.

Why it matters

T60 is the descriptor every acoustic assessment of an interior starts from — the most used, and the one design references exist for. That it is “the most important” in absolute terms is not demonstrable in general: for intelligibility, STI and C50 correlate more directly with performance, for music rooms EDT, C80 and G matter, and open-plan offices have a standard of their own (ISO 3382-3). It can be viewed through three lenses.

Speech and intelligibility

In a classroom a T60 that is too high is a concrete problem: the tail of one syllable overlaps the next, intelligibility collapses and the children at the back of the room do not understand. The acoustic literature indicates optimal T60 values for speech rooms typically around 0.6–0.8 s; that is an order of magnitude to orient by, not a requirement. In Italy the reference for school acoustics is UNI 11532-2:2020, which prescribes no single interval but descriptors and reference values by room type, volume and occupancy condition, deferring to Part 1 for prediction and verification. The standard remains referenced by the Minimum Environmental Criteria for construction, today those adopted by DM 24/11/2025, in force since 2 February 2026, which repealed the earlier DM 256/2022. In open-plan offices T60 affects acoustic privacy and the ability to concentrate.

Music

For music the optimal T60 depends on the repertoire. The literature (Beranek) indicates for large orchestral concert halls values around 1.8–2.2 s — the “sonic cathedrals” that give body to symphonic sound; for chamber and jazz rooms lower values, around 1.2–1.6 s; for amplified rooms (rock, pop) T60 below 1.0 s, because amplification already provides the energy and a long reverberation would blur the rhythmic detail.

General comfort

In restaurants, lobbies and atria a high T60 triggers a vicious circle: cumulative background noise rises, people raise their voices, reverberation amplifies — the “cocktail party effect” in reverse. In indoor sports venues a high T60 makes communication between referee and players difficult.

It should be said that T60 is one of the descriptors of acoustic quality, not the only one: intelligibility is also measured with STI, clarity with C50/C80, sound strength with G. T60 remains, however, the starting point of any assessment.

The formulas: Sabine, Eyring, Millington

The tool estimates T60 from volume and absorption with three classic formulas, which differ in how they treat the mean absorption.

The Sabine formula (1900) is the simplest and most used:

$$T_{60}=\frac{0.161V}{A},A=\sum _i{S}_i{\alpha }_i$$

where V is the volume in m³, S_i the surface areas and α_i their absorption coefficients. The 0.161 s/m coefficient embeds the speed of sound at room temperature. Sabine assumes a perfectly diffuse field and low, uniform absorption; it overestimates T60 when the mean absorption is high — in the limit ᾱ → 1 (a fully absorptive room) it still returns a finite value, physically absurd.

The Eyring formula (1930) fixes exactly this, starting from the per-reflection decay:

$$T_{60}=\frac{0.161V}{-S\ln (1-\bar{\alpha })},\bar{\alpha }=\frac{A}{S}$$

with S the total surface and ᾱ the mean absorption. For ᾱ → 1 the term −ln(1−ᾱ) diverges and T60 → 0, as it should. When absorption is low the two formulas coincide.

The Millington-Sette formula treats each surface with its own logarithmic term, and is better suited when absorption is very non-uniform (one treated wall and three bare):

$$T_{60}=\frac{0.161V}{-{\sum }_i{S}_i\ln (1-{\alpha }_i)}$$

A worked example

A classroom of 8 × 6 × 3 m has V = 144 m³ and S = 2·(48 + 24 + 18) = 180 m². With a mean absorption ᾱ = 0.15 (mostly reflective surfaces) the total absorption is A = 27 m² and Sabine gives T60 = 0.161·144 / 27 ≈ 0.86 s — at the high end for a classroom. Raising ᾱ to 0.30 with an absorptive suspended ceiling, A rises to 54 m² and T60 drops to ≈ 0.43 s: doubling the absorption halves the reverberation.

Two caveats on this example, which is there to show the formula and not to verify anything. First, 0.86 s is “high for a classroom” only against the order of magnitude quoted above: saying whether it meets UNI 11532-2 requires the room category, the volume, the occupancy condition and the band, none of which are here. Second, α and T60 are not single numbers but functions of frequency: a material can absorb little at 125 Hz and a great deal at 1 kHz, and a mean α does not preserve that. The tool in fact works per octave band from 125 to 4000 Hz with ISO 354 catalogue α, as UNI EN 12354-6 requires; the single-α examples on this page are didactic. The formulas shown here also neglect air absorption, which the tool includes as the 4mV term — of little weight in small volumes at mid frequencies, not always negligible in large volumes at high ones.

How wrong the three formulas are

Saying that Sabine “overestimates at high absorption” is not enough to decide when to stop using it. On the same classroom as the example (V = 144 m³, S = 180 m²), varying mean absorption alone:

The gap does not depend on the room: it is a function of ᾱ alone, because both Sabine and Eyring carry 0.161·V on top and differ only in the denominator.

The two reference values can be read straight off the curve: the gap reaches 10 % at ᾱ = 0.176 and 20 % at ᾱ = 0.314. Below the first — reflective rooms, the case of most untreated buildings — the choice between the two formulas changes the result by less than a tenth; above the second, that is as soon as you design a serious treatment, the choice is worth more than a fifth and should be stated.

That said, do not read it as a validity criterion. The gap in the table is the difference between two formulas, not the error of either against the real room: that also depends on field diffusion, geometry, spatial distribution of absorption, volume, frequency, furnishings and coupling between volumes. Two models that agree can both be wrong. And the uncertainty of a catalogue α is a third quantity again, which neither adds to nor compares directly with this one.

And Millington?

Millington-Sette was made for non-uniform absorption, but the remedy has a strong side effect. On the same classroom, with a highly absorbing suspended ceiling (48 m² at α = 0.90) and every other surface bare (α = 0.05), we get A = 49.8 m², ᾱ = 0.277, and the three formulas give:

Millington returns less than half of Sabine. The reason is structural: every surface enters with its own −ln(1−αᵢ), and that term diverges as αᵢ → 1. A single 48 m² surface at α = 0.99 would contribute 221 m² of equivalent absorption, more than the room’s entire surface. It is as if every ray, before dying out, struck all surfaces in proportion to their area — an assumption that does not hold with one nearly perfect absorber.

In this example the three estimates order themselves this way, with Sabine at the top, Millington at the bottom and Eyring in between. Do not read them as an interval containing the true value, though: they are three predictions built on different assumptions, not a confidence interval, and nothing guarantees the measured T60 falls between the first and the last. What so wide a divergence does indicate for certain is that the result is highly sensitive to the model’s assumptions — useful information in itself, and a good reason to move to the formulas built for non-uniformity (Fitzroy, Arau-Puchades — in the bibliography), to a geometric simulation like the room simulator, or to a measurement.

One implementation detail comes straight out of Millington: coefficients measured in a reverberation room per ISO 354 can exceed 1, through edge and diffraction effects on the specimen. The term −ln(1−αᵢ) diverges at α = 1 and is undefined beyond it, so a catalogue figure can blow the formula up. The tool treats α ≥ 1 as total absorption with a finite contribution and flags it in the table; it is a declared convention, not a physical result.

The Schroeder frequency

T60 is a statistical quantity: it presumes that many overlapping room modes respond at each frequency. Below a certain frequency this fails, the modes separate and the room behaves as a set of distinct resonances. The threshold is the Schroeder frequency:

$$f_S\approx 2000\sqrt{\frac{T_{60}}{V}}$$

with T60 in seconds and V in m³. Applied to four typical rooms:

Before reading the numbers, a note on what f_S means: it is not a sharp boundary between “T60 holds here” and “it does not there”, it is an estimate of the centre of a transition region between modal and statistical behaviour. Around that frequency the two regimes coexist.

In the concert hall f_S = 23 Hz, below any musically relevant frequency: T60 is therefore an appropriate descriptor across the useful spectrum — which does not by itself guarantee ideal diffusion or clean exponential decays. In a 20 m³ control room f_S = 245 Hz: the 125 Hz octave band lies entirely below, while the 250 Hz one (roughly 177–354 Hz) straddles the transition, its lower half in the modal regime. The T60 measured there largely describes the decay of a few individual modes, not of a diffuse field.

The design consequence is not that panels are useless in a small room: porous absorbers of adequate thickness, mounted with an air gap, and bass traps are precisely how modes are damped. It is that sizing on the equivalent area A alone — a scalar, averaged quantity — is not enough, if it ignores which modes get damped and where source and listener sit.

This also refines the “below ~30 m³” criterion mentioned further down: the threshold is not volume alone, it is the ratio of T60 to volume. A small but very absorbing room can have a lower f_S than a larger, more reverberant one.

How it is measured

This Open Lab tool estimates T60 from geometry and materials. Measuring it in a real room is another matter.

Impulse response

Measurement starts by exciting the room and recording its tail. An impulsive source (a bursting balloon, a clapper) or a broadband source (interrupted pink noise, a sine sweep) is used together with one or more microphones. From this the room’s impulse response (IR) is obtained, from which the decay curve is extracted. A single microphone at one point is enough to grasp the principle, not for a standardised measurement: ISO 3382-2 also prescribes the number and layout of source and receiver positions. And the four sources listed are not metrologically equivalent: a balloon is convenient and instructive, but low-band energy, signal-to-noise ratio and repeatability are what an electroacoustic chain designed for measurement provides.

Extrapolating T60

Measuring a clean decay of a full 60 dB is rare: background noise “eats” the final part of the tail. In practice T20 (decay from −5 to −25 dB) or T30 (−5 to −35 dB) is measured and extrapolated linearly to the 60 dB value. The EDT (Early Decay Time), computed over the first 10 dB of decay, is closer to the subjective perception of early reverberation and often differs from T30.

ISO 3382-2

Measuring T60 in ordinary rooms is governed by ISO 3382-2:2008, which specifies source and receiver positions, the number of positions, per-band analysis, and distinguishes three accuracy levels: survey, engineering, precision. The typical instrument is a class 1 sound level meter (IEC 61672) with analysis software.

Limits of measurement

Measurement too has its uncertainty, and two components are worth separating because they are often conflated. One is genuine uncertainty — positions, background noise, repetitions, propagation conditions as temperature and humidity vary — and ISO 3382-2 addresses it through the number of positions required for each accuracy level. The other is not uncertainty at all: moving the furniture or changing how many people are present changes the room, that is the measurand, and two different values are then both correct. Background noise is the practical limit: in an urban environment it is often hard to guarantee a signal-to-noise ratio sufficient for a precision-level measurement.

How it is reduced

The principle is simple: T60 is high when the mean absorption coefficient ᾱ is low. To reduce it, the total absorption A = Σ αᵢ Sᵢ is increased. The real question is where it is worth intervening — where there is little current absorption, where the available surface is large, where it is aesthetically and functionally acceptable.

Sound-absorbing panels

Mineral-wool or melamine-foam panels are the main tool. The figures below are orders of magnitude for typical products, not properties of the material: real α depends on flow resistivity, density, thickness, mounting, air gap and facing, and should be taken from the product’s ISO 354 data sheet. A 50 mm thickness typically gives high α (0.7–0.9) at medium and high frequencies and little at low ones; 100 mm extends the effectiveness downwards (of the order of 0.5 at 125 Hz). Position matters: a corner absorber works at low frequencies if it has adequate thickness and stand-off — a thin panel leaned into a corner does not become a bass trap by position; ceiling panels intercept the direct reflection.

One thing about that datasheet figure which the datasheets do not state. ISO 354:2003 is under revision, and the stated reason is inter-laboratory reproducibility: in round-robin comparisons the reproducibility limit of α reaches 0.7 at 125 Hz and stays above 0.2 even at 5 kHz. The causes are in the method — an insufficiently diffuse field in the chamber with the sample in place, chamber shape, diffuser placement — not in the product. The practical consequence for sizing: an α of 0.45 at low frequencies read off a datasheet is not an exact number, and a treatment designed right at the requirement in the low bands can miss it because of measurement spread rather than a calculation error. One more reason to verify in situ with an ISO 3382-2 measurement instead of stopping at the arithmetic.

Acoustic suspended ceilings

It is the typical solution for offices, schools and conference rooms: suspended mineral-fibre panels, with α 0.5–0.8 at medium-high frequencies. The advantage is surface area: the suspended ceiling covers the entire ceiling area, hence many m² of absorption. The disadvantage is that it is generally far less effective at low frequencies; how much less depends on the plenum, the suspension height, the perforation and any backing blanket, and a system designed for it can work lower than one might expect. For the low end, thick wall panels remain more effective.

Carpets, curtains

A heavy carpet has α 0.4–0.6 at medium frequencies but little at low ones; a heavy rug draped on a wall performs better. Heavy curtains well draped (not stretched) reach α 0.3–0.7 at medium-high frequencies and are the natural solution in front of glazing, which is reflective. What these materials have in common is small thickness, and therefore an effectiveness that falls off rapidly as frequency drops: they are useful against excessive brightness and of little use against low-frequency boom, where their absorption is not zero but is too small to count in the budget.

Furnishings and audience

Upholstered furnishings absorb a lot: empty upholstered seats reach α 0.5–0.7 and a seated audience 0.7–0.9, referred to the floor area occupied. The rigorous accounting does not use an α, though: ISO 354 distinguishes the absorption coefficient, which applies to wall and ceiling treatments, from the equivalent absorption area in m², the quantity used for discrete objects such as furniture, space absorbers and people. Attributing an α to “a person” without saying what reference surface it is referred to is ambiguous. A hall full of audience can have a T60 30–50 % lower than the same hall empty — how much depends on the audience’s weight in the empty hall’s total absorption, so it is not a universal rule — a decisive factor in hall design, which must be calculated for the real condition of use. Bookshelves filled with books also contribute as loosely structured volumetric absorbers.

Where not to intervene

The floor should be seen for what it is: a carpet genuinely contributes to the budget, whereas linoleum and parquet on a massive substrate are essentially reflective surfaces — a non-zero α does not make them “absorbing” in any design sense. Treating the floor mainly makes sense where there is no soft covering at all. Glazing cannot be easily covered: the practical solution is a curtain in front of the window.

When treatment really helps

Not every room needs treatment. Treatment is justified in classrooms, school canteens and gyms, conference and meeting rooms, auditoria, noisy restaurants, open-plan offices, recording studios, music rehearsal rooms. It is, instead, of little use in already “soft” rooms (a furnished bedroom already has ᾱ around 0.2–0.3), in churches or cathedrals, where the long reverberation is part of the intended acoustic experience.

One case deserves to be taken out of that list, because it is often dismissed wrongly: very small volumes — booths, control rooms, small rehearsal spaces under 30 m³. There a single statistical T60 is a poor descriptor, especially at low frequencies, but it does not follow that treatment is useless: they are on the contrary among the rooms that need it most. What changes is the method, not the need — broadband absorption of adequate thickness and modal control instead of square metres computed from a mean equivalent area.

Sizing an intervention follows an orderly path: measure or estimate the current T60; define a target T60 (the reference standards for classrooms, the literature for other rooms); compute the target absorption A = 0.161·V/T60; compute the current absorption and the gap ΔA to be filled; choose panels and treatments that cover ΔA, giving priority to the bands critical for the use (typically 250–2000 Hz for speech).

How much it takes, in square metres

The fourth step of that path — the ΔA to be closed — is worth seeing in figures, because it is where quotations surprise people. Start from the untreated classroom (ᾱ = 0.15, A = 27 m², T60 = 0.86 s) and add panels at α = 0.80 over a wall that had 0.15: the net gain is 0.65 per square metre covered, not 0.80.

The first 0.06 s cost 3 m² of panel; the last 0.10 s — from 0.40 to 0.30 s — cost 30, ten times as much. Bringing the classroom into the speech range quoted above (0.6–0.8 s) takes between 3 and 18 m²: a portion of suspended ceiling, an ordinary job. Chasing 0.30 s takes 77 m², more than the whole ceiling (48 m²).

One caveat on the last row: at T60 = 0.30 s mean absorption reaches ᾱ = 0.43, where Sabine overestimates by about 30 %. Recomputing the target with Eyring, 55 m² are enough instead of 77. Sizing done with Sabine, at high absorption, over-specifies the treatment: comfortable as a margin, less so as a quotation.

The underlying limit remains: this tool is demonstrative and preliminary. A definitive design calls for a prediction model suited to the room — in complex cases a geometric or wave simulation, not necessarily “3D software”, which is no regulatory requirement — and usually an in-situ measurement. Compliance checks within the CAM framework, and expert use, require a registered competent acoustic technician.

Tool status and roadmap

• v0.1 — Pure Sabine/Eyring/Millington calculator, flat material + m² input (released and then reworked).
• v0.2 — Full UX: rectangular L×W×H dimensions, categorized materials, subtractive openings, distinct additive treatments, parametric axonometric diagram with numbered walls, order-of-magnitude sanity check (current release).
• v0.3 — Spatial positioning of treatments on the walls.
• v0.4 — Treatment suggester to reach a target T60.
• v1.0 — Integration with SoundPro as a “Building acoustics” module.

References

Historical formulas: Sabine W.C. (1900), Reverberation, The American Architect; Eyring C.F. (1930), Reverberation Time in “Dead” Rooms, J. Acoust. Soc. Am.; Millington G. (1932), A Modified Formula for Reverberation, J. Acoust. Soc. Am.

Alternative formulas for non-uniform absorption: Fitzroy D. (1959), Reverberation Formula Which Seems to be More Accurate with Nonuniform Distribution of Absorption, J. Acoust. Soc. Am. 31, 893; Arau-Puchades H. (1988), An improved reverberation formula, Acustica 65, 163–180. Modal/statistical regime: Schroeder M.R. (1962), Frequency-Correlation Functions of Frequency Responses in Rooms, J. Acoust. Soc. Am. 34, 1819.

Measurement standards: ISO 3382-2:2008 (reverberation time in ordinary rooms); ISO 354:2003 (sound absorption in a reverberation room; edition 2, reconfirmed in 2024 and currently under revision over inter-laboratory reproducibility); ISO 9613-1:1993 (absorption of sound by the atmosphere).

Italian regulatory framework: UNI 11532-1:2018 and UNI 11532-2:2020, with corrigenda EC1:2020 and EC2:2023 (internal acoustic characteristics of confined spaces); UNI EN 12354-6 (prediction of equivalent absorption and reverberation time, per frequency band); DM 24/11/2025 (Minimum Environmental Criteria for construction, in force since 2 February 2026, which reference UNI 11532-2 and repealed the earlier DM 256/2022, subject to the transitional provisions for procedures already under way). The DM 18/12/1975 — technical standards for school buildings should also be mentioned: formally no longer applicable since 03/02/1996 under art. 12 of Law 23/1996, but still referenced transitionally in recent regional and ministerial acts for sizing school buildings, pending the new technical standards envisaged by art. 5 §3 of the same law; for the acoustic aspect (optimal T60 versus volume and frequency, figs. 4–5 of the decree) the modern technical reference is UNI 11532-2:2020.

Literature: Cremer & Müller, Principles and Applications of Room Acoustics; Vorländer, Auralization; Beranek, Concert Halls and Opera Houses.

The tool is available as an executable tool at /en/tools/reverberation-time/.